[feature extraction] feature selection of target recognition information based on sparse PCA with Matlab source code

1 brief introduction

Bag-of-words (BoW) methods are a popular class of object recognition methods that use image features (e.g. SIFT) to form visual dictionaries and subsequent histogram vectors to represent object images in the recognition process. The accuracy of the BoW classifiers, however, is often limited by the presence of uninformative features extracted from the background or irrelevant image segments. Most existing solutions to prune out uninformative features rely on enforcing pairwise epipolar geometry via an expensive structure-from- motion (SfM) procedure. Such solutions are known to break down easily when the camera transformation is large or when the features are extracted from low- resolution low-quality images. In this paper, we propose a novel method to select informative object features using a more efficient algorithm called Sparse PCA. First, we show that using a large-scale multiple-view object database, informative features can be reliably identified from a high- dimensional visual dictionary by applying Sparse PCA on the histograms of each object category. Our experiment shows that the new algorithm improves recognition accuracy compared to the traditional BoW methods and SfM methods. Second, we present a new solution to Sparse PCA as a semidefinite programming problem using Augmented Lagrange Multiplier methods. The new solver outperforms the state of the art for estimating sparse principal vectors as a basis for a low-dimensional subspace model. The source code of our algorithms will be made public on our website.​

2 Part of the code

​clc;T = 5; % Number of trials to average run times overdimensions = [10 50 100 150 200 250 300 350 400 450 500];ALMTimes = zeros(length(dimensions), T);DSPCATimes = zeros(length(dimensions), T);ALMPrec = zeros(length(dimensions), T);DSPCAPrec = zeros(length(dimensions), T);​for i = 1:length(dimensions)        % Initialize parameters ****************    n=dimensions(i); p = 1;               % Dimension    ratio=1;         % "Signal to noise" ratio    % rand('state',25);   % Fix random seed​    for j = 1:T        % Form test matrix as: rank one sparse + noise        testvec=rand(n,p);        testvec = testvec - ones(n,1)*mean(testvec);        numZero = n - floor(0.1*n);        randInd = randperm(n); randInd1 = randInd(1:numZero); randInd2 = randInd(numZero+1:end);        testvec(randInd1,:) = 0;        testvec=ratio*testvec; % + rand(n,p);        testvec = testvec/norm(testvec);        A = testvec*testvec'/p;        lambda = max(1e-5,min(diag(A))*0.5);%(min(diag(A)) + max(diag(A)))/2;                tstartDSPCA = tic;        [x1, DSPCAIter] = DSPCA(A, lambda);        tstopDSPCA = toc(tstartDSPCA);        DSPCAPrec(i,j) = norm(abs(x1) - abs(testvec));​        tstartALM = tic;        [x, ALMIter] = SPCA_ALM(A, lambda);        tstopALM = toc(tstartALM);        ALMPrec(i,j) = norm(abs(x) - abs(testvec));                ALMTimes(i,j) = tstopALM;        DSPCATimes(i,j) = tstopDSPCA;        fprintf('\n [dim,trial] = [%i, %i]: [DSPCA time, SPCA-ALM time] = [%0.4f %0.4f]\t[DSPCA Iter, SPCA-ALM Iter] = [%i, %i]',n, j, tstopDSPCA, tstopALM, DSPCAIter, ALMIter);    end    fprintf('\n');endfprintf('\n');ALMTimes = mean(ALMTimes,2);DSPCATimes = mean(DSPCATimes,2);ALMPrec = mean(ALMPrec,2);DSPCAPrec = mean(DSPCAPrec,2);​figurehold onplot(dimensions, DSPCATimes, '-bx', 'linewidth', 2)plot(dimensions, ALMTimes, '-ro', 'linewidth', 2)legend('DSPCA', 'SPCAALM');xlabel('Dimension (n)');ylabel('Compute time (sec)');title('Time comparison of DSPCA and SPCAALM')​figurehold onplot(dimensions, DSPCAPrec, '-gx', 'linewidth', 2)plot(dimensions, ALMPrec, '-mo', 'linewidth', 2)legend('DSPCA', 'SPCAALM');xlabel('Dimension (n)');ylabel('Error');title('Precision comparison of DSPCA and SPCAALM')

3 Simulation results

4 reference

[1] Naikal N ,  Yang A Y ,  Sastry S S . Informative feature selection for object recognition via Sparse PCA[C]// International Conference on Computer Vision. IEEE, 2011.

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