We present a comparative evaluation of various techniques for action recognition while keeping as many variables as possible controlled. We employ two categories of Riemannian manifolds: symmetric positive definite matrices and linear subspaces. For both categories we use their corresponding nearest neighbour classifiers, kernels, and recent kernelised sparse representations. We compare against traditional action recognition techniques based on Gaussian mixture models and Fisher vectors (FVs). We evaluate these action recognition techniques under ideal conditions, as well as their sensitivity in more challenging conditions (variations in scale and translation). Despite recent advancements for handling manifolds, manifold based techniques obtain the lowest performance and their kernel representations are more unstable in the presence of challenging conditions. The FV approach obtains the highest accuracy under ideal conditions. Moreover, FV best deals with moderate scale and translation changes.
Recently, the traditional sparse representation (SR) on vectors has been generalised to sparse representations in SPD matrices and LS @cite_11 @cite_43 @cite_48 @cite_12 . While the objective of SR is to find a representation that efficiently approximates elements of a signal class with as few atoms as possible, for the Riemannian SR, any given point can be represented as a sparse combination of dictionary elements @cite_43 @cite_48 . @cite_48 , LS are embedded into the space via isometric mapping, which leads to a closed-form solution for updating a LS representation, atom by atom. Moreover, @cite_48 presents a kernelised version of the dictionary learning algorithm to deal with non-linearity in data. @cite_43 outlines the sparse coding and dictionary learning problem for SPD matrices. To this end, SPD matrices are embedded into the RKHS to perform sparse coding.
@cite_43 @cite_48 @cite_12 @cite_11
1989243451 1539012881 2142848040 2088254198
Applications of sparse signal representation in image processing and pattern recognition have attracted a great deal of attention. Sparse representation based classification (SRC) methods emphasizes on sparse representation computed by l"1-minimization to exploit the underlying sparsity in the problem domain, and argued the importance of sparse representation that improved the discrimination to achieve robust and accurate classification results. Recently, many studies have shown the role of collaborative representation (CR) in SRC, which actually improved the classification accuracy. In this paper, we proposed a novel collaborative neighbor representation method for multi-class classification based on l"2-minimization approach with the assumption of locally linear embedding (LLE). The proposed method represents a test sample over the dictionary by automatically choosing optimal nearest basis spanned in the same linear subspace as of test sample. The proposed representation method achieves competitive classification accuracy via optimal neighbor representation having discriminative learning power. Extensive experiments on real-world face and digit databases are performed to analyze the performance of the proposed method against SRC methods. Result clearly shows that the proposed method achieves competitive results for face recognition and pattern classification, and is significantly much faster and comparably accurate than SRC based classification methods. Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved using a recently introduced tree-structured sparse regularization norm, which has proven useful in several applications. This norm leads to regularized problems that are difficult to optimize, and in this paper, we propose efficient algorithms for solving them. More precisely, we show that the proximal operator associated with this norm is computable exactly via a dual approach that can be viewed as the composition of elementary proximal operators. Our procedure has a complexity linear, or close to linear, in the number of atoms, and allows the use of accelerated gradient techniques to solve the tree-structured sparse approximation problem at the same computational cost as traditional ones using the l1-norm. Our method is efficient and scales gracefully to millions of variables, which we illustrate in two types of applications: first, we consider fixed hierarchical dictionaries of wavelets to denoise natural images. Then, we apply our optimization tools in the context of dictionary learning, where learned dictionary elements naturally self-organize in a prespecified arborescent structure, leading to better performance in reconstruction of natural image patches. When applied to text documents, our method learns hierarchies of topics, thus providing a competitive alternative to probabilistic topic models. Sparse representation-based classifier (SRC), a combined result of machine learning and compressed sensing, shows its good classification performance on face image data. However, SRC could not well classify the data with the same direction distribution. The same direction distribution means that the sample vectors belonging to different classes distribute on the same vector direction. This paper presents a new classifier, kernel sparse representation-based classifier (KSRC), based on SRC and the kernel trick which is a usual technique in machine learning. KSRC is a nonlinear extension of SRC and can remedy the drawback of SRC. To make the data in an input space separable, we implicitly map these data into a high-dimensional kernel feature space by using some nonlinear mapping associated with a kernel function. Since this kernel feature space has a very high (or possibly infinite) dimensionality, or is unknown, we have to avoid working in this space explicitly. Fortunately, we can indeed reduce the dimensionality of the kernel feature space by exploiting kernel-based dimensionality reduction methods. In the reduced subspace, we need to find sparse combination coefficients for a test sample and assign a class label to it. Similar to SRC, KSRC is also cast into an l1-minimization problem or a quadratically constrained l1 -minimization problem. Extensive experimental results on UCI and face data sets show KSRC improves the performance of SRC. In this paper, we propose a novel coupled dictionary training method for single-image super-resolution (SR) based on patchwise sparse recovery, where the learned couple dictionaries relate the low- and high-resolution (HR) image patch spaces via sparse representation. The learning process enforces that the sparse representation of a low-resolution (LR) image patch in terms of the LR dictionary can well reconstruct its underlying HR image patch with the dictionary in the high-resolution image patch space. We model the learning problem as a bilevel optimization problem, where the optimization includes an l1-norm minimization problem in its constraints. Implicit differentiation is employed to calculate the desired gradient for stochastic gradient descent. We demonstrate that our coupled dictionary learning method can outperform the existing joint dictionary training method both quantitatively and qualitatively. Furthermore, for real applications, we speed up the algorithm approximately 10 times by learning a neural network model for fast sparse inference and selectively processing only those visually salient regions. Extensive experimental comparisons with state-of-the-art SR algorithms validate the effectiveness of our proposed approach.