Multi-view Discriminative Manifold Embedding for Pattern Classification

Transcription

1 Multi-view Discriinative Manifold Ebedding for Pattern Classification X. Wang Departen of Inforation Zhenghzou , China Y. Guo Departent of Digestive Zhengzhou , China Z. Wang Henan University of Technology Zhengzhou 45000, China ABSTRACT: While any diensionality reduction algoriths have been proposed in recent years, ost of the are designed for single view data and cannot cope with ulti-view data directly. Diensionality reduction algoriths in recent ten years, both in theory and application have great breakthrough. In the face of dozens, hundreds or even thousands of diension by diension reduction to the data fro high diensional space to a low diensional space and extract the essential characteristics of low diensional data. In any real-world pattern applications such as face recognition, ultiple feature descriptors can provide copleentary inforation in characterizing iage fro different viewpoints. Motivated by this concern, we propose a new ulti-view discriinative anifold ebedding (MDME) ethod for classification by aking use of intra-class geoetry and inter-class arginal inforation as well as copleentary inforation of ultiple feature representations. Experiental results on face recognition deonstrate the effectiveness of the proposed algorith. Keywords: Discriinative anifold ebedding, Multi-view learning, Diensionality reduction, Pattern classification Received: 2 February 207, Revised 8 March 207, Accepted 24 April DLINE. All Rights Reserved. Introduction Diensionality reduction is a fundaental proble in any achine learning and pattern recognition applications []. Recent researches show that higher diensional data (such as face iage) lie on a low-diensional nonlinear anifold. To fully discover the anifold structure of high-diensional data, the ost representative anifold learning algorith is a locality preserving projection (LPP) [2]. Although LPP can preserve the local geoetry of saples with a weighted adjacency graph, it is unsupervised and ignores the interactions of saples fro different classes. To utilize discriinant inforation for pattern classification, soe supervised anifold learning algoriths have been developed. Despite the various otivations of different 58 Journal of Intelligent Coputing Volue 8 Nuber 2 June 207

