matlab 特征选择算法 序列浮动前向选择算法 SFFS

function [ALL_INDICES, P_CORRECT] = sequential_floating_forward_selection(DATA, PARAMETERS) %在主函数中调用这个函数 %SEQUENTIAL_FLOATING_FORWARD_SELECTION - uses the SFFS algorithm out of [1] to determine the best features % % [1]: Floating Search Methods for Feature Selection with Nonmonotonic Criterion Functions % P. Pudial et al., IEEE Pattern Recognition (Conference B), 1994 % % % Possible parameters are: % % PARAMETERS.SFFS_DIMENSION - 应该选择的特征数量number of features that should be selected % PARAMETERS.CLASSIFIER - 包含应该用于分析的分类器 contains the classifier that should be used for % the analysis % PARAMETERS.TCR - trainings to classification ratio % if NaN then use all features for training and classification % else use given ratio % PARAMETERS.ITERATIONS - 获得数值稳定结果的迭代次数number of iterations that are done to get numerical stable % results. % PARAMETERS.FEATURE_REDUCTION - 1: Fisher transformation (determinant criterion) % 2: Fisher transformation (trace criterion) % 3: PCA % NaN: no Transformation (Default) % PARAMETERS.REDUCED_DIMENSION -如果参数为，则忽略。FEATURE_REDUCTION == NaN ignored if PARAMETERS.FEATURE_REDUCTION == NaN % = 1,... then reduce feature dimension (Default: 3) % PARAMETERS.CONSTRAIN_DIAGONAL - if '0', no constrain is applied otherwise % -1 is added to P_CORRECT if any element of the diagonal % is smaller then PARAMETERS.CONSTRAIN_DIAGONAL % PARAMETERS.VERBOSE ?????? 0: Suppress all output % ????????????????1: Show intermediate results and progress bar (Default) % ????????????????2: Additionally show status of evaluate_classifier % % NOTE: use normalize_matrix to get the same value range for all features % this is useful to avoid singular covariance matrices % % NOTE: DATA.FEATURES is used instead of DATA.TRAINING and DATA.CLASSIFICATION % % NOTE: It is possilbe to set additional parameters in PARAMETERS. As PARAMETERS % are passed on to the classificator this enables the user to select certain % options of the classifier, i.e. PARAMETERS.GMM_DIM = 2 will tell % gmm_classifier to use a constant dimension of two for the mixtures. %% 1. INITIALISATION % if DATA.FEATURES does not exist -> create it if isfield(DATA,'FEATURES') == 0 DATA.FEATURES = [DATA.TRAINING; DATA.CLASSIFICATION]; end [TRAINING_LENGTH, CLASSIFICATION_LENGTH, NUM_CLASSES, CLASSES, FEATURE_LENGTH] = get_lengths(DATA, PARAMETERS); if exist('PARAMETERS','var') == 0 || isfield(PARAMETERS,'SFFS_DIMENSION') == 0 % PARAMETERS.SFFS_DIMENSION = min(10, FEATURE_LENGTH); PARAMETERS.SFFS_DIMENSION = min(10, FEATURE_LENGTH); end if exist('PARAMETERS','var') == 0 || isfield(PARAMETERS,'CONSTRAIN_DIAGONAL') == 0 PARAMETERS.CONSTRAIN_DIAGONAL = 0; end if exist('PARAMETERS','var') == 0 || isfield(PARAMETERS,'VERBOSE') == 0 PARAMETERS.VERBOSE = 1; end if PARAMETERS.VERBOSE > 1 PARAMETERS.SHOW_STATUS = 1; end if PARAMETERS.SFFS_DIMENSION > FEATURE_LENGTH warning('Changed SFFS_DIMENSION from %d to %d', PARAMETERS.SFFS_DIMENSION, FEATURE_LENGTH); PARAMETERS.SFFS_DIMENSION = FEATURE_LENGTH; end %% SEQUENTIAL FLOATING FORWARD SELECTION - ALGORITHM % This Vector contains all indices that are currently selected INDICES = []; P_CORRECT = zeros(1, PARAMETERS.SFFS_DIMENSION); % at the beginning we can apply Sequential floating selection twice to fill INDICES with