Mengyang Yu

Yuming Shen, Jie Qin, Jiaxin Chen et al.

Conventional unsupervised hashing methods usually take advantage of similarity graphs, which are either pre-computed in the high-dimensional space or obtained from random anchor points. On the one hand, existing methods uncouple the procedures of hash function learning and graph construction. On the other hand, graphs empirically built upon original data could introduce biased prior knowledge of data relevance, leading to sub-optimal retrieval performance. In this paper, we tackle the above problems by proposing an efficient and adaptive code-driven graph, which is updated by decoding in the context of an auto-encoder. Specifically, we introduce into our framework twin bottlenecks (i.e., latent variables) that exchange crucial information collaboratively. One bottleneck (i.e., binary codes) conveys the high-level intrinsic data structure captured by the code-driven graph to the other (i.e., continuous variables for low-level detail information), which in turn propagates the updated network feedback for the encoder to learn more discriminative binary codes. The auto-encoding learning objective literally rewards the code-driven graph to learn an optimal encoder. Moreover, the proposed model can be simply optimized by gradient descent without violating the binary constraints. Experiments on benchmarked datasets clearly show the superiority of our framework over the state-of-the-art hashing methods. Our source code can be found at https://github.com/ymcidence/TBH.

Jun Xu, Mengyang Yu, Ling Shao et al.

The self-expressive property of data points, i.e., each data point can be linearly represented by the other data points in the same subspace, has proven effective in leading subspace clustering methods. Most self-expressive methods usually construct a feasible affinity matrix from a coefficient matrix, obtained by solving an optimization problem. However, the negative entries in the coefficient matrix are forced to be positive when constructing the affinity matrix via exponentiation, absolute symmetrization, or squaring operations. This consequently damages the inherent correlations among the data. Besides, the affine constraint used in these methods is not flexible enough for practical applications. To overcome these problems, in this paper, we introduce a scaled simplex representation (SSR) for subspace clustering problem. Specifically, the non-negative constraint is used to make the coefficient matrix physically meaningful, and the coefficient vector is constrained to be summed up to a scalar s<1 to make it more discriminative. The proposed SSR based subspace clustering (SSRSC) model is reformulated as a linear equality-constrained problem, which is solved efficiently under the alternating direction method of multipliers framework. Experiments on benchmark datasets demonstrate that the proposed SSRSC algorithm is very efficient and outperforms state-of-the-art subspace clustering methods on accuracy. The code can be found at https://github.com/csjunxu/SSRSC.

H. Xiong, L. Huang, M. Yu et al.

One fundamental problem in deep learning is understanding the outstanding performance of deep Neural Networks (NNs) in practice. One explanation for the superiority of NNs is that they can realize a large class of complicated functions, i.e., they have powerful expressivity. The expressivity of a ReLU NN can be quantified by the maximal number of linear regions it can separate its input space into. In this paper, we provide several mathematical results needed for studying the linear regions of CNNs, and use them to derive the maximal and average numbers of linear regions for one-layer ReLU CNNs. Furthermore, we obtain upper and lower bounds for the number of linear regions of multi-layer ReLU CNNs. Our results suggest that deeper CNNs have more powerful expressivity than their shallow counterparts, while CNNs have more expressivity than fully-connected NNs per parameter.

Huan Xiong, Mengyang Yu, Li Liu et al.

Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are NP-hard and difficult to solve due to the binary constraints, especially when the number of variables is very large. Existing methods often suffer from high computational costs or large accumulated quantization errors, or are only designed for specific tasks. In this paper, we propose a fast algorithm to find effective approximate solutions for general binary optimization problems. The proposed algorithm iteratively solves minimization problems related to the linear surrogates of loss functions, which leads to the updating of some binary variables most impacting the value of loss functions in each step. Our method supports a wide class of empirical objective functions with/without restrictions on the numbers of $1$s and $-1$s in the binary variables. Furthermore, the theoretical convergence of our algorithm is proven, and the explicit convergence rates are derived, for objective functions with Lipschitz continuous gradients, which are commonly adopted in practice. Extensive experiments on several binary optimization tasks and large-scale datasets demonstrate the superiority of the proposed algorithm over several state-of-the-art methods in terms of both effectiveness and efficiency.

Li Liu, Mengyang Yu, Ling Shao

Recently, very high-dimensional feature representations, e.g., Fisher Vector, have achieved excellent performance for visual recognition and retrieval. However, these lengthy representations always cause extremely heavy computational and storage costs and even become unfeasible in some large-scale applications. A few existing techniques can transfer very high-dimensional data into binary codes, but they still require the reduced code length to be relatively long to maintain acceptable accuracies. To target a better balance between computational efficiency and accuracies, in this paper, we propose a novel embedding method called Binary Projection Bank (BPB), which can effectively reduce the very high-dimensional representations to medium-dimensional binary codes without sacrificing accuracies. Instead of using conventional single linear or bilinear projections, the proposed method learns a bank of small projections via the max-margin constraint to optimally preserve the intrinsic data similarity. We have systematically evaluated the proposed method on three datasets: Flickr 1M, ILSVR2010 and UCF101, showing competitive retrieval and recognition accuracies compared with state-of-the-art approaches, but with a significantly smaller memory footprint and lower coding complexity.

Mengyang Yu, Li Liu, Ling Shao

Conventional vision algorithms adopt a single type of feature or a simple concatenation of multiple features, which is always represented in a high-dimensional space. In this paper, we propose a novel unsupervised spectral embedding algorithm called Kernelized Multiview Projection (KMP) to better fuse and embed different feature representations. Computing the kernel matrices from different features/views, KMP can encode them with the corresponding weights to achieve a low-dimensional and semantically meaningful subspace where the distribution of each view is sufficiently smooth and discriminative. More crucially, KMP is linear for the reproducing kernel Hilbert space (RKHS) and solves the out-of-sample problem, which allows it to be competent for various practical applications. Extensive experiments on three popular image datasets demonstrate the effectiveness of our multiview embedding algorithm.