Dimensionality Reduction Based On Approximated Zero And Infinite Norm

We are stepping into big data era, information is growing explosively, which onthe one hand is convenient for people to see things more comprehensively andconcretely, on the other hand makes data storage and computing more difficultly. As akind of effective measure to reduce data dimension, dimension reduction is gettingmore people’s attention. The main methods of data dimension reduction includePrincipal Component Analysis, PCA, Linear Discriminant Analysis, LDA, CanonicalCorrelation Analysis, CCA, and Kernel Principal Component Analysis, KPCA and soon.It is different from PCA is a kind of linear data dimension reduction method,KPCA can effective deal with non-linear data. The main idea of KPCA is projectingoriginal data to high dimensional feature space by map function, and taking the PCAprocess in the feature space. The kernel function is greatly reducing the calculation ofKPCA. The process of data dimension reduction is a linear superposition of testingsamples and main ingredient vectors of train samples, which make the computationdependent on all train samples, thus leading lower efficiency. In order to improveefficiency of KPCA, this paper proposes applying a sparse constraint by anapproximate zero norm to superposition coefficients, and obtaining the coefficientshave good sparsity. When extracting features, many train samples whose coefficient iszero are rejected, thus significant improving speed of dimension reduction. Theexperiments on ORL face database demonstrate the proposed method in this paperimprove the speed of feature extraction. Beside, we also find this technique showsstrong robustness for outliers in experiments.Linear Discriminant Analysis (LDA) is a supervised method of feature extraction.It has been widely used in the field of computer vision such as face recognition. Toincrease the efficiency of LDA-based feature extraction, this paper proposes aninfinite norm based LDA method. Traditional LDA methods express their objectivefunctions in the L2norm of either difference or ratio of between-class scatter matrixand within-class scatter matrix. Consequently, these methods are involved in matrixinversion and eigen-value decomposition. By contrast, the proposed method utilizesL-norm (infinite norm) instead of L2norm to formulate the objective function with respect to the difference between between-class scatter matrix and within-class scattermatrix. Because the solution is obtained iteratively, this method avoidstime-consuming eigen-decomposition. Moreover, the projection vector realizesbinarization, and the value of elements is-1or1, resulting in high efficiency becausevoids computing the inner product between a sample and the projection vector.Experimental results in ORL database and Yale database demonstrate the efficiencyand effectiveness of the proposed method.