two features [INDEX, P_CORRECT(length(INDICES) + 1)] = get_most_significant_feature(); INDICES = [INDICES INDEX]; ALL_INDICES{length(INDICES)} = INDICES; if PARAMETERS.VERBOSE > 0 print_status(); end [INDEX, P_CORRECT(length(INDICES) + 1)] = get_most_significant_feature(); INDICES = [INDICES INDEX]; ALL_INDICES{length(INDICES)} = INDICES; while length(INDICES) ~= PARAMETERS.SFFS_DIMENSION if PARAMETERS.VERBOSE > 0 print_status(); end % 1. step: inclusion [INDEX, P_CORRECT(length(INDICES) + 1)] = get_most_significant_feature(); INDICES = [INDICES INDEX]; ALL_INDICES{length(INDICES)} = INDICES; % 2. step: exclusion [INDEX, P_CORRECT_EXCLUSION] = get_least_significant_feature(); while (P_CORRECT_EXCLUSION > P_CORRECT(length(INDICES) - 1) && length(INDICES) > 2) % only do backward step if obtained P_CORRECT is better as before at this step if PARAMETERS.VERBOSE > 0 fprintf('Deleting %d\n', INDICES(INDEX)); end % delete INDEX INDICES(INDEX) = []; ALL_INDICES{length(INDICES)} = INDICES; % Update P_CORRECT P_CORRECT(length(INDICES)) = P_CORRECT_EXCLUSION; % determine next feature to exclude [INDEX, P_CORRECT_EXCLUSION] = get_least_significant_feature(); end end if PARAMETERS.VERBOSE > 0 fprintf('Result for dimension %d: P_CORRECT = %f\n',length(INDICES),P_CORRECT(length(INDICES))) fprintf('Selected features: %d\n', INDICES) [VAL,IND] = max(P_CORRECT); if IND ~= length(INDICES) warning('Best result for dimension %d with P_CORRECT %f and not for dimension %d with P_CORRECT %f \n\n',IND,VAL,length(INDICES),P_CORRECT(end)); end end %% NESTED FUNCTION: get_most_significant_feature function [INDEX, P_CORRECT] = get_most_significant_feature() % this function obtains the most significant feature among all % features that are currently not selected EVAL_MATRIX = zeros(FEATURE_LENGTH,1); if PARAMETERS.VERBOSE > 0 % h = waitbar(0,'Please wait'); end for INDEX_C = 1:length(DATA.FEATURES(1,1:FEATURE_LENGTH)) if PARAMETERS.VERBOSE > 0 PR = INDEX_C/length(DATA.FEATURES(1,1:FEATURE_LENGTH)); % waitbar(PR, h) end if ~any(INDICES == INDEX_C) TMP_DATA.FEATURES = DATA.FEATURES(:,[INDICES INDEX_C end]); TMP = evaluate_classifier(TMP_DATA, PARAMETERS); EVAL_MATRIX(INDEX_C) = sum(TMP(:,1) == TMP(:,2))/length(TMP(:,1)); if PARAMETERS.CONSTRAIN_DIAGONAL ~= 0 if all(isnan(TMP) == 0) CONF_MATRIX_DIAGONAL = diag(generate_confusion_matrix(TMP)); if any(CONF_MATRIX_DIAGONAL(2:end) < PARAMETERS.CONSTRAIN_DIAGONAL) EVAL_MATRIX(INDEX_C) = EVAL_MATRIX(INDEX_C) - 1; end else EVAL_MATRIX(INDEX_C) = EVAL_MATRIX(INDEX_C) - 1; end end else EVAL_MATRIX(INDEX_C) = -inf; % to avoid to be selected end end if PARAMETERS.VERBOSE > 0 % close(h) end [P_CORRECT, INDEX] = max(EVAL_MATRIX); end %% NESTED FUNCTION: get_least_significant_feature function [INDEX, P_CORRECT] = get_least_significant_feature() % this function obtains the least significant feature among all % features that are currently selected EVAL_MATRIX = zeros(length(INDICES), 1); for INDEX_C = 1:length(INDICES) TMP_INDICES = INDICES; TMP_INDICES(INDEX_C) = []; TMP_DATA.FEATURES = DATA.FEATURES(:,[TMP_INDICES end]); TMP = evaluate_classifier(TMP_DATA, PARAMETERS); EVAL_MATRIX(INDEX_C) = sum(TMP(:,1) == TMP(:,2))/length(TMP(:,1)); if PARAMETERS.CONSTRAIN_DIAGONAL ~= 0 if all(isnan(TMP) == 0) CONF_MATRIX_DIAGONAL = dia