identify_fault.m

function [faultyIdx, suspectSet, confidence] = identify_fault(subsets, clusterLabels, winnerIdx, N)
% IDENTIFY_FAULT  Identify faulty measurement from the winning (healthy) cluster.
%
%   [faultyIdx, suspectSet, confidence] = identify_fault(subsets, clusterLabels, winnerIdx, N)
%
%   LOGIC:
%     The healthy cluster contains subsets that all exclude the faulty measurement.
%     Therefore the faulty index is the one ABSENT from the union of all
%     measurement indices present in the winning cluster's subsets.
%
%     present  = union of all indices that appear in any winning-cluster subset
%     faulty   = {1,...,N} \ present
%
%   INPUTS:
%     subsets       cell array  all subsets (from enumerate_subsets), each a row
%                               vector of 1-indexed measurement indices
%     clusterLabels [M x 1]    cluster label for each subset (from cluster_estimates)
%     winnerIdx     integer     label of the winning cluster
%     N             scalar      total number of measurements
%
%   OUTPUTS:
%     faultyIdx   integer (or [])  1-indexed measurement(s) identified as faulty.
%                                  Empty if identification is ambiguous.
%     suspectSet  vector           the absent index set (complement of union)
%     confidence  scalar           fraction of winning-cluster subsets that exclude
%                                  faultyIdx (1.0 = perfect identification)

    M = numel(subsets);
    assert(numel(clusterLabels) == M, 'identify_fault: subsets and clusterLabels must have the same length.');

    % --- Gather subsets belonging to the winning cluster ---
    winnerMask    = (clusterLabels == winnerIdx);
    winnerSubsets = subsets(winnerMask);

    if isempty(winnerSubsets)
        warning('identify_fault: winning cluster is empty. Cannot identify fault.');
        faultyIdx  = [];
        suspectSet = [];
        confidence = 0;
        return;
    end

    % --- Union of all measurement indices present in winning cluster ---
    presentSet = [];
    for k = 1:numel(winnerSubsets)
        presentSet = union(presentSet, winnerSubsets{k});
    end

    % --- Complement: indices absent from all winning-cluster subsets ---
    fullSet    = 1:N;
    suspectSet = setdiff(fullSet, presentSet);

    if isempty(suspectSet)
        warning('identify_fault: all measurements appear in the winning cluster. Identification ambiguous.');
        faultyIdx  = [];
        confidence = 0;
        return;
    end

    if numel(suspectSet) > 1
        warning('identify_fault: multiple absent indices %s. System may have multiple faults or insufficient redundancy.', ...
                mat2str(suspectSet));
        faultyIdx  = suspectSet;   % return all suspects
        confidence = 0.5;          % flag ambiguity
        return;
    end

    faultyIdx = suspectSet;   % single faulty measurement index

    % --- Confidence: fraction of winning-cluster subsets that exclude faultyIdx ---
    excludeCount = 0;
    for k = 1:numel(winnerSubsets)
        if ~ismember(faultyIdx, winnerSubsets{k})
            excludeCount = excludeCount + 1;
        end
    end
    confidence = excludeCount / numel(winnerSubsets);
end