High-dimensional Face Research Articles

Topology Preserving Non-negative Matrix Factorization for Face Recognition

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.

Perturbation scheme for online learning of features: Incremental principal component analysis

A new incremental online feature extraction approach is proposed based on principal component analysis in conjunction with perturbation theory which for its validity requires the perturbation parameter to be small. Our approach is found to be computationally more efficient in comparison to batch method which for its applicability requires simultaneous availability of all observations for computation of features. It is found on the basis of numerical experiments that the results based on our approach besides being in good agreement with the batch method and other incremental methods are also computationally more efficient. To demonstrate the efficacy of the proposed scheme, experiments have been performed on randomly generated datasets as well as on low and high dimensional datasets, i.e. UCI and face datasets which are available in public domain.

A linear discriminant analysis framework based on random subspace for face recognition

Linear discriminant analysis (LDA) often suffers from the small sample size problem when dealing with high-dimensional face data. Random subspace can effectively solve this problem by random sampling on face features. However, it remains a problem how to construct an optimal random subspace for discriminant analysis and perform the most efficient discriminant analysis on the constructed random subspace. In this paper, we propose a novel framework, random discriminant analysis (RDA), to handle this problem. Under the most suitable situation of the principal subspace, the optimal reduced dimension of the face sample is discovered to construct a random subspace where all the discriminative information in the face space is distributed in the two principal subspaces of the within-class and between-class matrices. Then we apply Fisherface and direct LDA, respectively, to the two principal subspaces for simultaneous discriminant analysis. The two sets of discriminant analysis features from dual principal subspaces are first combined at the feature level, and then all the random subspaces are further integrated at the decision level. With the discriminating information fusion at the two levels, our method can take full advantage of useful discriminant information in the face space. Extensive experiments on different face databases demonstrate its performance.

ICA-factorial 표현법을 이용한 얼굴감정인식

본 논문에서는 효과적인 정보를 표현하는 Independent Component Analysis(ICA)-factorial 표현방법을 이용하여 얼굴감정 인식을 수행한다. 얼굴감정인식은 두 단계인 특징추출 과정과 인식과정에 의해 이루어진다. 먼저 특징추출방법은 주성분 분석(Principal Component Analysis)을 이용하여 얼굴영상의 고차원 공간을 저차원 특징공간으로 변환한 후 ICA-factorial 표현방법을 통해 좀 더 효과적으로 특징벡터를 추출한다. 인식단계는 최소거리 분류방법인 유클리디안 거리에 근거한 K-Nearest Neighbor 알고리즘으로 얼굴감정을 인식한다. 6개의 기본감정(기쁨, 슬픔, 화남, 놀람, 공포, 혐오)에 대해 얼굴 감정 데이터베이스를 구축하고 실험해본 결과 기존의 방법보다 좋은 인식 성능을 얻었다. In this paper, we proposes a method for recognizing the facial expressions using ICA(Independent Component Analysis)-factorial representation method. Facial expression recognition consists of two stages. First, a method of Feature extraction transforms the high dimensional face space into a low dimensional feature space using PCA(Principal Component Analysis). And then, the feature vectors are extracted by using ICA-factorial representation method. The second recognition stage is performed by using the Euclidean distance measure based KNN(K-Nearest Neighbor) algorithm. We constructed the facial expression database for six basic expressions(happiness, sadness, angry, surprise, fear, dislike) and obtained a better performance than previous works.

Predicting face similarity judgements with a computational model of face space

Current models of face representation involve the notion of a high-dimensional face space. Computational models of face space based on principal components analysis (PCA) have been successfully used to predict human judgements of face sex or race. In this work the capability of PCA-based face spaces to predict human judgements of face similarity is examined. Three different paradigms were used. In Experiment 1 subjects learned face-name associations for 18 faces and identified these faces on tachistoscopic presentation. The number of confusions was used as a measure of face similarity. In Experiment 2 the same subjects subjectively rated the similarity of all 153 possible face pairs. In Experiment 3 reaction time to identify a face in an odd-man-out task was measured as an index of face similarity. These empirical measures were correlated with distance of the faces in PCA-based spaces of different dimensionalities. For Experiments 1 and 2 these correlations were highest for one-or two-dimensional face spaces ( r=−0.27 vs. −0.28). For Experiment 3 the correlation was highest for a space consisting of 13 dimensions ( r=−0.51). Thus PCA-based spaces seem capable to predict human similarity judgements to some extent. Possible reasons for the differences in predictability between paradigms are discussed.

Reformulation of capacitated facility location problems:How redundant information can help

When solving hard combinatorial optimization problems by branch-and-bound, obtaininga good lower bound (considering a minimization problem) from the linear relaxation iscrucial for the performance of the algorithm. On the other hand, we want to avoid an initialformulation that is too large. This requires careful modeling of the problem. One way ofobtaining a good linear formulation is by applying a cutting plane algorithm where strongcutting planes are added if they violate the current fractional solution. By “strong” cuttingplanes, we mean linear inequalities that define high-dimensional faces of the convex hull offeasible solutions. For some classes of inequalities, effective algorithms for identifyingviolated inequalities belonging to these classes have been implemented as standard featuresin commercial branch-and-bound packages. Such classes are for instance the knapsack coverinequalities and the flow cover inequalities that were originally developed for the knapsackproblem and the single-node flow problem. These problems form relaxations of severalcapacitated combinatorial optimization problems such as various capacitated facility locationproblems. If, however, we consider traditional models for location problems, then theknapsack and single-node flow relaxations are not explicitly stated in the models, andunless we modify the models, the mentioned classes of inequalities will not be generated“automatically” by the systems. The extra variables and constraints that we need to add tothe traditional models in order to make the various relaxations explicit are redundant, notonly to the integer formulation but also to the linear relaxation. Computational experimentsdo, however, indicate that the inequalities that are generated based on the relaxations arevery effective and that the gain from the stronger linear relaxation far outweighs the drawbackof expanding the traditional models.

The upper bound theorem for polytopes: an easy proof of its asymptotic version

Since at least half of the d edges incident to a vertex v of a simple d-polytope P either all point “up” or all point “down,” v must be the unique “bottom” or “top” vertex of a face of P of dimension at least d 2 . Thus the number of P's vertices is at most twice the number of such high-dimensional faces, which is at most ∑ d/2 ≤ i ≤ d( n d−v ) = 0(n ⌊d/2⌋) , if P has n facets. This, in a nutshell, provides a proof of the asymptotic version of the famous upper bound theorem: A convex d-polytope with n facets (or, dually, with n vertices) has O(n [ d 2 ]) faces, when d is constant.