Ch_05_DimensionalityReduction_PCA_LDA_tSNE.ipynb

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    "***Reference:***<br>\n",
    "***Raschka, Sebastian; Liu, Yuxi (Hayden); Mirjalili, Vahid. Machine Learning with PyTorch and Scikit-Learn: Develop machine learning and deep learning models with Python. Packt Publishing.*** "
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    "# ***<u>Chapter 5</u>***\n",
    "\n",
    "## ***Compressing Data via Dimensionality Reduction***"
   ]
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    "## PCA\n",
    "\n",
    "- **Principal Component Analysis(PCA)**, an unsupervised linear transformation technique that is widely used across different fields, most prominently for feature extraction and dimensionality reduction. Other popular applications of PCA include exploratory data analysis.\n",
    "\n",
    "\n",
    "- PCA helps us to identify patterns in data based on the correlation between features. **In a nutshell, PCA aims to find the directions of maximum variance in high-dimensional data and projects the data onto a new subspace with equal or fewer dimensions than the original one.**<br>*The orthogonal axes (principal components) of the new subspace can be interpreted as the directions of maximum variance given the constraint that the new feature axes are orthogonal to each other*, as illustrated in Figure 5.1:\n",
    "<div>\n",
    "<img src=\"Images/pca.png\" style=\"width: 300px;\"/>\n",
    "</div>\n",
    "------------------------------------------------------------------------------"
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    "- ***The difference between feature selection and feature extraction*** is that while *we maintain the original features when we use feature selection algorithms,* such as sequential backward selection, *we use feature extraction to transform or project the data onto a new feature space.* \n",
    "\n",
    "- In the context of dimensionality reduction, feature extraction can be understood as an approach to data compression with the goal of maintaining most of the relevant information. \n",
    "\n",
    "- *In practice, feature extraction can also improve the predictive performance by reducing the* ***curse of dimensionality****—especially if we are working with non-regularized models.*\n",
    "\n",
    "---------------------------------------"
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    "### **PCA for dimensionality reduction**\n",
    "The process is as follows. Suppose we have a feature vector, $\\textbf{x}:$\n",
    "\n",
    "$$\\textbf{x} = [x_1,x_2,\\cdots,x_d], \\textbf{x} \\in \\mathbb{R}^d$$\n",
    "\n",
    "which is then transformed by a transformation matrix, $\\textbf{W} \\in \\mathbb{R}^{d \\times k}:$\n",
    "\n",
    "$$\\textbf{xW} = \\textbf{z}$$\n",
    "\n",
    "resulting in the o/p vector: \n",
    "\n",
    "$$\\textbf{z} = [z_1,z_2,\\cdots,z_k], \\textbf{z} \\in \\mathbb{R}^k$$\n",
    "\n",
    "As a result of transforming the original $d$-dimensional data onto this new $k$-dimensional subspace (typically $k << d)$, the first principal component will have the largest possible variance.<br><br>**Note that the PCA directions are highly sensitive to data scaling, and we need to standardize the features prior to PCA if the features were measured on different scales and we want to assign equal importance to all features.**\n",
    "\n",
    "-------------------------------------------------------------------------------"
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    "## **Steps in PCA for dimensionality reduction:**\n",
    "1. Standardize the $d-dimensional$ dataset.\n",
    "\n",
    "2. Construct the covariance matrix.\n",
    "\n",
    "3. Decompose the covariance matrix into eigen vectors & eigen values.\n",
    "\n",
    "4. Sort the eigen values by decreasing order to rank the corresponding eigen vectors.\n",
    "\n",
    "5. Select $k$ eigen-vectors, corresponding to $k$ largest eigen values,<br>where $k$ is the dimensionality of the new feature subspace$(k \\leq d)$.\n",
    "\n",
    "6. Construct the projection matrix, $\\textbf{W}$, from the \"top\" $k$ eigen-vectors.\n",
    "\n",
    "7. Transform the $d$-dimensional input dataset, $\\textbf{X}$, using the projection matrix, $\\textbf{W}$, to obtain the new $k$-dimensional feature subspace.\n",
    "$$\\textbf{X}^{'} = \\textbf{XW}$$\n",
    "    \n",
    "    \n",
    "----------------------------------------------------------------------------"
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    "#### **Eigendecomposition: Decomposing a Matrix into Eigenvectors and Eigenvalues**\n",
    "\n",
    "The covariance matrix is a special case of a square matrix: it’s a symmetric matrix, which means that the matrix is equal to its transpose, $A = A^T$. \n",
    "\n",
    "When we decompose such a symmetric matrix, the eigenvalues are real (rather than complex) numbers, and the eigenvectors are orthogonal (perpendicular) to each other.Furthermore, eigenvalues and eigenvectors come in pairs. \n",
    "\n",
    "If we decompose a covariance matrix into its eigenvectors and eigenvalues, the eigenvectors associated with the highest eigenvalue corresponds to the direction of maximum variance in the dataset. Here, this “direction” is a linear transformation of the dataset’s feature columns.\n",
    "\n",
    "---------------------------------------------------------------------------"
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    "## Extracting the principal components step-by-step\n",
    "\n",
    "In this subsection, we will tackle the first four steps of a PCA: \n",
    "\n",
    "    1. Standardizing the data \n",
    "    2. Constructing the covariance matrix \n",
    "    3. Obtaining the eigenvalues and eigenvectors of the covariance matrix\n",
    "    4. Sorting the eigenvalues by decreasing order to rank the eigenvectors"
   ]
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Class label</th>\n",
       "      <th>Alcohol</th>\n",
       "      <th>Malic acid</th>\n",
       "      <th>Ash</th>\n",
       "      <th>Alcalinity of ash</th>\n",
       "      <th>Magnesium</th>\n",
       "      <th>Total phenols</th>\n",
       "      <th>Flavanoids</th>\n",
       "      <th>Nonflavanoid phenols</th>\n",
       "      <th>Proanthocyanins</th>\n",
       "      <th>Color intensity</th>\n",
       "      <th>Hue</th>\n",
       "      <th>OD280/OD315 of diluted wines</th>\n",
       "      <th>Proline</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>14.23</td>\n",
       "      <td>1.71</td>\n",
       "      <td>2.43</td>\n",
       "      <td>15.6</td>\n",
       "      <td>127</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.06</td>\n",
       "      <td>0.28</td>\n",
       "      <td>2.29</td>\n",
       "      <td>5.64</td>\n",
       "      <td>1.04</td>\n",
       "      <td>3.92</td>\n",
       "      <td>1065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>13.20</td>\n",
       "      <td>1.78</td>\n",
       "      <td>2.14</td>\n",
       "      <td>11.2</td>\n",
       "      <td>100</td>\n",
       "      <td>2.65</td>\n",
       "      <td>2.76</td>\n",
       "      <td>0.26</td>\n",
       "      <td>1.28</td>\n",
       "      <td>4.38</td>\n",
       "      <td>1.05</td>\n",
       "      <td>3.40</td>\n",
       "      <td>1050</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>13.16</td>\n",
       "      <td>2.36</td>\n",
       "      <td>2.67</td>\n",
       "      <td>18.6</td>\n",
       "      <td>101</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.24</td>\n",
       "      <td>0.30</td>\n",
