ترغب بنشر مسار تعليمي؟ اضغط هنا

Sparse Representation Classification Beyond L1 Minimization and the Subspace Assumption

72   0   0.0 ( 0 )
 نشر من قبل Cencheng Shen
 تاريخ النشر 2015
  مجال البحث الاحصاء الرياضي
والبحث باللغة English




اسأل ChatGPT حول البحث

The sparse representation classifier (SRC) has been utilized in various classification problems, which makes use of L1 minimization and works well for image recognition satisfying a subspace assumption. In this paper we propose a new implementation of SRC via screening, establish its equivalence to the original SRC under regularity conditions, and prove its classification consistency under a latent subspace model and contamination. The results are demonstrated via simulations and real data experiments, where the new algorithm achieves comparable numerical performance and significantly faster.


قيم البحث

اقرأ أيضاً

One of the main challenges of planning legged locomotion in complex environments is the combinatorial contact selection problem. Recent contributions propose to use integer variables to represent which contact surface is selected, and then to rely on modern mixed-integer (MI) optimization solvers to handle this combinatorial issue. To reduce the computational cost of MI, we exploit the sparsity properties of L1 norm minimization techniques to relax the contact planning problem into a feasibility linear program. Our approach accounts for kinematic reachability of the center of mass (COM) and of the contact effectors. We ensure the existence of a quasi-static COM trajectory by restricting our plan to quasi-flat contacts. For planning 10 steps with less than 10 potential contact surfaces for each phase, our approach is 50 to 100 times faster that its MI counterpart, which suggests potential applications for online contact re-planning. The method is demonstrated in simulation with the humanoid robots HRP-2 and Talos over various scenarios.
275 - Zhiyuan Zha , Xin Yuan , Bei Li 2017
Rank minimization methods have attracted considerable interest in various areas, such as computer vision and machine learning. The most representative work is nuclear norm minimization (NNM), which can recover the matrix rank exactly under some restr icted and theoretical guarantee conditions. However, for many real applications, NNM is not able to approximate the matrix rank accurately, since it often tends to over-shrink the rank components. To rectify the weakness of NNM, recent advances have shown that weighted nuclear norm minimization (WNNM) can achieve a better matrix rank approximation than NNM, which heuristically set the weight being inverse to the singular values. However, it still lacks a sound mathematical explanation on why WNNM is more feasible than NNM. In this paper, we propose a scheme to analyze WNNM and NNM from the perspective of the group sparse representation. Specifically, we design an adaptive dictionary to bridge the gap between the group sparse representation and the rank minimization models. Based on this scheme, we provide a mathematical derivation to explain why WNNM is more feasible than NNM. Moreover, due to the heuristical set of the weight, WNNM sometimes pops out error in the operation of SVD, and thus we present an adaptive weight setting scheme to avoid this error. We then employ the proposed scheme on two low-level vision tasks including image denoising and image inpainting. Experimental results demonstrate that WNNM is more feasible than NNM and the proposed scheme outperforms many current state-of-the-art methods.
In this paper, we propose a subspace representation learning (SRL) framework to tackle few-shot image classification tasks. It exploits a subspace in local CNN feature space to represent an image, and measures the similarity between two images accord ing to a weighted subspace distance (WSD). When K images are available for each class, we develop two types of template subspaces to aggregate K-shot information: the prototypical subspace (PS) and the discriminative subspace (DS). Based on the SRL framework, we extend metric learning based techniques from vector to subspace representation. While most previous works adopted global vector representation, using subspace representation can effectively preserve the spatial structure, and diversity within an image. We demonstrate the effectiveness of the SRL framework on three public benchmark datasets: MiniImageNet, TieredImageNet and Caltech-UCSD Birds-200-2011 (CUB), and the experimental results illustrate competitive/superior performance of our method compared to the previous state-of-the-art.
Despite significant recent advances in deep neural networks, training them remains a challenge due to the highly non-convex nature of the objective function. State-of-the-art methods rely on error backpropagation, which suffers from several well-know n issues, such as vanishing and exploding gradients, inability to handle non-differentiable nonlinearities and to parallelize weight-updates across layers, and biological implausibility. These limitations continue to motivate exploration of alternative training algorithms, including several recently proposed auxiliary-variable methods which break the complex nested objective function into local subproblems. However, those techniques are mainly offline (batch), which limits their applicability to extremely large datasets, as well as to online, continual or reinforcement learning. The main contribution of our work is a novel online (stochastic/mini-batch) alternating minimization (AM) approach for training deep neural networks, together with the first theoretical convergence guarantees for AM in stochastic settings and promising empirical results on a variety of architectures and datasets.
The sparse representation classifier (SRC) is shown to work well for image recognition problems that satisfy a subspace assumption. In this paper we propose a new implementation of SRC via screening, establish its equivalence to the original SRC unde r regularity conditions, and prove its classification consistency for random graphs drawn from stochastic blockmodels. The results are demonstrated via simulations and real data experiments, where the new algorithm achieves comparable numerical performance but significantly faster.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا