As a widely used approach for feature extraction and data reduction, Principal Components Analysis (PCA) suffers from high computational cost, large memory requirement and low efficacy in dealing with large dimensional datasets such as Hyperspectral Imaging (HSI). Consequently, a novel Folded-PCA is proposed, where the spectral vector is folded into a matrix to allow the covariance matrix to be determined more efficiently. With this matrix-based representation, both global and local structures are extracted to provide additional information for data classification. Moreover, both the computational cost and the memory requirement have been significantly reduced. Using Support Vector Machine (SVM) for classification on two well-known HSI datasets and one Synthetic Aperture Radar (SAR) dataset in remote sensing, quantitative results are generated for objective evaluations. Comprehensive results have indicated that the proposed Folded-PCA approach not only outperforms the conventional PCA but also the baseline approach where the whole feature sets are used.

Novel Folded-PCA for improved feature extraction and data reduction with hyperspectral imaging and SAR in remote sensing

An approach for directly extracting features from matrix data and its application in face recognition

Principal component analysis (PCA) and linear discriminant analysis (LDA) are two important feature extraction methods and have been widely applied in a variety of areas. A limitation of PCA and LDA is that when dealing with image data, the image matrices must be first transformed into vectors, which are usually of very high dimensionality. This causes expensive computational cost and sometimes the singularity problem. Recently two methods called two-dimensional PCA (2DPCA) and two-dimensional LDA (2DLDA) were proposed to overcome this disadvantage by working directly on 2-D image matrices without a vectorization procedure. The 2DPCA and 2DLDA significantly reduce the computational effort and the possibility of singularity in feature extraction. In this paper, we show that these matrices based 2-D algorithms are equivalent to special cases of image block based feature extraction, i.e., partition each image into several blocks and perform standard PCA or LDA on the aggregate of all image blocks. These results thus provide a better understanding of the 2-D feature extraction approaches.

/pdf/on-image-matrix-based-feature-extraction-algorithms-38wdxpciug.pdf

On image matrix based feature extraction algorithms

The 2-D principal component analysis (2-DPCA) is a widely used method for image feature extraction. However, it can be equivalently implemented via image-row-based principal component analysis. This paper presents a structured 2-D method called nuclear norm-based 2-DPCA (N-2-DPCA), which uses a nuclear norm-based reconstruction error criterion. The nuclear norm is a matrix norm, which can provide a structured 2-D characterization for the reconstruction error image. The reconstruction error criterion is minimized by converting the nuclear norm-based optimization problem into a series of F-norm-based optimization problems. In addition, N-2-DPCA is extended to a bilateral projection-based N-2-DPCA (N-B2-DPCA). The virtue of N-B2-DPCA over N-2-DPCA is that an image can be represented with fewer coefficients. N-2-DPCA and N-B2-DPCA are applied to face recognition and reconstruction and evaluated using the Extended Yale B, CMU PIE, FRGC, and AR databases. Experimental results demonstrate the effectiveness of the proposed methods.

Nuclear Norm-Based 2-DPCA for Extracting Features From Images

Multivariate time series (MTS) are used in very broad areas such as multimedia, medicine, finance and speech recognition. A new approach for MTS classification using two-dimensional singular value decomposition (2dSVD) is proposed. 2dSVD is an extension of standard SVD, it captures explicitly the two-dimensional nature of MTS samples. The eigenvectors of row-row and column-column covariance matrices of MTS samples are computed for feature extraction. After the feature matrix is obtained for each MTS sample, one-nearest-neighbor classifier is used for MTS classification. Experimental results performed on five real-world datasets demonstrate the effectiveness of our proposed approach.

Xiao Wang

Papers

The equivalence of two-dimensional PCA to line-based PCA