       "      <td>2.81</td>\n",
       "      <td>5.68</td>\n",
       "      <td>1.03</td>\n",
       "      <td>3.17</td>\n",
       "      <td>1185</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>14.37</td>\n",
       "      <td>1.95</td>\n",
       "      <td>2.50</td>\n",
       "      <td>16.8</td>\n",
       "      <td>113</td>\n",
       "      <td>3.85</td>\n",
       "      <td>3.49</td>\n",
       "      <td>0.24</td>\n",
       "      <td>2.18</td>\n",
       "      <td>7.80</td>\n",
       "      <td>0.86</td>\n",
       "      <td>3.45</td>\n",
       "      <td>1480</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>13.24</td>\n",
       "      <td>2.59</td>\n",
       "      <td>2.87</td>\n",
       "      <td>21.0</td>\n",
       "      <td>118</td>\n",
       "      <td>2.80</td>\n",
       "      <td>2.69</td>\n",
       "      <td>0.39</td>\n",
       "      <td>1.82</td>\n",
       "      <td>4.32</td>\n",
       "      <td>1.04</td>\n",
       "      <td>2.93</td>\n",
       "      <td>735</td>\n",
       "    </tr>\n",
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       "   Class label  Alcohol  Malic acid   Ash  Alcalinity of ash  Magnesium  \\\n",
       "0            1    14.23        1.71  2.43               15.6        127   \n",
       "1            1    13.20        1.78  2.14               11.2        100   \n",
       "2            1    13.16        2.36  2.67               18.6        101   \n",
       "3            1    14.37        1.95  2.50               16.8        113   \n",
       "4            1    13.24        2.59  2.87               21.0        118   \n",
       "\n",
       "   Total phenols  Flavanoids  Nonflavanoid phenols  Proanthocyanins  \\\n",
       "0           2.80        3.06                  0.28             2.29   \n",
       "1           2.65        2.76                  0.26             1.28   \n",
       "2           2.80        3.24                  0.30             2.81   \n",
       "3           3.85        3.49                  0.24             2.18   \n",
       "4           2.80        2.69                  0.39             1.82   \n",
       "\n",
       "   Color intensity   Hue  OD280/OD315 of diluted wines  Proline  \n",
       "0             5.64  1.04                          3.92     1065  \n",
       "1             4.38  1.05                          3.40     1050  \n",
       "2             5.68  1.03                          3.17     1185  \n",
       "3             7.80  0.86                          3.45     1480  \n",
       "4             4.32  1.04                          2.93      735  "
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   "source": [
    "import pandas as pd\n",
    "\n",
    "df_wine = pd.read_csv('https://archive.ics.uci.edu/ml/'\n",
    "                      'machine-learning-databases/wine/wine.data',\n",
    "                      header=None)\n",
    "\n",
    "df_wine.columns = ['Class label', 'Alcohol', 'Malic acid', 'Ash',\n",
    "                   'Alcalinity of ash', 'Magnesium', 'Total phenols',\n",
    "                   'Flavanoids', 'Nonflavanoid phenols', 'Proanthocyanins',\n",
    "                   'Color intensity', 'Hue',\n",
    "                   'OD280/OD315 of diluted wines', 'Proline']\n",
    "\n",
    "df_wine.head()"
   ]
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    "# Splitting the data into 70% training and 30% test subsets.\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X, y = df_wine.iloc[:, 1:].values, df_wine.iloc[:, 0].values\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, \n",
    "                                                    stratify=y,\n",
    "                                                    random_state=0)"
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    "# Standardizing the data.\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "sc = StandardScaler()\n",
    "X_train_std = sc.fit_transform(X_train)\n",
    "X_test_std = sc.transform(X_test)"
   ]
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    "### Eigendecomposition of the covariance matrix.\n",
    "\n",
    "- After completing the mandatory preprocessing, let’s advance to the **$2^{nd}$ step:<br> Constructing the Covariance Matrix.** \n",
    "\n",
    "- ***The symmetric $d×d$-dimensional covariance matrix, where $d$ is the number of dimensions in the dataset, stores the pairwise covariances between the different features.*** \n",
    "\n",
    "- For example, the covariance between two features, $x_j$ and $x_k$, on the population level can be calculated via the following equation:$$\\sigma_{jk} = \\frac{1}{n-1}\\sum_{i=1}^{n}\\left(x_j^i - \\mu_j\\right)\\left(x_k^i - \\mu_k\\right)$$ Here, $\\mu_j$ and $\\mu_k$ are the sample means of features j and k, respectively. **Note that the sample means are zero if we standardized the dataset.** \n",
    "\n",
    "- *A positive covariance between two features indicates that the features increase or decrease together, whereas a negative covariance indicates that the features vary in opposite directions.* For example, the covariance matrix of three features can then be written as follows\n",
    "$$\\Sigma = \\begin{bmatrix}\n",
    "\\sigma_1^2 & \\sigma_{12} & \\sigma_{13}\\\\\n",
    "\\sigma_{21} & \\sigma_2^2 & \\sigma_{23}\\\\\n",
    "\\sigma_{31} & \\sigma_{32} & \\sigma_3^2\n",
    "\\end{bmatrix} = \\textbf{X}^T\\textbf{X}$$\n",
    "\n",
    "\n",
    "- ***The eigenvectors of the covariance matrix represent the principal components (the directions of maximum variance), whereas the corresponding eigenvalues will define their magnitude.***<br>*In the case of the Wine dataset, we would obtain 13 eigenvectors and eigenvalues from the 13×13-dimensional covariance matrix.* \n",
    "\n",
    "- Now, for our **third step,**<br>let’s obtain the ***eigenpairs of the covariance matrix.***<br>Eigenvector, $\\nu$, satisfies the following condition:$$\\Sigma\\nu = \\lambda\\nu$$ **Here, $\\lambda$ is a scalar: the eigenvalue.** \n",
    "\n",
    "- we will use the ```linalg.eig``` function from NumPy to obtain the eigenpairs of the Wine covariance matrix:"
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      "\n",
      "Eigenvalues:\n",
      " [4.84274532 2.41602459 1.54845825 0.96120438 0.84166161 0.6620634\n",
      " 0.51828472 0.34650377 0.3131368  0.10754642 0.21357215 0.15362835\n",
      " 0.1808613 ]\n"
     ]
    }
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    "# Eigendecomposition of the covariance matrix.\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "# Computing the dxd covarince matrix form standardized dataset(nxd) \n",
    "cov_mat = np.cov(X_train_std.T)\n",
    "\n",
    "# computing eigen values & eigen vectors\n",
    "eigen_vals, eigen_vecs = np.linalg.eig(cov_mat)\n",
    "\n",
    "print('\\nEigenvalues:\\n', eigen_vals)"
   ]
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    "#### **Note:**\n",
    "\n",
    "\n",
    "Above, I used the ```numpy.linalg.eig``` function to decompose the symmetric covariance matrix into its eigenvalues and eigenvectors.\n",
    "\n",
    ">>> eigen_vals, eigen_vecs = np.linalg.eig(cov_mat)\n",
    "\n",
    "This is not really a \"mistake,\" but probably suboptimal. **It would be better to use ```numpy.linalg.eigh``` in such cases, which has been designed for <a href=\"https://en.wikipedia.org/wiki/Hermitian_matrix\">Hermetian matrices</a>.** The latter always returns real eigenvalues; whereas the numerically less stable ```np.linalg.eig``` can decompose non-symmetric square matrices, you may find that it returns complex eigenvalues in certain cases."
