Zhaohui Wu

Wenjia Meng, Zonghua Gu, Ming Zhang et al.

With the rapid proliferation of Internet of Things and intelligent edge devices, there is an increasing need for implementing machine learning algorithms, including deep learning, on resource-constrained mobile embedded devices with limited memory and computation power. Typical large Convolutional Neural Networks (CNNs) need large amounts of memory and computational power, and cannot be deployed on embedded devices efficiently. We present Two-Bit Networks (TBNs) for model compression of CNNs with edge weights constrained to (-2, -1, 1, 2), which can be encoded with two bits. Our approach can reduce the memory usage and improve computational efficiency significantly while achieving good performance in terms of classification accuracy, thus representing a reasonable tradeoff between model size and performance.

Zhenfang Hu, Gang Pan, Yueming Wang et al.

Dimensionality reduction, cluster analysis, and sparse representation are basic components in machine learning. However, their relationships have not yet been fully investigated. In this paper, we find that the spectral graph theory underlies a series of these elementary methods and can unify them into a complete framework. The methods include PCA, K-means, Laplacian eigenmap (LE), ratio cut (Rcut), and a new sparse representation method developed by us, called spectral sparse representation (SSR). Further, extended relations to conventional over-complete sparse representations (e.g., method of optimal directions, KSVD), manifold learning (e.g., kernel PCA, multidimensional scaling, Isomap, locally linear embedding), and subspace clustering (e.g., sparse subspace clustering, low-rank representation) are incorporated. We show that, under an ideal condition from the spectral graph theory, PCA, K-means, LE, and Rcut are unified together. And when the condition is relaxed, the unification evolves to SSR, which lies in the intermediate between PCA/LE and K-mean/Rcut. An efficient algorithm, NSCrt, is developed to solve the sparse codes of SSR. SSR combines merits of both sides: its sparse codes reduce dimensionality of data meanwhile revealing cluster structure. For its inherent relation to cluster analysis, the codes of SSR can be directly used for clustering. Scut, a clustering approach derived from SSR reaches the state-of-the-art performance in the spectral clustering family. The one-shot solution obtained by Scut is comparable to the optimal result of K-means that are run many times. Experiments on various data sets demonstrate the properties and strengths of SSR, NSCrt, and Scut.

Zhenfang Hu, Gang Pan, Yueming Wang et al.

Sparse principal component analysis (sparse PCA) aims at finding a sparse basis to improve the interpretability over the dense basis of PCA, meanwhile the sparse basis should cover the data subspace as much as possible. In contrast to most of existing work which deal with the problem by adding some sparsity penalties on various objectives of PCA, in this paper, we propose a new method SPCArt, whose motivation is to find a rotation matrix and a sparse basis such that the sparse basis approximates the basis of PCA after the rotation. The algorithm of SPCArt consists of three alternating steps: rotate PCA basis, truncate small entries, and update the rotation matrix. Its performance bounds are also given. SPCArt is efficient, with each iteration scaling linearly with the data dimension. It is easy to choose parameters in SPCArt, due to its explicit physical explanations. Besides, we give a unified view to several existing sparse PCA methods and discuss the connection with SPCArt. Some ideas in SPCArt are extended to GPower, a popular sparse PCA algorithm, to overcome its drawback. Experimental results demonstrate that SPCArt achieves the state-of-the-art performance. It also achieves a good tradeoff among various criteria, including sparsity, explained variance, orthogonality, balance of sparsity among loadings, and computational speed.