Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction

It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local geometry of samples is well preserved for low dimensional data representation, 2) both the margin maximization and the classification error minimization are considered for sparse projection calculation, 3) the projection matrix of MEN improves the parsimony in computation, 4) the elastic net penalty reduces the over-fitting problem, and 5) the projection matrix of MEN can be interpreted psychologically and physiologically. Experimental evidence on face recognition over various popular datasets suggests that MEN is superior to top level dimensionality reduction algorithms.Comment: 33 pages, 12 figure

A Convex Formulation for Spectral Shrunk Clustering

Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning in the original space. However, the manifold in reduced-dimensional subspace is likely to exhibit altered properties in contrast with the original space. Thus, applying manifold information obtained from the original space to the clustering process in a low-dimensional subspace is prone to inferior performance. Aiming to address this issue, we propose a novel convex algorithm that mines the manifold structure in the low-dimensional subspace. In addition, our unified learning process makes the manifold learning particularly tailored for the clustering. Compared with other related methods, the proposed algorithm results in more structured clustering result. To validate the efficacy of the proposed algorithm, we perform extensive experiments on several benchmark datasets in comparison with some state-of-the-art clustering approaches. The experimental results demonstrate that the proposed algorithm has quite promising clustering performance.Comment: AAAI201

Joint optimization of manifold learning and sparse representations for face and gesture analysis

Face and gesture understanding algorithms are powerful enablers in intelligent vision systems for surveillance, security, entertainment, and smart spaces. In the future, complex networks of sensors and cameras may disperse directions to lost tourists, perform directory lookups in the office lobby, or contact the proper authorities in case of an emergency. To be effective, these systems will need to embrace human subtleties while interacting with people in their natural conditions. Computer vision and machine learning techniques have recently become adept at solving face and gesture tasks using posed datasets in controlled conditions. However, spontaneous human behavior under unconstrained conditions, or in the wild, is more complex and is subject to considerable variability from one person to the next. Uncontrolled conditions such as lighting, resolution, noise, occlusions, pose, and temporal variations complicate the matter further. This thesis advances the field of face and gesture analysis by introducing a new machine learning framework based upon dimensionality reduction and sparse representations that is shown to be robust in posed as well as natural conditions. Dimensionality reduction methods take complex objects, such as facial images, and attempt to learn lower dimensional representations embedded in the higher dimensional data. These alternate feature spaces are computationally more efficient and often more discriminative. The performance of various dimensionality reduction methods on geometric and appearance based facial attributes are studied leading to robust facial pose and expression recognition models. The parsimonious nature of sparse representations (SR) has successfully been exploited for the development of highly accurate classifiers for various applications. Despite the successes of SR techniques, large dictionaries and high dimensional data can make these classifiers computationally demanding. Further, sparse classifiers are subject to the adverse effects of a phenomenon known as coefficient contamination, where for example variations in pose may affect identity and expression recognition. This thesis analyzes the interaction between dimensionality reduction and sparse representations to present a unified sparse representation classification framework that addresses both issues of computational complexity and coefficient contamination. Semi-supervised dimensionality reduction is shown to mitigate the coefficient contamination problems associated with SR classifiers. The combination of semi-supervised dimensionality reduction with SR systems forms the cornerstone for a new face and gesture framework called Manifold based Sparse Representations (MSR). MSR is shown to deliver state-of-the-art facial understanding capabilities. To demonstrate the applicability of MSR to new domains, MSR is expanded to include temporal dynamics. The joint optimization of dimensionality reduction and SRs for classification purposes is a relatively new field. The combination of both concepts into a single objective function produce a relation that is neither convex, nor directly solvable. This thesis studies this problem to introduce a new jointly optimized framework. This framework, termed LGE-KSVD, utilizes variants of Linear extension of Graph Embedding (LGE) along with modified K-SVD dictionary learning to jointly learn the dimensionality reduction matrix, sparse representation dictionary, sparse coefficients, and sparsity-based classifier. By injecting LGE concepts directly into the K-SVD learning procedure, this research removes the support constraints K-SVD imparts on dictionary element discovery. Results are shown for facial recognition, facial expression recognition, human activity analysis, and with the addition of a concept called active difference signatures, delivers robust gesture recognition from Kinect or similar depth cameras

Effective Discriminative Feature Selection with Non-trivial Solutions

Feature selection and feature transformation, the two main ways to reduce dimensionality, are often presented separately. In this paper, a feature selection method is proposed by combining the popular transformation based dimensionality reduction method Linear Discriminant Analysis (LDA) and sparsity regularization. We impose row sparsity on the transformation matrix of LDA through ${\ell}_{2,1}$-norm regularization to achieve feature selection, and the resultant formulation optimizes for selecting the most discriminative features and removing the redundant ones simultaneously. The formulation is extended to the ${\ell}_{2,p}$-norm regularized case: which is more likely to offer better sparsity when $0<p<1$. Thus the formulation is a better approximation to the feature selection problem. An efficient algorithm is developed to solve the ${\ell}_{2,p}$-norm based optimization problem and it is proved that the algorithm converges when $0<p\le 2$. Systematical experiments are conducted to understand the work of the proposed method. Promising experimental results on various types of real-world data sets demonstrate the effectiveness of our algorithm

Gaussian processes for modeling of facial expressions

Automated analysis of facial expressions has been gaining significant attention over the past years. This stems from the fact that it constitutes the primal step toward developing some of the next-generation computer technologies that can make an impact in many domains, ranging from medical imaging and health assessment to marketing and education. No matter the target application, the need to deploy systems under demanding, real-world conditions that can generalize well across the population is urgent. Hence, careful consideration of numerous factors has to be taken prior to designing such a system. The work presented in this thesis focuses on tackling two important problems in automated analysis of facial expressions: (i) view-invariant facial expression analysis; (ii) modeling of the structural patterns in the face, in terms of well coordinated facial muscle movements. Driven by the necessity for efficient and accurate inference mechanisms we explore machine learning techniques based on the probabilistic framework of Gaussian processes (GPs). Our ultimate goal is to design powerful models that can efficiently handle imagery with spontaneously displayed facial expressions, and explain in detail the complex configurations behind the human face in real-world situations. To effectively decouple the head pose and expression in the presence of large out-of-plane head rotations we introduce a manifold learning approach based on multi-view learning strategies. Contrary to the majority of existing methods that typically treat the numerous poses as individual problems, in this model we first learn a discriminative manifold shared by multiple views of a facial expression. Subsequently, we perform facial expression classification in the expression manifold. Hence, the pose normalization problem is solved by aligning the facial expressions from different poses in a common latent space. We demonstrate that the recovered manifold can efficiently generalize to various poses and expressions even from a small amount of training data, while also being largely robust to corrupted image features due to illumination variations. State-of-the-art performance is achieved in the task of facial expression classification of basic emotions. The methods that we propose for learning the structure in the configuration of the muscle movements represent some of the first attempts in the field of analysis and intensity estimation of facial expressions. In these models, we extend our multi-view approach to exploit relationships not only in the input features but also in the multi-output labels. The structure of the outputs is imposed into the recovered manifold either from heuristically defined hard constraints, or in an auto-encoded manner, where the structure is learned automatically from the input data. The resulting models are proven to be robust to data with imbalanced expression categories, due to our proposed Bayesian learning of the target manifold. We also propose a novel regression approach based on product of GP experts where we take into account people's individual expressiveness in order to adapt the learned models on each subject. We demonstrate the superior performance of our proposed models on the task of facial expression recognition and intensity estimation.Open Acces