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    "### Total & Explained Variance\n",
    "\n",
    "- Since we want to reduce the dimensionality of our dataset by compressing it onto a new feature subspace, we only select the subset of the eigenvectors (principal components) that contains most of the information (variance). \n",
    "\n",
    "- The eigenvalues define the magnitude of the eigenvectors, so we have to sort the eigenvalues by decreasing magnitude; we are interested in the top $k$ eigenvectors based on the values of their corresponding eigenvalues. \n",
    "\n",
    "- But before we collect those $k$ most informative eigenvectors, let’s plot the **variance explained ratios** of the eigenvalues. ***The variance explained ratio of an eigenvalue, $\\lambda_j$, is simply the fraction of an eigenvalue, $\\lambda_j$, and the total sum of the eigenvalues:***$$\\text{Explained Variance Ratio} = \\frac{\\lambda_j}{\\sum_{j=1}^{d}\\lambda_j}$$\n",
    "\n",
    "Using the NumPy ```cumsum``` function, we can then calculate the cumulative sum of explained variances, which we will then plot via Matplotlib’s ```step``` function:"
   ]
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    "tot = sum(eigen_vals)\n",
    "\n",
    "var_exp = [(i/tot) for i in sorted(eigen_vals, reverse=True)]\n",
    "\n",
    "cum_var_exp = np.cumsum(var_exp)"
   ]
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "plt.bar(range(1, 14), var_exp, align='center',\n",
    "        label='Individual explained variance')\n",
    "\n",
    "plt.step(range(1, 14), cum_var_exp, where='mid',\n",
    "         label='Cumulative explained variance')\n",
    "\n",
    "plt.ylabel('Explained variance ratio')\n",
    "plt.xlabel('Principal component index')\n",
    "plt.legend(loc='best')\n",
    "plt.tight_layout()\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0e7647f-06d8-4528-a540-a0cedd92d2e7",
   "metadata": {},
   "source": [
    "**The resulting plot indicates that the first principal component alone accounts for approximately 40% of the variance. Also, we can see that the first two principal components combined explain almost 60% of the variance in the dataset.**\n",
    "\n",
    "Although the explained variance plot reminds us of the feature importance values that we computed in Chapter 4, Building Good Training Datasets – Data Preprocessing, via random forests, ***we should remind ourselves that PCA is an unsupervised method, which means that information about the class labels is ignored. Whereas a random forest uses the class membership information to compute the node impurities, variance measures the spread of values along a feature axis.***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de80f7b9-5825-480f-81da-30956a44e714",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## Feature Tranformation\n",
    "\n",
    "Now, after decomposing the covarince matrix, let's proceed with the **last 3 steps** to transform the Wine dataset onto the new principal component axes. The  last 3 steps are:\n",
    "\n",
    "   5. Select $k$ eigen-vectors, corresponding to $k$ largest eigen values,<br>where $k$ is the dimensionality of the new feature subspace$(k \\leq d)$.\n",
    "\n",
    "   6. Construct the projection matrix, $\\textbf{W}$, from the \"top\" $k$ eigen-vectors.\n",
    "\n",
    "   7. Transform the $d$-dimensional input dataset, $\\textbf{X}$, using the projection matrix, $\\textbf{W}$, to obtain the new $k$-dimensional feature subspace.\n",
    "    \n",
    "\n",
    "***Or, in less technical terms, we will sort the eigenpairs by descending order of the eigenvalues, construct a projection matrix from the selected eigenvectors, and use the projection matrix to transform the data onto the lower-dimensional subspace.***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e47ed69d-d168-4c64-9858-6fbbd86bfddd",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We start by sorting the eigenpairs by decreasing order of the eigenvalues:\n",
    "\n",
    "# Make a list of (eigenvalue, eigenvector) tuples\n",
    "eigen_pairs = [(np.abs(eigen_vals[i]), eigen_vecs[:,i])\n",
    "               for i in range(len(eigen_vals))]\n",
    "\n",
    "# Sort the (eigenvalue, eigenvector) tuples from high to low\n",
    "eigen_pairs.sort(key = lambda k: k[0], reverse=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "da579cd4-3ed9-4a76-a3c1-25756cdd5c27",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix W:\n",
      " [[-0.13724218  0.50303478]\n",
      " [ 0.24724326  0.16487119]\n",
      " [-0.02545159  0.24456476]\n",
      " [ 0.20694508 -0.11352904]\n",
      " [-0.15436582  0.28974518]\n",
      " [-0.39376952  0.05080104]\n",
      " [-0.41735106 -0.02287338]\n",
      " [ 0.30572896  0.09048885]\n",
      " [-0.30668347  0.00835233]\n",
      " [ 0.07554066  0.54977581]\n",
      " [-0.32613263 -0.20716433]\n",
      " [-0.36861022 -0.24902536]\n",
      " [-0.29669651  0.38022942]]\n"
     ]
    }
   ],
   "source": [
    "# Next, we collect the two eigenvectors that correspond to the two largest \n",
    "# eigenvalues, to capture about 60% of the variance in this dataset.\n",
    "\n",
    "# In practice, the number of principal components has to be determined by a \n",
    "# tradeoff between computational efficiency and the performance of the classifier\n",
    "\n",
    "\n",
    "# eigen_pairs[0][1][:, np.newaxis]\n",
    "\n",
    "w = np.hstack((eigen_pairs[0][1][:, np.newaxis],\n",
    "               eigen_pairs[1][1][:, np.newaxis]))\n",
    "\n",
    "print('Matrix W:\\n', w)\n",
    "\n",
    "# By executing the code, we have created a 13×2-dimensional\n",
    "# projection matrix, W, from the top two eigenvectors."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15d7a7a8-3fd1-407a-a6c1-9925b4a7ac54",
   "metadata": {},
   "source": [
    "Depending on which versions of NumPy and LAPACK you are using, you may obtain the matrix, $\\textbf{W}$, with its signs flipped. Please note that this is not an issue; if $\\textbf{v}$ is an eigenvector then $\\textbf{-v}$ is also an eigenvector.\n",
    "\n",
    "\n",
    "Using the projection matrix, we can now transform an example, $\\textbf{x}$ (represented as a $13$-dimensional row vector), onto the PCA subspace (the principal components one and two) obtaining $\\textbf{x}^{′}$, now a two-dimensional example vector consisting of two new features: $$\\textbf{x}^{′} = \\textbf{xW}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "36345562-66ef-4c4c-8da4-3d2415d2ff7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.38299011, 0.45458499])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_std[0].dot(w)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8cf4232-395a-4fff-aca0-95045dde5e9c",
   "metadata": {},
   "source": [
    "Similarly, we can transform the entire $124×13$-dimensional training dataset onto the two principal components by calculating the matrix dot product: $$\\textbf{X}^{′} = \\textbf{XW}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1611e652-4551-42b2-b50e-e96b58effaaf",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_pca = X_train_std.dot(w)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "326f6b08-1e7c-4dc4-a2e2-de540cc7e7a4",
   "metadata": {},
   "source": [
    "Lastly, let’s visualize the transformed Wine training dataset, now stored as an $124×2$-dimensional matrix, in a two-dimensional scatterplot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5a9a9c34-9081-47fe-8414-ca467439c1ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_train_pca = X_train_std.dot(w)\n",
