Elsevier

Knowledge-Based Systems

Volume 89, November 2015, Pages 47-55
Knowledge-Based Systems

Discriminant sparse local spline embedding with application to face recognition

https://doi.org/10.1016/j.knosys.2015.06.016Get rights and content

Abstract

In this paper, an efficient feature extraction algorithm called discriminant sparse local spline embedding (D-SLSE) is proposed for face recognition. A sparse neighborhood graph of the input data is firstly constructed based on a sparse representation framework, and then the low-dimensional embedding of the data is obtained by faithfully preserving the intrinsic geometry of the data samples based on such sparse neighborhood graph and best holding the discriminant power based on the class information of the input data. Finally, an orthogonalization procedure is perfomred to improve discriminant power. The experimental results on the two face image databases demonstrate that D-SLSE is effective for face recognition.

Introduction

It is well known that there are large volumes of high-dimensional data in numerous real-world applications. Operating directly on such high-dimensional image space is ineffective and may lead to high computational and storage demands as well as poor performance. From the perspective of pattern recognition, dimensionality reduction is a typical way to circumvent the “curse of dimensionality” problem [1] and other undesired properties of high-dimensional spaces. The goal of dimensionality reduction is to construct a meaningful low-dimensional representation of high-dimensional data. Ideally the reduced representation in the low-dimensional space should have a dimensionality that corresponds to the intrinsic dimensionality of the data.

Researchers have developed many useful dimensionality reduction techniques. These techniques can be broadly categorized into two classes: linear and nonlinear. Classical linear dimensionality reduction approaches seek to find a meaningful low-dimensional subspace in a high-dimensional input space by linear transformation. This subspace can provide a compact representation of high-dimensional input data when the intrinsic structure of data embedded in the input space is linear. Among them, the most well known are principal component analysis (PCA) [2] and linear discriminant analysis (LDA) [3]. Linear models have been extensively used in pattern recognition and computer vision areas and have become the most popular techniques for face recognition [4], [5], [6], [7], [8].

Linear techniques, however, may fail to discover the intrinsic structures of complex nonlinear data. In order to address this problem, a number of nonlinear manifold learning techniques have been proposed under the assumption that the input data set lies on or near some low-dimensional manifold embedded in a high-dimensional unorganized Euclidean space [9]. The motivation of manifold learning techniques is straightforward as it seeks to directly find the intrinsic low-dimensional nonlinear data structures hidden in the observation space. Examples include isometric feature mapping (ISOMAP) [10], locally linear embedding (LLE) [11], Laplacian eigenmaps (LE) [12], Hessian-based locally linear embedding (HLLE) [13], maximum variance unfolding (MVU) [14], manifold charting [15], local tangent space alignment (LTSA) [16], Riemannian manifold learning (RML) [17], and local spline embedding (LSE) [18], elastic embedding (EE) [19], Cauchy graph embedding (CGE) [20], adaptive manifold learning [21], and neighborhood preserving polynomial embedding (NPPE) [22]. Each manifold learning algorithm attempts to preserve a different geometrical property of the underlying manifold. Local approaches, such as LLE, HLLE, LE, LTSA, and LSE, aim to preserve the proximity relationship among the data, while global approaches like ISOMAP and LOGMAP aim to preserve the metrics at all scales. Some experiments have shown that these methods can find perceptually meaningful embeddings for face or digit images. They also do yield impressive results on other artificial and real-world data sets. However, these manifold learning methods have to confront with the out-of-sample problem when they are applied to pattern recognition. They can yield an embedding directly based on the training data set, but, because of the implicitness of the nonlinear map, when applied to a new sample, they cannot find the image of the sample in the embedding space. It limits the applications of these algorithms to pattern recognition problems. To overcome the drawback, Bengio et al. proposed a kernel method to embed the new data points by utilizing the generalization ability of Mercer kernel [23]. He et al. proposed a method named locality preserving projection (LPP) to approximate the eigen-functions of the Laplace–Beltrami operator on the manifold and the new testing points can be mapped to the learned subspace without trouble [24]. Yan et al. utilized the graph embedding framework for developing a novel algorithm called marginal Fisher analysis (MFA) to solve the out-of-sample problem [25].

Recently, sparse representation has attracted considerable interests in machine learning and pattern recognition. Some researchers proposed some new methods integrating the theory of sparse representation and subspace learning. They are considered as a special family of dimensionality reduction methods which consider “sparsity”. It has either of the following two characteristics: (1) Finding a subspace spanned by sparse base vectors. The sparsity is enforced on the projection vectors and associated with the feature dimensionality. The representative techniques are sparse principal component analysis (SPCA) [26] and nonnegative sparse PCA [27]. (2) Aiming at the sparse reconstructive weight which is associated with the sample size. The representative methods include sparse neighborhood preserving embedding (SNPE) [28] and sparsity preserving projections (SPP) [29].

In this paper, inspired by the idea of LSE [18] and sparse representation, we propose a novel sparse subspace learning technique, called discriminant sparse local spline embedding (D-SLSE). Specifically, A sparse neighborhood graph of the input data is firstly constructed based on a sparse representation framework, and then the low-dimensional embedding of the data is obtained by faithfully preserving the intrinsic geometry of the data samples based on such sparse neighborhood graph and best holding the discriminant power based on the class information of the input data. Finally, an orthogonalization procedure is perfomred to improve discriminant power. We now enumerate several characteristics of our proposed algorithm as follows:

  • (1)

    D-SLSE does not have to encounter setting the neighborhood size in constructing a neighborhood graph incurred in LSE. An unsuitable neighborhood may result in “short-circuit” edges (see Fig. 1a) or a large number of disconnected regions (see Fig. 1b). In contrast, graph construction based on sparse representation makes our proposed method very simple to use in practice.

