Fusion Tensor Subspace Transformation Framework

PLOS ONE, Dec 2019

Tensor subspace transformation, a commonly used subspace transformation technique, has gained more and more popularity over the past few years because many objects in the real world can be naturally represented as multidimensional arrays, i.e. tensors. For example, a RGB facial image can be represented as a three-dimensional array (or 3rd-order tensor). The first two dimensionalities (or modes) represent the facial spatial information and the third dimensionality (or mode) represents the color space information. Each mode of the tensor may express a different semantic meaning. Thus different transformation strategies should be applied to different modes of the tensor according to their semantic meanings to obtain the best performance. To the best of our knowledge, there are no existing tensor subspace transformation algorithm which implements different transformation strategies on different modes of a tensor accordingly. In this paper, we propose a fusion tensor subspace transformation framework, a novel idea where different transformation strategies are implemented on separate modes of a tensor. Under the framework, we propose the Fusion Tensor Color Space (FTCS) model for face recognition.

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Fusion Tensor Subspace Transformation Framework

Citation: Wang S-J, Zhou C-G, Fu X ( Fusion Tensor Subspace Transformation Framework Su-Jing Wang 0 Chun-Guang Zhou 0 Xiaolan Fu 0 Randen Lee Patterson, UC Davis School of Medicine, United States of America 0 1 State Key Laboratory of Brain and Cognitive Science, Institute of Psychology, Chinese Academy of Sciences , Beijing , China , 2 College of Computer Science and Technology, Jilin University , Changchun, Jilin , China , 3 Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University , Changchun , P.R. China Tensor subspace transformation, a commonly used subspace transformation technique, has gained more and more popularity over the past few years because many objects in the real world can be naturally represented as multidimensional arrays, i.e. tensors. For example, a RGB facial image can be represented as a three-dimensional array (or 3rd-order tensor). The first two dimensionalities (or modes) represent the facial spatial information and the third dimensionality (or mode) represents the color space information. Each mode of the tensor may express a different semantic meaning. Thus different transformation strategies should be applied to different modes of the tensor according to their semantic meanings to obtain the best performance. To the best of our knowledge, there are no existing tensor subspace transformation algorithm which implements different transformation strategies on different modes of a tensor accordingly. In this paper, we propose a fusion tensor subspace transformation framework, a novel idea where different transformation strategies are implemented on separate modes of a tensor. Under the framework, we propose the Fusion Tensor Color Space (FTCS) model for face recognition. - Funding: This work was supported in part by grants from 973 Program (2011CB302201), the National Natural Science Foundation of China (61075042, 61175023), China Postdoctoral Science Foundation funded project (2012M520428) and the open project program (93K172013K04) of Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. Subspace transformation (or subspace analysis [1]), a main type of feature extraction, has gained huge popularity over the past few years. Principal Component Analysis (PCA) [2] seeks the optimal projection directions according to maximal variances. Linear Discriminant Analysis (LDA) [3] uses discriminant information to search for the directions which are most effective for discrimination by maximizing the ratio between the between-class and within-class scatters. Both PCA and LDA aim to preserve global structures of the samples. Locality Preserving Projections (LPP) [4] aims to preserve the local structure of the original space in the projective subspace. Discriminant Locality Preserving Projections (DLPP) [5] encodes discriminant information into LPP to further improve the discriminant performance of LPP for face recognition. These algorithms need to vectorize the objects (samples). In the real world, however, many objects are naturally represented by multidimensional arrays, i.e., tensors, such as a color facial image used in face recognition (see Fig. 1). If these objects are vectorized, their natural structure information will be lost [6]. As such, a great deal of interests are aroused in the field of tensor [7][8][9][10][11]. Among the subspace transformation techniques, tensor subspace transformation has also become a highly discussed topic. Multilinear Principal Component Analysis (MPCA) [12], a tensor version of PCA, applies PCA transformation on each mode (or dimensionality) of tensors. Similarly, Discriminant Analysis with Tensor Representation (DATER) [13], General Tensor Discriminant Analysis (GTDA) [14], Tensor Subspace Analysis (TSA) [15], and Discriminant Tensor Subspace Analysis (DTSA) [16] apply LDA, Maximum Scatter Difference (MSD) [17], LPP, and DLPP to transform each mode of tensors, respectively. These tensor subspace transformation methods use a certain vector subspace transformation method to transform every modes of tensors. However, each mode of tensors may express a different semantic meaning. For example, a color facial image can be treated as a 3rd-order tensor, where mode-1 and mode-2 represent the facial spatial information and mode-3 representing the color space information (see Fig. 1). The facial spatial information and color space information are two different types of information, which should be handled by two different transformations to obtain better performance. In other words, for color facial images, we should implement a transformation strategy on the first two modes and another transformation strategy on the third mode. As such, each typ (...truncated)


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Su-Jing Wang, Chun-Guang Zhou, Xiaolan Fu. Fusion Tensor Subspace Transformation Framework, PLOS ONE, 2013, Volume 8, Issue 7, DOI: 10.1371/journal.pone.0066647