    "\n",
    "colors = ['r', 'b', 'g']\n",
    "markers = ['o', 's', '^']\n",
    "\n",
    "for l, c, m in zip(np.unique(y_train), colors, markers):\n",
    "    plt.scatter(X_train_pca[y_train == l, 0], \n",
    "                X_train_pca[y_train == l, 1], \n",
    "                c=c, label=f'Class {l}', marker=m)\n",
    "\n",
    "plt.xlabel('PC 1')\n",
    "plt.ylabel('PC 2')\n",
    "plt.legend(loc='lower left')\n",
    "plt.tight_layout()\n",
    "plt.title(f\"Data records from the Wine dataset projected\\n onto a 2D feature space via PCA\")\n",
    "# plt.savefig('figures/05_03.png', dpi=300)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e146066-c4e7-427f-99c0-01daaf4225ed",
   "metadata": {},
   "source": [
    "***As we can see above, the data is more spread along the first principal component (x axis) than the second principal component (y axis), which is consistent with the explained variance ratio plot that we created in the previous subsection.*** However, we can tell that a linear classifier will likely be able to separate the classes well.\n",
    "\n",
    "\n",
    "Although we encoded the class label info. for the purpose of illustration in the above scatterplot, ***we have to keep in mind that PCA is an unsupervised technique that doesn't use any class label information.*** "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09ed87f7-fe42-41b2-8978-38c706cce5fb",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## PCA in scikit-learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "91360297-8517-4960-8588-f86c8867da3e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.36951469, 0.18434927, 0.11815159, 0.07334252, 0.06422108,\n",
       "       0.05051724, 0.03954654, 0.02643918, 0.02389319, 0.01629614,\n",
       "       0.01380021, 0.01172226, 0.00820609])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components=None)\n",
    "X_train_pca = pca.fit_transform(X_train_std)\n",
    "pca.explained_variance_ratio_\n",
    "\n",
    "\n",
    "# Note that we set n_components=None when we initialized the PCA class \n",
    "# so that it will return all principal components in a sorted order, \n",
    "# instead of performing a dimensionality reduction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "edf5b591-fe2a-4a83-9284-9d67eb490527",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(range(1, 14), pca.explained_variance_ratio_, align='center')\n",
    "plt.step(range(1, 14), np.cumsum(pca.explained_variance_ratio_), where='mid')\n",
    "plt.ylabel('Explained variance ratio')\n",
    "plt.xlabel('Principal components')\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9e59d59d-8422-4e3c-a0f5-54ce191ee682",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Using 2 principal components as above we see the first two principal components\n",
    "# explain almost 60% of the data\n",
    "\n",
    "pca = PCA(n_components=2)\n",
    "X_train_pca = pca.fit_transform(X_train_std)\n",
    "X_test_pca = pca.transform(X_test_std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "17b0741f-9752-4aa7-ab1c-1a2fddbdd683",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_train_pca[:, 0], X_train_pca[:, 1])\n",
    "plt.xlabel('PC 1')\n",
    "plt.ylabel('PC 2')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c517cd1c-93f7-4b5c-ba16-2895beabe8e6",
   "metadata": {},
   "source": [
    "Using PCA with Logistic Regression & vizualizing the decision boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "49f55367-deea-4a5f-9b88-b12ba1483f4b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(multi_class=&#x27;ovr&#x27;, random_state=1)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(multi_class=&#x27;ovr&#x27;, random_state=1)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression(multi_class='ovr', random_state=1)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "# initializing PCA transformer & Logistic Regression estimator\n",
    "pca = PCA(n_components=2)\n",
    "lr = LogisticRegression(multi_class='ovr', random_state=1,\n",
    "                        solver='lbfgs')\n",
    "\n",
    "# dimensionality reduction\n",
    "X_train_pca = pca.fit_transform(X_train_std)\n",
    "X_test_pca = pca.transform(X_test_std)\n",
    "\n",
    "# fitting the LR model on reduced dataset\n",
    "lr.fit(X_train_pca, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a3ccaa06-04a5-49cc-a42b-f953a953d440",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting the decison regions\n",
    "\n",
    "# plot_decision_regions function to visualize the decision regions\n",
    "\n",
    "from utils.plot_decision_regions_script import plot_decision_regions\n",
    "\n",
    "\n",
    "plot_decision_regions(X_train_pca, y_train, classifier=lr)\n",
    "plt.xlabel('PC 1')\n",
    "plt.ylabel('PC 2')\n",
    "plt.legend(loc='lower left')\n",
    "plt.tight_layout()\n",
    "# plt.savefig('figures/05_04.png', dpi=300)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1993087e-7833-4e28-8389-21155e8af658",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# for the test dataset\n",
    "\n",
    "plot_decision_regions(X_test_pca, y_test, classifier=lr)\n",
    "plt.xlabel('PC 1')\n",
    "plt.ylabel('PC 2')\n",
    "plt.legend(loc='lower left')\n",
    "plt.tight_layout()\n",
    "# plt.savefig('figures/05_05.png', dpi=300)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa067026-d3dd-4607-a97d-340cc54c78e6",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## Assessing feature contributions\n",
    "\n",
    "***In this section, we will take a brief look at how we can assess the contributions of the original features to the principal components.*** \n",
    "\n",
    "\n",
    "As we learned, via PCA, **we create principal components that represent linear combinations of the features.** *Sometimes, we are interested to know about how much each original feature contributes to a given principal component.* **These contributions are often called <u>loadings.</u>** \n",
    "\n",
    "$$\\text{loadings} = \\sqrt{\\text{eigenValues}} \\times \\text{eigenVectors}$$\n",
    "\n",
    "**The factor loadings can be computed by scaling the eigenvectors by the square root of the eigenvalues.** ***The resulting values can then be interpreted as the correlation between the original features and the principal component.***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77f95c8a-5ac7-4bd2-9517-ae1ea125cbd8",
   "metadata": {},
   "source": [
    "To illustrate this, let us plot the loadings for the first principal component. First, we compute the $13×13$-dimensional loadings matrix by multiplying the eigenvectors by the square root of the eigenvalues:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "47f2efca-4734-42f5-808a-f47e721c7786",
   "metadata": {},
   "outputs": [],
   "source": [
    "loadings = eigen_vecs*np.sqrt(eigen_vals)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a62df01-9aa2-4fdf-9325-87ae51a0c23f",
   "metadata": {},
   "source": [
    "Then, we plot the loadings for the first principal component, ```loadings[:, 0]```, which is the first column in this matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b95dc3c5-2bda-441f-9a73-59efc5fc25be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.bar(range(13), loadings[:, 0], align='center')\n",
    "ax.set_ylabel('Loadings for PC 1')\n",
    "ax.set_xticks(range(13))\n",
    "ax.set_xticklabels(df_wine.columns[1:], rotation=90)\n",