2 anifold learning algoriths, they can be unified into a general graph ebedding fraework (GEF) [3] with different constraints. Data diension reduction of pattern recognition of face recognition has been widely used. Because usually face iage data of high diension will not only cause the proble of diension disaster, but also can ake people found it difficult to structure of the underlying data set inforation. If the data diension reduction preprocessing, on one hand, can overcoe the diension disaster proble; on the other hand can greatly reduce the coputational coplexity and noise. So data diension reduction ethods now attract the attention of the researchers. 2. Related Work and Background Most existing diensionality reduction algoriths assue that the data are represented in a single view. In any practical applications such as face recognition, ultiple feature descriptors can provide copleentary inforation in characterizing iage inforation fro different viewpoints. Therefore, existing single-view-based ethods cannot directly cope with data described with ultiple views. Recent studies have shown that leveraging inforation contained in ultiple views potentially has a discriinating advantage over only a single view. Hence, it is ore reasonable to incorporate ulti-view learning into diensionality reduction so that the copleentary property of different views can be fully exploited for low-diensional ebedding. To achieve this goal, there have been soe attepts which include distributed ulti-view subspace learning (DMSL), ulti-view stochastic neighbor ebedding (MSNE), and ulti-view spectral ebedding (MSE) [4]. Although DMSL and MSNE can obtain low-diensional ebedding fro ulti-view high-diensional data, they are unsupervised and classification abilities ay be liited, since the class label inforation is not used in the learning process [5]. While MSE can solve the ulti-view subspace learning proble by using the patch alignent fraework, it ignores the flexibility of allowing shared inforation between different views owing to the global coordinate alignent process [6]. More recently, ulti-view subspace learning has been successfully applied to iage annotation, cartoon retrieval and synthesis. By jointly considering the local anifold structure and the class label inforation, we propose a new ethod, called ulti-view discriinative anifold ebedding (DME) [7]. Experiental results on face recognition are presented to deonstrate the effectiveness of the proposed approach [8]. The huan face is one of the ost coon ode of people s vision, face recognition have attracted uch attention because of its non-contact, safe, natural, intuitive and convenient characteristics and has becoe one of the bioetric identification technology currently. Face recognition is currently a hot research topic in the field of artificial intelligence and pattern recognition [9]. Extracting effective features (data diension reduction) plays a key role in the pattern classification of high diensional data. According to the bioetric recognition of the huan face, the diension reduction algorith directly affects the recognition rate of face recognition [0]. 3. Proposed Approaches In face recognition, generally use a high diensional vector to represent an iage, but because of the face recognition feature diension is too high and not stable, diension reduction is the ost coon ethod to solve this proble. The extraction of effective features is the key to reduce the ipact of loss of inforation on the recognition rate [,2]. Diensionality reduction (feature extraction) siply by apping function (including nonlinear apping and linear apping) apping high-diensional data into low diensional space, reduce the data diension, reduce the tie coplexity of the algorith and extract the essential features of the data, for data classification and visualization analysis etc. So far, any linear and nonlinear diensionality reduction ethods have been proposed. Recent studies show that although the different data diensionality reduction algoriths based on different theories and ethods, they also have soe contact. So expect data diensionality reduction ethods into a unified fraework to discuss and research [3, 4, 5], through this fraework to a certain extent, can proote diension reduction algorith. Given a ulti-view data set consisting of n saples with different features is denoted as a set of atrices X = {X (i) R pi n } i=, wherein X (i) is the feature atrix of the ith view representation, p i is the diensionality of the ith view X (i). The ai of MDME is to seek a low-diensional and sufficient sooth ebedding Y (i) R d n of X (i) via Y (i) = V T X (i), wherein d < p i (i =, 2,..., ). In order to well explore the copleentary inforation of ultiple views for feature extraction, a set of nonnegative weights β Journal of Intelligent Coputing Volue 8 Nuber 2 June

3 = [β, β 2,..., β ] is iposed on the objective function of DME of each view. The larger β i is, the ore contribution of the view Figure. Face recognition X (i) akes learning the low-diensional ebedding. Hence, by suing over all views, the optial objective function of MDME can be forulated as follows. With the constraint V, β T () i ( β) ( β) α 3( β) βi ( ) ax J V, = J V, J V, = Tr V H V () i= T V V = I, βi =, β 0. (2) i= i T T T ( α ( )( ) ) () i () i () i () i () i () i () i () i () i () i H = X L X X I R I R X (3) The solution to (2) subject to (3) is β i = corresponding to the axiu Tr (V T H (i) V) over different views, and β i = 0 otherwise. This eans that only the best view is finally selected by our ethod, thus resulting in failing to exploit the copleentary inforation fro different views for diensionality reduction. To tackle this proble, following the trick adopted in, we odify β i to be β i q with q >. Then, the new objective function is defined as follows. V, β q T () i T βi Tr ( V H V ) V V = I βi = βi (4) ax, s.t.,, 0. i= i= Since (7) is a nonlinearly constrained nonconvex optiization proble which has no closed-for solution, we derive an alternating optiization-based iterative algorith to obtain local optial solution. First, we fix V and update β. By utilizing the Lagrange ultiplier λ to incorporate the constraint into objective function, we obtain the following Lagrange function: q T () i ( βλ, ) = βi ( ) λ βi (5) L Tr V H V Let (, ) = 0and L ( βλ) L βλ β i i= i=, λ= 0, we have 60 Journal of Intelligent Coputing Volue 8 Nuber 2 June 207