  • (2)

    D-SLSE computes an explicit linear mapping from the input space to the reduced space, which attempts to manage the trade-off between holding discriminant power and preserving local geometry structure.

  • (3)

    D-SLSE seeks to find a set of orthogonal basis functions and significantly improves its recognition accuracy.

The rest of this paper is organized as follows: The D-SLSE algorithm is developed in Section 2. Section 3 demonstrates the experimental results. Finally, conclusions are presented in Section 4.

Section snippets

Local spline embedding

Xiang et al. [18] proposed a general dimensionality reduction framework called compatible mapping. They used the compatible mapping framework as a platform and developed a novel local spline embedding (LSE) manifold learning algorithm. This method includes two steps: part optimization and whole alignment. Each data point is represented in different local coordinate systems by part optimization. But its global coordinate should be maintained unique. Whole spline alignment is used to achieve this

Experimental results

This section evaluates the performance of the proposed D-SLSE in comparison with five representative algorithms, i.e., MMC [31], LDA [4], SLPP [32], SLLTSA [33], and MFA [25] on two face image databases, i.e., Yale database1 and Olivetti Research Laboratory (ORL) database.2 Among these algorithms, SLPP, SLLTSA, and MFA are recently proposed manifold learning algorithms. Preprocessing was performed

Conclusions

In this paper, we have introduced a novel sparse subspace learning technique, called discriminant sparse local spline embedding (D-SLSE). The most prominent property for D-SLSE is the faithful preservation of the local geometrical structure hidden in the data and the improvement of the discriminant power based on the class information and orthogonalization procedure. We have applied our algorithm to face recognition. The experimental results on Yale and ORL databases show that the new method is

Acknowledgments

This work is supported by the grants of the National Science Foundation of China, Nos. 61272333, 61273302, 61171170 & 61473237, the Anhui Provincial Natural Science Foundation under Grant Nos. 1308085QF99 & 1408085MF129, and the Foundation of State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System of China under Grant No. CEMEE2014K0103B. The authors would like to thank all the guest editors and anonymous reviewers for their constructive advices.

References (33)

  • H.S. Seung et al.

    The manifold ways of perception

    Science

    (2000)
  • J. Tenenbaum et al.

    A global geometric framework for nonlinear dimensionality reduction

    Science

    (2000)
  • S. Roweis et al.

    Nonlinear dimensionality reduction by locally linear embedding

    Science

    (2000)
  • M. Belkin et al.

    Laplacian eigenmaps for dimensionality reduction and data representation

    Neural Comput.

    (2003)
  • D. Donoho et al.

    Hessian eigenmaps: new locally linear embedding techniques for high-dimensional data

    Proc. Nat’l. Acad. Sci.

    (2003)
  • K. Weinberger et al.

    Unsupervised learning of image manifolds by semidefinite programming

    Proc. of CVPR

    (2004)
  • Cited by (11)

    • A survey of emotion recognition methods with emphasis on E-Learning environments

      2019, Journal of Network and Computer Applications
      Citation Excerpt :

      Then, by applying these filters, the feature vector is extracted from the input video. The face appearance changes modeled by Local Binary Patterns (LBP), Histograms of Oriented Gradients (HOG) (Li et al., 2009), Gabor wavelets and discriminant sparse local spline approaches (Lei et al., 2015) represent the appearance features. Many recent researches are based on local texture extraction from face images.

    • Local appearance-based face recognition using adaptive directional wavelet transform

      2019, Journal of King Saud University - Computer and Information Sciences
    • Face recognition using Angular Radial Transform

      2018, Journal of King Saud University - Computer and Information Sciences
      Citation Excerpt :

      The modular Eigenspace approach, introduced by Pentland et al. (1994), belongs to the above mentioned category. Another efficient feature extraction algorithm, called Discriminant Sparse Local Spline Embedding (D-SLSE), which can be considered as a hybrid approach for face recognition was proposed by Lei et al. (2015). During the second phase of recognition, namely the classification phase, the system must decide whether the person belongs to the database and if so, to what class he belongs; in other words: who is the person?

    • Exponential elastic preserving projections for facial expression recognition

      2018, Neurocomputing
      Citation Excerpt :

      The massive experiments [18–20] have shown that forcing an orthogonal relationship between the projection directions is more effective for preserving the manifold structure of high-dimensional data. Furthermore, in order to improve the discriminant power for classification tasks, lots of manifold-learning-based discriminant analysis algorithms [21–25] have been proposed. In 2014, Chang et al. [26] integrated manifold learning with clustering and proposed Spectral Shrunk Clustering (SSC), which has obtained quite promising clustering performance.

    • Sparse learning based fuzzy c-means clustering

      2017, Knowledge-Based Systems
      Citation Excerpt :

      Fortunately, a discriminant feature which reflects the degree of similarity between any two samples can be learned by sparse representation methods. Recently, sparse representation (SR) [36–37] has attracted a lot of attention and has been successfully used to image classification [38–45] and data clustering [46–48]. Among them, the most representative methods are sparse representation based classification [49] and sparse subspace clustering [50] algorithms.

    • Dictionary learning based on discriminative energy contribution for image classification

      2016, Knowledge-Based Systems
      Citation Excerpt :

      In some degree, the sparse representation can be considered as a kind of feature extraction method and the sparse coefficient is the characteristic of the signal. In recent years, sparse representation has been successfully applied to face recognition [26-28] and other classification tasks. In the classical sparse representation based classification (SRC) [26], the training samples are consider as the atoms of dictionary without dictionary learning, and the query signal is first sparsely coded over the template images.

    View all citing articles on Scopus
    View full text