    "\n",
    "plt.ylim([-1, 1])\n",
    "plt.tight_layout()\n",
    "# plt.savefig('figures/05_05_02.png', dpi=300)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63e0015d-d61d-4acc-a09a-352cc324b56f",
   "metadata": {},
   "source": [
    "Above, we can see that, for example, Alcohol has a negative correlation with the first principal component (approximately –0.3), whereas Malic acid has a positive correlation (approximately 0.54). Note that a value of 1 describes a perfect positive correlation whereas a value of –1 corresponds to a perfect negative correlation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "256820cc-23f9-431c-a743-59f5df23d54a",
   "metadata": {},
   "source": [
    "In the preceding code example, we compute the factor loadings for our own PCA implementation. We can obtain the loadings from a fitted scikit-learn PCA object in a similar manner, where ```pca.components_``` represents the eigenvectors and ```pca.explained_variance_``` represents the eigenvalues:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "eee6ecb9-36a7-479f-89a3-a0591b3dca5a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.3020184 ,  0.54408942, -0.05600938,  0.45540829, -0.33970111,\n",
       "       -0.8665386 , -0.9184327 ,  0.67279444, -0.67489496,  0.16623657,\n",
       "       -0.71769524, -0.81117245, -0.65291742])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loadings[:, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "90c9a5db-bc35-468d-97bb-de1adee94a2d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# sklearn_loadings = eigenVectors * sqrt(eigenValues)\n",
    "\n",
    "sklearn_loadings = pca.components_.T*np.sqrt(pca.explained_variance_)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60ebfc90-aa93-4bb9-945a-537d54311005",
   "metadata": {},
   "source": [
    "To compare the scikit-learn PCA loadings with those we created previously, let us create a similar bar plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "1d7a800f-edcd-40e4-ba88-502b4068662a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.3020184 ,  0.54408942, -0.05600938,  0.45540829, -0.33970111,\n",
       "       -0.8665386 , -0.9184327 ,  0.67279444, -0.67489496,  0.16623657,\n",
       "       -0.71769524, -0.81117245, -0.65291742])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sklearn_loadings[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "5333e9de-378c-4614-935b-8af8afdefad2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.bar(range(13), sklearn_loadings[:, 0], align='center')\n",
    "ax.set_ylabel('Loadings for PC 1')\n",
    "ax.set_xticks(range(13))\n",
    "ax.set_xticklabels(df_wine.columns[1:], rotation=90)\n",
    "\n",
    "plt.ylim([-1, 1])\n",
    "plt.tight_layout()\n",
    "# plt.savefig('figures/05_05_03.png', dpi=300)\n",
    "plt.show();\n",
    "\n",
    "\n",
    "# As we can see the bar plots look the same"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54d30ee3-09bd-4672-ba1d-aceb6cb85b05",
   "metadata": {},
   "source": [
    "After exploring PCA as an unsupervised feature extraction technique, the next section will introduce **linear discriminant analysis (LDA)**, ***which is a linear transformation technique that takes class label information into account.***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e26e6e3d-56e3-4326-87d0-29cfa548bf95",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## Supervised data compression via Linear Discriminant Analysis(LDA)\n",
    "\n",
    "*LDA can be used as a technique for feature extraction to increase computational efficiency and reduce the degree of overfitting due to the curse of dimensionality in non-regularized models.* \n",
    "\n",
    "\n",
    "### PCA v/s LDA\n",
    "\n",
    "- ***The general concept behind LDA is very similar to PCA, but whereas PCA attempts to find the orthogonal component axes of maximum variance in a dataset, <u>the goal in LDA is to find the feature subspace that optimizes class separability.</u>***\n",
    "\n",
    "- *Both PCA and LDA are linear transformation techniques that can be used to reduce the number of dimensions in a dataset; the former is an unsupervised algorithm, whereas the latter is supervised.* \n",
    "\n",
    "- Thus, we might think that LDA is a superior feature extraction technique for classification tasks compared to PCA. However, A.M. Martinez reported that preprocessing via PCA tends to result in better classification results in an image recognition task in certain cases, for instance, if each class consists of only a small number of examples\n",
    "\n",
    "--------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3217b17d-e644-438b-b5b6-4b41d51ab58b",
   "metadata": {},
   "source": [
    "Figure summarizes the concept of LDA for a two-class problem. Examples from class 1 are shown as circles, and examples from class 2 are shown as crosses:\n",
    "\n",
    "<table><tr>\n",
    "<td> <img src=\"Images/lda.png\" alt=\"Drawing\" style=\"width: 400px;\"/> </td>\n",
    "<td> <img src=\"Images/lda_1.png\" alt=\"Drawing\" style=\"width: 600px;\"/> </td>\n",
    "</tr></table>\n",
    "\n",
    "\n",
    "A linear discriminant, as shown on the $x-axis$(LD 1), would separate the two normal distributed classes well. Although the exemplary linear discriminant shown on the $y-axis$(LD 2) captures a lot of the variance in the dataset, it would fail as a good linear discriminant since it does not capture any of the class-discriminatory information. \n",
    "\n",
    "--------------------------------------------------------------------------\n",
    "- **One assumption in LDA is that the data is normally distributed.** \n",
    "\n",
    "- **Also, we assume that the classes have identical covariance matrices and that the training examples are statistically independent of each other.** \n",
    "\n",
    "- However, even if one, or more, of those assumptions is (slightly) violated, LDA for dimensionality reduction can still work reasonably well\n",
    "\n",
    "----------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "006e37c3-3060-4717-ad1c-450a842db6a3",
   "metadata": {},
   "source": [
    "###  <a href=\"https://sebastianraschka.com/Articles/2014_python_lda.html#what-is-a-good-feature-subspace\">What is a “good” feature subspace?</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48e81039-2e37-4901-9979-4c9bcfceff5d",
   "metadata": {
    "tags": []
   },
   "source": [
    "## ***Steps to perform LDA***\n",
    "\n",
    "1. Standardize the $d-dimensional$ dataset($d$ is the # of features).\n",
    "\n",
    "2. **For each class, compute $d-dimensional$ mean vector.**\n",
    "\n",
    "3. **Construct the <u>between-class scatter matrix</u>, $\\textbf{S}_B$, and the <u>within-class scatter matrix</u>, $\\textbf{S}_W$.**\n",
    "\n",
    "4. **Compute eigen-vectors & their eigen-values of matrix, $\\textbf{S}^{-1}_W\\textbf{S}_B$.**\n",
    "\n",
    "5. Sort the eigen-values by decreasing order to rank the corresponding eigen-vecotrs.\n",
    "\n",
    "6. Choose the $k$ eigen-vectors corresponding to $k$-largest eigen-values to construct a $d \\times k$-dimensional transformation matrix, $\\textbf{W}$; the eigen-vectors are the columns of this matrix.\n",
    "\n",
    "7. Project the example onto the new feature subspace using the transformation matrix, $\\textbf{W}$. \n",
    "\n",
    "\n",
