In the scope of gestural action recognition , the size of the feature vector representing movements is in general quite large especially when full body movements are considered. Furthermore, this feature vector evolves during the movement performance so that a complete movement is fully represented by a matrix M of size DxT, whose element (M_ i,j ) represents the value of feature i at timestamps j. Many studies have addressed dimensionality reduction considering only the size of the feature vector lying in ( R ^D ) to reduce both the variability of gestural sequences expressed in the reduced space, and the computational complexity of their processing. In return, very few of these methods have explicitly addressed the dimensionality reduction along the time axis. Yet this is a major issue when considering the use of elastic distances which are characterized by a quadratic complexity along the time axis. We present in this paper an evaluation of straightforward approaches aiming at reducing the dimensionality of the matrix M for each movement, leading to consider both the dimensionality reduction of the feature vector as well as its reduction along the time axis. The dimensionality reduction of the feature vector is achieved by selecting remarkable joints in the skeleton performing the movement, basically the extremities of the articulatory chains composing the skeleton. The temporal dimensionality reduction is achieved using either a regular or adaptive down-sampling that seeks to minimize the reconstruction error of the movements. Elastic and Euclidean kernels are then compared through support vector machine learning. Two data sets that are widely referenced in the domain of human gesture recognition, and quite distinctive in terms of quality of motion capture, are used for the experimental assessment of the proposed approaches. On these data sets we experimentally show that it is feasible, and possibly desirable, to significantly reduce simultaneously the size of the feature vector and the number of skeleton frames to represent body movements while maintaining a very good recognition rate. The method proves to give satisfactory results at a level currently reached by state-of-the-art methods on these data sets. We experimentally show that the computational complexity reduction that is obtained makes this approach eligible for real-time applications.
Numerous method are available to carry out such dimensionality reduction, the most popular being linear approaches such as Principal Component Analysis (PCA, @cite_34 , @cite_21 ), Linear Discriminant Analysis (LDA, @cite_29 ), or linear projections preserving locally neighborhoods (Locality Preserving Projection) @cite_19 . Among non-linear approaches, Locally Linear Embeddings (LLE, @cite_30 ), Metric Multidimensional Scaling (MDS, @cite_27 ) and variants like Laplacian Eigenmap @cite_0 , Isomap @cite_9 have been implemented to embed postures in low dimensional spaces in which a more efficient time warp (DTW, see section ) algorithm can be used to classify movements. An extension of this method, called ST-Isomap, considers temporal relationships in local neighborhoods that can be propagated globally via a shortest-path mechanism @cite_37 . Models based on Gaussian processes with latent variables are also largely used, for instance a hierarchical version has been recently exploited for gesture recognition @cite_8 .
@cite_30 @cite_37 @cite_8 @cite_29 @cite_21 @cite_9 @cite_0 @cite_19 @cite_27 @cite_34
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We propose an appearance-based face recognition method called the Laplacianface approach. By using locality preserving projections (LPP), the face images are mapped into a face subspace for analysis. Different from principal component analysis (PCA) and linear discriminant analysis (LDA) which effectively see only the Euclidean structure of face space, LPP finds an embedding that preserves local information, and obtains a face subspace that best detects the essential face manifold structure. The Laplacianfaces are the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the face manifold. In this way, the unwanted variations resulting from changes in lighting, facial expression, and pose may be eliminated or reduced. Theoretical analysis shows that PCA, LDA, and LPP can be obtained from different graph models. We compare the proposed Laplacianface approach with Eigenface and Fisherface methods on three different face data sets. Experimental results suggest that the proposed Laplacianface approach provides a better representation and achieves lower error rates in face recognition. We derive a least-squares formulation for MDDMp technique.A novel multi-label feature extraction algorithm is proposed.Our algorithm maximizes both feature variance and feature-label dependence.Experiments show that our algorithm is a competitive candidate. Dimensionality reduction is an important pre-processing procedure for multi-label classification to mitigate the possible effect of dimensionality curse, which is divided into feature extraction and selection. Principal component analysis (PCA) and multi-label dimensionality reduction via dependence maximization (MDDM) represent two mainstream feature extraction techniques for unsupervised and supervised paradigms. They produce many small and a few large positive eigenvalues respectively, which could deteriorate the classification performance due to an improper number of projection directions. It has been proved that PCA proposed primarily via maximizing feature variance is associated with a least-squares formulation. In this paper, we prove that MDDM with orthonormal projection directions also falls into the least-squares framework, which originally maximizes Hilbert-Schmidt independence criterion (HSIC). Then we propose a novel multi-label feature extraction method to integrate two least-squares formulae through a linear combination, which maximizes both feature variance and feature-label dependence simultaneously and thus results in a proper number of positive eigenvalues. Experimental results on eight data sets show that our proposed method can achieve a better performance, compared with other seven state-of-the-art multi-label feature extraction algorithms. Over the past few years, some embedding methods have been proposed for feature extraction and dimensionality reduction in various machine learning and pattern classification tasks. Among the methods proposed are Neighborhood Preserving Embedding (NPE), Locality Preserving Projection (LPP) and Local Discriminant Embedding (LDE) which have been used in such applications as face recognition and image video retrieval. However, although the data in these applications are more naturally represented as higher-order tensors, the embedding methods can only work with vectorized data representations which may not capture well some useful information in the original data. Moreover, high-dimensional vectorized representations also suffer from the curse of dimensionality and the high computational demand. In this paper, we propose some novel tensor embedding methods which, unlike previous methods, take data directly in the form of tensors of arbitrary order as input. These methods allow the relationships between dimensions of a tensor representation to be efficiently characterized. Moreover, they also allow the intrinsic local geometric and topological properties of the manifold embedded in a tensor space to be naturally estimated. Furthermore, they do not suffer from the curse of dimensionality and the high computational demand. We demonstrate the effectiveness of the proposed tensor embedding methods on a face recognition application and compare them with some previous methods. Extensive experiments show that our methods are not only more effective but also more efficient. In this paper, we learn explicit representations for dynamic shape manifolds of moving humans for the task of action recognition. We exploit locality preserving projections (LPP) for dimensionality reduction, leading to a low-dimensional embedding of human movements. Given a sequence of moving silhouettes associated to an action video, by LPP, we project them into a low-dimensional space to characterize the spatiotemporal property of the action, as well as to preserve much of the geometric structure. To match the embedded action trajectories, the median Hausdorff distance or normalized spatiotemporal correlation is used for similarity measures. Action classification is then achieved in a nearest-neighbor framework. To evaluate the proposed method, extensive experiments have been carried out on a recent dataset including ten actions performed by nine different subjects. The experimental results show that the proposed method is able to not only recognize human actions effectively, but also considerably tolerate some challenging conditions, e.g., partial occlusion, low-quality videos, changes in viewpoints, scales, and clothes; within-class variations caused by different subjects with different physical build; styles of motion; etc