4 i q T ( i) T ( i) Tr V H V Tr V H V q (6) Then, we update V by using the obtained The optial proble (7) is equivalent to i T ( i) T ax Tr V H V, s.t. V V I. V i (7) and V is given by the axiu eigenvalue solution to the eigenvalue proble. ( i) H V V i (8) 4. Experiental Results In this section, we evaluate the effectiveness of our proposed MDME approach for face recognition task. We also copare the proposed algorith with soe traditional single- view- based diensionality reduction algoriths, such as PCA, LDA, LPP, and MFA, as well as the three latest ulti-view diensionality reduction algoriths, including DMSL, MSNE, and MSE. For a fair coparison, all the results reported here are based on the best tuned paraeters of all the coparison algoriths. We have used the ORL and AR face databases in our experients. The ORL database contains 400 iages of 40 people. Each person provides different iages with various facial expressions and lighting conditions. The AR database contains over 4000 face iages of 26 people (70 en and 56 woen). For all the iages in the above two databases, the facial parts of each iage was anually cropped, aligned, and resized to pixels according to eye s positions, with 256 gray levels per pixel. In order to coprehensively describe face iages, we extract three kinds of low-level visual features to represent three different views, i.e., SIFT, Gabor, and LBP features. Because the three views are generally copleentary to each other, we epirically set q in MDME to 5. The diensionality of the low-diensional subspace d is set to 20 for ORL database and 30 for AR database. Table I tabulates the rank- recognition rates of different ethods with different features on the ORL and AR databases. Figure 2. Recognition rate versus in MDME on ORL and AR databases Journal of Intelligent Coputing Volue 8 Nuber 2 June 207 6

5 Figure 3. Recognition rate versus iteration nuber in MDME on ORL and AR databases Fro the experiental results listed in Table, we can observe that the proposed MDME ethod significantly outperfors other ulti-view and single view ethods on the two databases, which iplies that extracting the discriinative feature space by aking use of intra-class geoetry and inter-class arginal inforation and explicitly exploring the copleentary characteristics of different visual features can achieve the best recognition perforance. As shown in Figure 3. In our proposed MDME algorith, the paraeter α is epirically set to in the previous experients. To investigate the influence of different choices of α, Fig. shows the recognition rate of MDME versus different values of α, we can observe that MDME deonstrates a stable recognition perforance over a large range of α. Hence, the paraeter selection is not a very crucial in MDME algorith. In addition, since MDME is an iterative algorith, we evaluate its recognition rate with different nuber of iterations in Fig.2. As can be seen, our proposed MDME algorith can converge to a local optial value in less than 5 iterations. 5. Conclusions Data reduction is an iportant step towards the process of large data processing, and has becoe a hot research topic in the field of pattern recognition. Feature extraction cannot only find the eaningful low diensional structure inforation in high diensional data, but also can reduce the ipact of the curse of diensionality to a certain extent, and proote the visualization and classification of data. Face recognition technology brings us to a lot of convenience, it has a wide range of application prospects. The developent of face recognition technology not only iprove the security of electronic technology products, but also can proote the developent of artificial intelligence, iage processing, coputer graphics, cognitive science and psychology and other disciplines. Because the face structure odel is too coplicated and diverse, and easily influenced by illuination, facial expressions, gestures and other factors, how to effectively extract features to achieve the purpose of diension reduction is the key in face recognition. Graph ebedding fraework is a better unified anifold learning linear diension reduction algorith and nonlinear diensionality reduction algorith, in order to understand the difference between the diension reduction algorith and the link is very helpful. This letter proposes a new anifold learning algorith, called ulti-view discriinative anifold ebedding (MDME) for feature extraction and classification. Copared with the conventional single-view-based subspace learning algoriths, MDME can consider local geoetry and discriinative inforation as well as copleentary inforation of ultiple feature representations to obtain an effective low-diensional ebedding. Experiental results on two face databases have deonstrated the efficacy of the proposed approach. Above is the ain work done in this paper, although in the diension of data reduction researchers has ade soe achieveents, 62 Journal of Intelligent Coputing Volue 8 Nuber 2 June 207

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