    "***As we can see, LDA is quite similar to PCA*** *in the sense that we are decomposing matrices into eigenvalues and eigenvectors, which will form the new lower-dimensional feature space. However, as mentioned before,* ***LDA takes class label information into account, which is represented in the form of the mean vectors computed in step 2.***\n",
    "\n",
    "----------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94d88eb0-b8e9-4c5a-b2a9-942156482f12",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "### Computing the Scatter Matrix\n",
    "\n",
    "- Since we already standardized the features of the Wine dataset in the PCA, we can proceed with the calculation of the ***mean vectors, which we will use to construct the within-class scatter matrix and between-class scatter matrix, respectively.*** \n",
    "\n",
    "- *Each mean vector, $\\textbf{m}_i$, stores the mean feature value, $\\mu_m$, with respect to the examples of class i:$$\\textbf{m}_i = \\frac{1}{n_i}\\sum_{x\\in D_i}\\textbf{x}_m$$ This results in three mean vectors, one for each wine class:*\n",
    "$$\\textbf{m}_i = \\begin{bmatrix}\n",
    "\\mu_{i,alcohol}\\\\\n",
    "\\mu_{i,\\text{malic acid}}\\\\\n",
    "\\vdots\\\\\n",
    "\\mu_{i,proline}\n",
    "\\end{bmatrix}^T\\;\\;\\;\\;\\; i \\in \\{1,2,3\\}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "09d42952-b239-4775-a251-e02e35b1dac5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MV 1: [ 0.9066 -0.3497  0.3201 -0.7189  0.5056  0.8807  0.9589 -0.5516  0.5416\n",
      "  0.2338  0.5897  0.6563  1.2075]\n",
      "\n",
      "MV 2: [-0.8749 -0.2848 -0.3735  0.3157 -0.3848 -0.0433  0.0635 -0.0946  0.0703\n",
      " -0.8286  0.3144  0.3608 -0.7253]\n",
      "\n",
      "MV 3: [ 0.1992  0.866   0.1682  0.4148 -0.0451 -1.0286 -1.2876  0.8287 -0.7795\n",
      "  0.9649 -1.209  -1.3622 -0.4013]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Calculate the mean vectors for each class:\n",
    "\n",
    "np.set_printoptions(precision=4)\n",
    "\n",
    "mean_vecs = []\n",
    "for label in range(1, 4):\n",
    "    mean_vecs.append(np.mean(X_train_std[y_train == label], axis=0))\n",
    "    print(f'MV {label}: {mean_vecs[label - 1]}\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4861fdc-68dd-4dcf-9933-4ea5bdbaee3b",
   "metadata": {},
   "source": [
    "#### Within-class Scatter Matrix\n",
    "\n",
    "**Using the mean vectors, we can compute the within-class scatter matrix, $\\textbf{S}_W$:**\n",
    "\n",
    "$$\\textbf{S}_W = \\sum_{i=1}^{c}\\textbf{S}_i$$\n",
    "\n",
    "**This is claculated by summing up the individual scatter matrices, $\\textbf{S}_i$, of each individual class i:**\n",
    "\n",
    "$$\\textbf{S}_i = \\sum_{x \\in D_i}\\left(x - m_i\\right)\\left(x - m_i\\right)^T$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "0781173e-a20c-4d68-b170-5f68ffe7ecdc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Within-class scatter matrix: 13x13\n"
     ]
    }
   ],
   "source": [
    "# Compute the within-class scatter matrix:\n",
    "\n",
    "d = 13 # number of features\n",
    "\n",
    "S_W = np.zeros((d, d))\n",
    "\n",
    "for label, mv in zip(range(1, 4), mean_vecs):\n",
    "    class_scatter = np.zeros((d, d))  # scatter matrix for each class\n",
    "    for row in X_train_std[y_train == label]:\n",
    "        row, mv = row.reshape(d, 1), mv.reshape(d, 1)  # make column vectors\n",
    "        class_scatter += (row - mv).dot((row - mv).T)\n",
    "    S_W += class_scatter                          # sum class scatter matrices\n",
    "\n",
    "print('Within-class scatter matrix: '\n",
    "      f'{S_W.shape[0]}x{S_W.shape[1]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "357b01fc-d380-4014-83ac-74e5f86d3828",
   "metadata": {},
   "source": [
    "***The assumption that we are making when we are computing the scatter matrices is that the class labels in the training dataset are uniformly distributed. However, if we print the number of class labels, we see that this assumption is violated:***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "d350900c-ecc0-440d-ae98-417df4ca530b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Class label distribution: [41 50 33]\n"
     ]
    }
   ],
   "source": [
    "# Better: covariance matrix since classes are not equally distributed:\n",
    "\n",
    "print('Class label distribution:',  \n",
    "      np.bincount(y_train)[1:])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df4807ff-e901-49c9-aca5-109408343f55",
   "metadata": {},
   "source": [
    "***Thus, we want to scale the individual scatter matrices, $\\textbf{S}_i$, before we sum them up as the scatter matrix, $\\textbf{S}_W$. When we divide the scatter matrices by the number of class-examples, $n_i$, we can see that computing the scatter matrix is in fact the same as computing the covariance matrix, $\\Sigma_i$ — the covariance matrix is a normalized version of the scatter matrix:***\n",
    "\n",
    "$$\\Sigma_i = \\frac{1}{n_i}\\textbf{S}_i = \\frac{1}{n_i}\\sum_{x \\in D_i}\\left(x - m_i\\right)\\left(x - m_i\\right)^T$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "fe26d063-75c2-49ad-b1f2-6ec18dc2cc16",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scaled within-class scatter matrix: 13x13\n"
     ]
    }
   ],
   "source": [
    "# computing the scaled within-class scatter matrix\n",
    "\n",
    "d = 13  # number of features\n",
    "\n",
    "S_W = np.zeros((d, d))\n",
    "\n",
    "for label, mv in zip(range(1, 4), mean_vecs):\n",
    "    class_scatter = np.cov(X_train_std[y_train == label].T)\n",
    "    S_W += class_scatter\n",
    "    \n",
    "print('Scaled within-class scatter matrix: '\n",
    "      f'{S_W.shape[0]}x{S_W.shape[1]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adae8798-f1d5-42b1-bd44-ca3389021480",
   "metadata": {},
   "source": [
    "#### Between-class Scatter Matrix\n",
    "\n",
    "After we compute the **scaled within-class scatter matrix (or covariance matrix)**, we can move on to the next step and compute the **between-class scatter matrix** $\\textbf{S}_B$: \n",
    "\n",
    "$$\\textbf{S}_B = \\sum_{i=1}^{c}n_i\\left(\\textbf{m}_i - \\textbf{m}\\right)\\left(\\textbf{m}_i - \\textbf{m}\\right)^T$$\n",
    "\n",
    "Here, **$m$ is the overall mean that is computed, including examples from all 'c' classes.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "6124eacc-8ee3-45a8-a09e-b001203c04ea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Between-class scatter matrix: 13x13\n"
     ]
    }
   ],
   "source": [
    "# Compute the between-class scatter matrix:\n",
    "\n",
    "mean_overall = np.mean(X_train_std, axis=0)\n",
    "mean_overall = mean_overall.reshape(d, 1)  # make column vector\n",
    "\n",
    "d = 13  # number of features\n",
    "S_B = np.zeros((d, d))\n",
    "\n",
    "for i, mean_vec in enumerate(mean_vecs):\n",
    "    n = X_train_std[y_train == i + 1, :].shape[0]\n",
    "    mean_vec = mean_vec.reshape(d, 1)  # make column vector\n",
    "    S_B += n * (mean_vec - mean_overall).dot((mean_vec - mean_overall).T)\n",
    "\n",
    "print('Between-class scatter matrix: '\n",
    "      f'{S_B.shape[0]}x{S_B.shape[1]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "885e2405-1891-483a-b247-18d5e727fcff",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "### Selecting linear discriminants for the new feature subspace\n",
    "\n",
    "**Solving the generalized eigenvalue problem for the matrix  $\\textbf{S}_W^{-1}\\textbf{S}_B$:**\n",
    "\n",
    "\n",
    "instead of using ```np.linalg.eig()```, we should/can also use ```np.linalg.eigh()```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "e5ad650d-7368-47d8-bea1-915946f50801",
