Binary Principal Component Analysis Research Articles

Sensing Matrix Design for Compressive Spectral Imaging via Binary Principal Component Analysis.

Compressive spectral imaging (CSI) is a framework that captures coded-and-multiplexed low-dimensional projections of spectral data-cubes. In general, the sensing process in many CSI architectures is described using binary matrices, so-called sensing/projection matrices, whose elements can be either random or designed. However, some characteristics of the spectral data, such as the ℓ2-norm or the second moment statistics, can be lost when this dimensionality reduction is performed. Similarly, principal component analysis (PCA) is a data dimensionality reduction technique that minimizes the least-squared error between the spectral data and its low-dimensional projection, but preserving its structure or variance. Thus, PCA can be used to guide the CSI acquisition process by designing the binary sensing matrix. Nonetheless, PCA requires to know the spectral image a-priori, and also, its associated projection matrix is not binary, as required by CSI optical architectures. Therefore, in this paper, an algorithm to design CSI sensing matrices by exploiting the structure-preserving property of the PCA projection is proposed. First, a set of compressive measurements obtained with random sensing matrices is used to rapidly estimate the covariance matrix associated with the spectral data. Then, a new sensing matrix is designed by solving a non-convex optimization problem that finds a set of binary vectors that approximate the principal components of the covariance matrix, thus maximizing the explanation of the data variance. Experimental results show an improvement of up to 3 dB in image reconstruction quality, in terms of the peak signal to noise ratio (PSNR), when the binary PCA-based sensing matrices are used and compared with conventional random sensing matrices and state-of-art designed matrices based on PCA.

Complex Activity Recognition Via Attribute Dynamics

The problem of modeling the dynamic structure of human activities is considered. Video is mapped to a semantic feature space, which encodes activity attribute probabilities over time. The binary dynamic system (BDS) model is proposed to jointly learn the distribution and dynamics of activities in this space. This is a non-linear dynamic system that combines binary observation variables and a hidden Gauss---Markov state process, extending both binary principal component analysis and the classical linear dynamic systems. A BDS learning algorithm, inspired by the popular dynamic texture, and a dissimilarity measure between BDSs, which generalizes the Binet---Cauchy kernel, are introduced. To enable the recognition of highly non-stationary activities, the BDS is embedded in a bag of words. An algorithm is introduced for learning a BDS codebook, enabling the use of the BDS as a visual word for attribute dynamics (WAD). Short-term video segments are then quantized with a WAD codebook, allowing the representation of video as a bag-of-words for attribute dynamics. Video sequences are finally encoded as vectors of locally aggregated descriptors, which summarize the first moments of video snippets on the BDS manifold. Experiments show that this representation achieves state-of-the-art performance on the tasks of complex activity recognition and event identification.

Binary Sparse Nonnegative Matrix Factorization

This paper presents a fast part-based subspace selection algorithm, termed the binary sparse nonnegative matrix factorization (B-SNMF). Both the training process and the testing process of B-SNMF are much faster than those of binary principal component analysis (B-PCA). Besides, B-SNMF is more robust to occlusions in images. Experimental results on face images demonstrate the effectiveness and the efficiency of the proposed B-SNMF.

Binary Two-Dimensional PCA

Fast training and testing procedures are crucial in biometrics recognition research. Conventional algorithms, e.g., principal component analysis (PCA), fail to efficiently work on large-scale and high-resolution image data sets. By incorporating merits from both two-dimensional PCA (2DPCA)-based image decomposition and fast numerical calculations based on Haarlike bases, this technical correspondence first proposes binary 2DPCA (B-2DPCA). Empirical studies demonstrated the advantages of B-2DPCA compared with 2DPCA and binary PCA.

Representing Images Using Nonorthogonal Haar-Like Bases

Efficient and compact representation of images is a fundamental problem in computer vision. In this paper, we propose methods that use Haar-like binary box functions to represent a single image or a set of images. A desirable property of these box functions is that their inner product operation with an image can be computed very efficiently. We propose two closely related novel subspace methods to model images: the non-orthogonal binary subspace (NBS) method and binary principal component analysis (B-PCA) algorithm. NBS is spanned directly by binary box functions and can be used for image representation, fast template matching and many other vision applications. B-PCA is a structure subspace that inherits the merits of both NBS (fast computation) and PCA (modeling data structure information). B-PCA base vectors are obtained by a novel PCA guided NBS method. We also show that BPCA base vectors are nearly orthogonal to each other. As a result, in the non-orthogonal vector decomposition process, the computationally intensive pseudo-inverse projection operator can be approximated by the direct dot product without causing significant distance distortion. Experiments on real image datasets show promising performance in image matching, reconstruction and recognition tasks with significant speed improvement.