Topology Preserving Non-negative Matrix Factorization for Face Recognition

Abstract

In this paper, a novel topology preserving non-negative matrix factorization (TPNMF) method is proposed for face recognition. We derive the TPNMF model from original NMF algorithm by preserving local topology structure. The TPNMF is based on minimizing the constraint gradient distance in the high-dimensional space. Compared with L(2) distance, the gradient distance is able to reveal latent manifold structure of face patterns. By using TPNMF decomposition, the high-dimensional face space is transformed into a local topology preserving subspace for face recognition. In comparison with PCA, LDA, and original NMF, which search only the Euclidean structure of face space, the proposed TPNMF finds an embedding that preserves local topology information, such as edges and texture. Theoretical analysis and derivation given also validate the property of TPNMF. Experimental results on three different databases, containing more than 12,000 face images under varying in lighting, facial expression, and pose, show that the proposed TPNMF approach provides a better representation of face patterns and achieves higher recognition rates than NMF.

Illumination-Robust Face Recognition form a Single Image per Person Using Matrix Polar Decomposition

“…This process is repeated until all images are classified. Comparison results together with the results conducted by [8], [16], [34], [43] are shown in Table 2. From this table, it can be seen that the proposed method achieved the highest recognition rate.…”

“…In modular PCA, a face image is partitioned into several sub-images and then a single conventional PCA is applied to each of them. Another approach for image analysis is the non-negative matrix factorization (NMF) which is based on the fact that image pixels are known to be non-negative [34]. Considering the illumination invariant face recognition, we find out that the unitary factor in the matrix polar form (defined later) of a face image can be regarded as an appropriate representation of the image.…”

The Research on the Multiple Kernel Learning-based Face Recognition in Pattern Matching

“…As the development of the modern information technologies, automatic face recognition has attached importance to broad fields such as military, commercial, security, in virtue of its good applicability and a non-intrusive property Face recognition has become one of the most representative and challenging research content of pattern recognition domain. Face recognition is an old but young academic problem, about which people have thought across three centuries [10].…”

Projected Gradients for Subclass Discriminant Nonnegative Subspace Learning

“…Other approaches that exploit the data geometric structure in order to extract discriminative information have been also proposed in [11] and [12]. Another notable variant of NMF which retains the manifold structure of facial space, is the topology preserving NMF (TPNMF) [13] specialized for face representation and recognition.…”

“…Focusing on applications operating on facial image data, numerous specialized NMF variants have been proposed for face recognition [7], [13], [14], face verification [15], [16], and facial expression recognition [17], [18]. In these approaches, the entire facial image is considered as a feature vector and NMF aims to find projections that optimize a given criterion.…”