   "metadata": {},
   "outputs": [],
   "source": [
    "eigen_vals, eigen_vecs = np.linalg.eig(np.linalg.inv(S_W).dot(S_B))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bb1ce8e-0ce7-4786-b12f-b8befad84b3f",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "### Sort eigenvectors in descending order of the eigenvalues:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "70b33713-cae5-4900-8c60-23d9cdfc7785",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues in descending order:\n",
      "\n",
      "349.6178089059941\n",
      "172.76152218979394\n",
      "2.927452713255748e-14\n",
      "2.927452713255748e-14\n",
      "1.480381625339196e-14\n",
      "1.3533650132059972e-14\n",
      "1.3533650132059972e-14\n",
      "1.0917306164816297e-14\n",
      "9.463628713182403e-15\n",
      "8.596407573242877e-15\n",
      "4.528090986998065e-15\n",
      "4.528090986998065e-15\n",
      "3.533213355930368e-15\n"
     ]
    }
   ],
   "source": [
    "# Make a list of (eigenvalue, eigenvector) tuples\n",
    "eigen_pairs = [(np.abs(eigen_vals[i]), eigen_vecs[:, i])\n",
    "               for i in range(len(eigen_vals))]\n",
    "\n",
    "# Sort the (eigenvalue, eigenvector) tuples from high to low\n",
    "eigen_pairs = sorted(eigen_pairs, key=lambda k: k[0], reverse=True)\n",
    "\n",
    "# Visually confirm that the list is correctly sorted by decreasing eigenvalues\n",
    "\n",
    "print('Eigenvalues in descending order:\\n')\n",
    "for eigen_val in eigen_pairs:\n",
    "    print(eigen_val[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b3ade03-592b-40e0-a9f5-66aa71f623c8",
   "metadata": {},
   "source": [
    "**In LDA, the number of linear discriminants is at most $c - 1$, where $c$ is the number of class labels, since the in-between scatter matrix, $\\textbf{S}_B$, is the sum of $c$ matrices with rank one or less.** *We can indeed see that we only have two nonzero eigenvalues (the eigenvalues 3-13 are not exactly zero, but this is due to the floating-point arithmetic in NumPy.)* \n",
    "\n",
    "------------------------------------------------------------\n",
    "\n",
    "Collinearity<br> \n",
    "Note that in the rare case of perfect collinearity (all aligned example points fall on a straight line), the covariance matrix would have rank one, which would result in only one eigenvector with a nonzero eigenvalue. \n",
    "\n",
    "---------------------------------------------------------------\n",
    "\n",
    "To measure how much of the class-discriminatory information is captured by the linear discriminants (eigenvectors), let’s plot the linear discriminants by decreasing eigenvalues, similar to the explained variance plot that we created in the PCA section. For simplicity, we will call the content of class-discriminatory information **discriminability**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "d62c3e68-1926-42b7-a2dc-e8b01be275be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tot = sum(eigen_vals.real)\n",
    "discr = [(i / tot) for i in sorted(eigen_vals.real, reverse=True)]\n",
    "cum_discr = np.cumsum(discr)\n",
    "\n",
    "plt.bar(range(1, 14), discr, align='center',\n",
    "        label='Individual discriminability')\n",
    "plt.step(range(1, 14), cum_discr, where='mid',\n",
    "         label='Cumulative discriminability')\n",
    "plt.ylabel('Discriminability ratio')\n",
    "plt.xlabel('Linear discriminants')\n",
    "plt.ylim([-0.1, 1.1])\n",
    "plt.legend(loc='best')\n",
    "plt.tight_layout()\n",
    "#plt.savefig('figures/05_07.png', dpi=300)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbe67438-7903-4915-bc62-a848a765d9de",
   "metadata": {},
   "source": [
    "**As we can see, the first 2 linear discriminants alone capture 100% of the useful information in the Wine dataset.**\n",
    "\n",
    "\n",
    "#### Now, creating the transformation matrix $\\textbf{W}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "35f91094-fc04-405e-9b1c-23b709ec6028",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix W:\n",
      " [[-0.1481  0.4092]\n",
      " [ 0.0908  0.1577]\n",
      " [-0.0168  0.3537]\n",
      " [ 0.1484 -0.3223]\n",
      " [-0.0163  0.0817]\n",
      " [ 0.1913 -0.0842]\n",
      " [-0.7338 -0.2823]\n",
      " [-0.075   0.0102]\n",
      " [ 0.0018 -0.0907]\n",
      " [ 0.294   0.2152]\n",
      " [-0.0328 -0.2747]\n",
      " [-0.3547  0.0124]\n",
      " [-0.3915  0.5958]]\n"
     ]
    }
   ],
   "source": [
    "w = np.hstack((eigen_pairs[0][1][:, np.newaxis].real,\n",
    "              eigen_pairs[1][1][:, np.newaxis].real))\n",
    "print('Matrix W:\\n', w)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0414ba1c-734a-4213-9bd3-ab3507e1cabb",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Projecting examples onto the new feature space\n",
    "\n",
    "$$\\textbf{X}^{'} = \\textbf{X}\\textbf{W}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "de0cfee0-0dec-4b39-86cd-2f9700497a85",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_train_lda = X_train_std.dot(w)\n",
    "\n",
    "\n",
    "colors = ['r', 'b', 'g']\n",
    "markers = ['o', 's', '^']\n",
    "\n",
    "for l, c, m in zip(np.unique(y_train), colors, markers):\n",
    "    plt.scatter(X_train_lda[y_train == l, 0],\n",
    "                X_train_lda[y_train == l, 1] * (-1),\n",
    "                c=c, label=f'Class {l}', marker=m)\n",
    "\n",
    "plt.xlabel('LD 1')\n",
    "plt.ylabel('LD 2')\n",
    "plt.legend(loc='lower right')\n",
    "plt.tight_layout()\n",
    "# plt.savefig('figures/05_08.png', dpi=300)\n",
    "plt.show();\n",
    "\n",
    "\n",
    "# As we can see, the three Wine classes are now perfectly\n",
    "# linearly separable in the new feature subspace:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "baa4e86c-dc06-45fe-bb27-46a48dd767c4",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## LDA via scikit-learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "4bd8bed7-df8a-4b61-ad6c-c24867e5ec86",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA\n",
    "\n",
    "lda = LDA(n_components=2)\n",
    "\n",
    "X_train_lda = lda.fit_transform(X_train_std, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "788517e6-3b3c-4a4a-a247-45e6f2ca2dff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let’s see how the logistic regression classifier handles the \n",
    "# lower-dimensional training dataset after the LDA transformation:\n",
    "\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from utils.plot_decision_regions_script import plot_decision_regions\n",
    "\n",
    "lr = LogisticRegression(multi_class='ovr', random_state=1,\n",
    "                        solver='lbfgs')\n",
    "\n",
    "lr.fit(X_train_lda, y_train)\n",
    "\n",
    "\n",
    "plot_decision_regions(X_train_lda, y_train, classifier=lr)\n",
    "plt.xlabel('LD 1')\n",
    "plt.ylabel('LD 2')\n",
    "plt.legend(loc='lower left')\n",
    "plt.tight_layout()\n",
    "# plt.savefig('figures/05_09.png', dpi=300)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "007a3bf4-a974-4284-b6d7-30a20d8b60b9",
   "metadata": {},
   "source": [
    "Looking at above fig, we can see that the logistic regression model misclassifies one of the examples from class 2. \n",
    "\n",
    "\n",
    "By lowering the regularization strength, we could probably shift the decision boundaries so that the logistic regression model classifies all examples in the training dataset correctly. \n",
