N-Dimensional Principal Component Analysis

In this paper, we first briefly introduce the multidimensional Principal Component Analysis (PCA) techniques, and then amend our previous N-dimensional PCA (ND-PCA) scheme by introducing multidirectional decomposition into ND-PCA implementation. For the case of high dimensionality, PCA technique is usually extended to an arbitrary n-dimensional space by the Higher-Order Singular Value Decomposition (HO-SVD) technique. Due to the size of tensor, HO-SVD implementation usually leads to a huge matrix along some direction of tensor, which is always beyond the capacity of an ordinary PC. The novelty of this paper is to amend our previous ND-PCA scheme to deal with this challenge and further prove that the revised ND-PCA scheme can provide a near optimal linear solution under the given error bound. To evaluate the numerical property of the revised ND-PCA scheme, experiments are performed on a set of 3D volume datasets

Metamorphic Detection Using Singular Value Decomposition

Metamorphic malware changes its internal structure with each infection, while maintaining its original functionality. Such malware can be difficult to detect using static techniques, since there may be no common signature across infections. In this research we apply a score based on Singular Value Decomposition (SVD) to the problem of metamorphic detection. SVD is a linear algebraic technique which is applicable to a wide range of problems, including facial recognition. Previous research has shown that a similar facial recognition technique yields good results when applied to metamorphic malware detection. We present experimental results and we analyze the effectiveness and efficiency of this SVD-based approach

Direct kernel biased discriminant analysis: a new content-based image retrieval relevance feedback algorithm

In recent years, a variety of relevance feedback (RF) schemes have been developed to improve the performance of content-based image retrieval (CBIR). Given user feedback information, the key to a RF scheme is how to select a subset of image features to construct a suitable dissimilarity measure. Among various RF schemes, biased discriminant analysis (BDA) based RF is one of the most promising. It is based on the observation that all positive samples are alike, while in general each negative sample is negative in its own way. However, to use BDA, the small sample size (SSS) problem is a big challenge, as users tend to give a small number of feedback samples. To explore solutions to this issue, this paper proposes a direct kernel BDA (DKBDA), which is less sensitive to SSS. An incremental DKBDA (IDKBDA) is also developed to speed up the analysis. Experimental results are reported on a real-world image collection to demonstrate that the proposed methods outperform the traditional kernel BDA (KBDA) and the support vector machine (SVM) based RF algorithms

Robust Rotation Synchronization via Low-rank and Sparse Matrix Decomposition

This paper deals with the rotation synchronization problem, which arises in global registration of 3D point-sets and in structure from motion. The problem is formulated in an unprecedented way as a "low-rank and sparse" matrix decomposition that handles both outliers and missing data. A minimization strategy, dubbed R-GoDec, is also proposed and evaluated experimentally against state-of-the-art algorithms on simulated and real data. The results show that R-GoDec is the fastest among the robust algorithms.Comment: The material contained in this paper is part of a manuscript submitted to CVI