    "\n",
    "However, and more importantly, let’s take a look at the results on the test dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "eed028c0-206c-4dc9-baa0-d035a17c3e10",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_test_lda = lda.transform(X_test_std)\n",
    "\n",
    "plot_decision_regions(X_test_lda, y_test, classifier=lr)\n",
    "plt.xlabel('LD 1')\n",
    "plt.ylabel('LD 2')\n",
    "plt.legend(loc='lower left')\n",
    "plt.tight_layout()\n",
    "# plt.savefig('figures/05_10.png', dpi=300)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d85aa5aa-9969-46cb-ae1d-55dd05df8b85",
   "metadata": {},
   "source": [
    "As we can see in above fig, the logistic regression classifier is able to get a perfect accuracy score for classifying the examples in the test dataset by only using a $2-dimensional$ feature subspace, instead of the original 13 Wine features."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f29426b8-4ed4-433a-b006-ca701e3d1ed0",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Non-linear Dimensionality Reduction Techniques"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdcca667-b007-4971-8cb0-b4dd9563ed3b",
   "metadata": {},
   "source": [
    "### Why comsider nonlinear dimensionality reduction?\n",
    "\n",
    "The development and application of nonlinear dimensionality reduction techniques is also often referred to as **manifold learning**, where a ***manifold refers to a lower dimensional topological space embedded in a high-dimensional space***. Algorithms for manifold learning have to capture the complicated structure of the data in order to project it onto a lower-dimensional space where the relationship between data points is preserved.\n",
    "\n",
    "\n",
    "A classic example of manifold learning is the 3D Swiss roll:\n",
    "<div>\n",
    "<img src=\"Images/swiss_roll.png\" width=\"500\"/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69580715-4c62-4001-a600-114a632ef0e2",
   "metadata": {},
   "source": [
    "### Visualizing data via ***t-distributed stochastic neighbor embedding(t-SNE)***\n",
    "\n",
    "t-SNE is often used for visualizing complex datasets in 2 or 3-dimensions. In a nutshell, t-SNE is modeling data points based on their pair-wise distances in the high-dimensional (original) feature space. Then, it finds a probability distribution of pair-wise distances in the new, lower-dimensional space that is close to the probability distribution of pair-wise distances in the original space. Or, in other words, t-SNE learns to embed data points into a lower-dimensional space such that the pairwise distances in the original space are preserved.\n",
    "\n",
    "However, as the research paper title suggests, t-SNE is a technique intended for visualization purposes as it requires the whole dataset for the projection. Since it projects the points directly (unlike PCA, it does not involve a projection matrix), we cannot apply t-SNE to new data points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "d70d0ddf-9020-494d-acc2-4b7163a6f326",
   "metadata": {},
   "outputs": [],
   "source": [
    "# t-SNE to plot images of handwritten images in 2-D feature space\n",
    "\n",
    "from sklearn.datasets import load_digits\n",
    "\n",
    "digits = load_digits()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "e51c1cd1-ea4f-4c18-8966-c73732437684",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Number of Instances: 1797\n",
    "#Number of Attributes: 64\n",
    "#Attribute Information: 8x8 image of integer pixels in the range 0..16."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "677dcce0-35cd-4184-b545-8c38177eb92c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting 4 images\n",
    "\n",
    "fig, ax = plt.subplots(1, 4)\n",
    "\n",
    "for i in range(4):\n",
    "    ax[i].imshow(digits.images[i], cmap='Greys')\n",
    "    \n",
    "# plt.savefig('figures/05_12.png', dpi=300)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "2d62c1dd-b57a-4b6f-805d-5fe83623d83c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "d6f9ef69-a7a2-45ad-b913-d08e1cbbf0b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# pd.DataFrame(digits.data, columns=digits.feature_names)\n",
    "\n",
    "y_digits = digits.target    \n",
    "X_digits = digits.data       # features(pixels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "90ee8747-85a0-4f37-812f-64fa81905955",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Amit Vikram Raj\\anaconda3\\lib\\site-packages\\sklearn\\manifold\\_t_sne.py:991: FutureWarning: The PCA initialization in TSNE will change to have the standard deviation of PC1 equal to 1e-4 in 1.2. This will ensure better convergence.\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "from sklearn.manifold import TSNE\n",
    "\n",
    "tsne = TSNE(n_components=2, init='pca', random_state=123, learning_rate='auto')\n",
    "\n",
    "X_digits_tsne = tsne.fit_transform(X_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "2a245b22-0c5b-46b7-9f19-3bad343ec060",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.patheffects as PathEffects\n",
    "\n",
    "\n",
    "def plot_projection(x, colors):\n",
    "    \n",
    "    f = plt.figure(figsize=(8, 8))\n",
    "    ax = plt.subplot(aspect='equal')\n",
    "    for i in range(10):\n",
    "        plt.scatter(x[colors == i, 0],\n",
    "                    x[colors == i, 1])\n",
    "\n",
    "    for i in range(10):\n",
    "\n",
    "        xtext, ytext = np.median(x[colors == i, :], axis=0)\n",
    "        txt = ax.text(xtext, ytext, str(i), fontsize=24)\n",
    "        txt.set_path_effects([\n",
    "            PathEffects.Stroke(linewidth=5, foreground=\"w\"),\n",
    "            PathEffects.Normal()])\n",
    "        \n",
    "plot_projection(X_digits_tsne, y_digits)\n",
    "# plt.savefig('figures/05_13.png', dpi=300)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fbbc43a-77a2-40cc-80fa-ed35340c2748",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "- In this chapter, you learned about two fundamental dimensionality reduction techniques for feature extraction: **PCA and LDA**. \n",
    "\n",
    "- ***Using PCA, we projected data onto a lower-dimensional subspace to maximize the variance along the orthogonal feature axes, while ignoring the class labels.*** \n",
    "\n",
    "- ***LDA, in contrast to PCA, is a technique for supervised dimensionality reduction, which means that it considers class information in the training dataset to attempt to maximize the class separability in a linear feature space.*** \n",
    "\n",
    "- Lastly, you also learned about t-SNE, which is a nonlinear feature extraction technique that can be used for visualizing data in 2 or 3-dimensions.\n",
    "\n",
    "\n",
    "- <a href=\"https://youtu.be/azXCzI57Yfc\">A Great Video on LDA: StatQuest</a>\n",
    "\n",
    "- <a href=\"https://youtu.be/_UVHneBUBW0\">A Great Video on PCA - 1: StatQuest</a> \n",
    "\n",
    "- <a href=\"https://youtu.be/FgakZw6K1QQ\">A Great Video on PCA - 2: StatQuest</a> "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1453bc1d-6578-439b-9f2f-5557f528fc87",
   "metadata": {},
   "source": [
    "***Reference:***<br>\n",
    "***Raschka, Sebastian; Liu, Yuxi (Hayden); Mirjalili, Vahid. Machine Learning with PyTorch and Scikit-Learn: Develop machine learning and deep learning models with Python. Packt Publishing.*** "
   ]
  }
 ],
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