Recently, nonnegative matrix factorization (NMF) has been widely adopted for community detection, because of its better interpretability. However, the existing NMF-based methods have the following three problems: 1) they directly transform the original network into community membership space, so it is difficult for them to capture the hierarchical information; 2) they often only pay attention to the topology of the network and ignore its node attributes; 3) it is hard for them to learn the global structure information necessary for community detection. Therefore, we propose a new community detection algorithm, named Contrastive Deep Nonnegative Matrix Factorization (CDNMF). Firstly, we deepen NMF to strengthen its capacity for information extraction. Subsequently, inspired by contrastive learning, our algorithm creatively constructs network topology and node attributes as two contrasting views. Furthermore, we utilize a debiased negative sampling layer and learn node similarity at the community level, thereby enhancing the suitability of our model for community detection. We conduct experiments on three public real graph datasets and the proposed model has achieved better results than state-of-the-art methods. Code available at https://github.com/6lyc/CDNMF.git.
We propose a fast non-gradient-based method of rank-1 non-negative matrix factorization (NMF) for missing data, called A1GM, that minimizes the KL divergence from an input matrix to the reconstructed rank-1 matrix. Our method is based on our new finding of an analytical closed-formula of the best rank-1 non-negative multiple matrix factorization (NMMF), a variety of NMF. NMMF is known to exactly solve NMF for missing data if positions of missing values satisfy a certain condition, and A1GM transforms a given matrix so that the analytical solution to NMMF can be applied. We empirically show that A1GM is more efficient than a gradient method with competitive reconstruction errors.
Deep convolutional neural networks (CNNs) with a large number of parameters require intensive computational resources, and thus are hard to be deployed in resource-constrained platforms. Decomposition-based methods, therefore, have been utilized to compress CNNs in recent years. However, since the compression factor and performance are negatively correlated, the state-of-the-art works either suffer from severe performance degradation or have relatively low compression factors. To overcome this problem, we propose to compress CNNs and alleviate performance degradation via joint matrix decomposition, which is different from existing works that compressed layers separately. The idea is inspired by the fact that there are lots of repeated modules in CNNs. By projecting weights with the same structures into the same subspace, networks can be jointly compressed with larger ranks. In particular, three joint matrix decomposition schemes are developed, and the corresponding optimization approaches based on Singular Value Decomposition are proposed. Extensive experiments are conducted across three challenging compact CNNs for different benchmark data sets to demonstrate the superior performance of our proposed algorithms. As a result, our methods can compress the size of ResNet-34 by 22X with slighter accuracy degradation compared with several state-of-the-art methods.
In this paper, we tackle two important problems in low-rank learning, which are partial singular value decomposition and numerical rank estimation of huge matrices. By using the concepts of Krylov subspaces such as Golub-Kahan bidiagonalization (GK-bidiagonalization) as well as Ritz vectors, we propose two methods for solving these problems in a fast and accurate way. Our experiments show the advantages of the proposed methods compared to the traditional and randomized singular value decomposition methods. The proposed methods are appropriate for applications involving huge matrices where the accuracy of the desired singular values and also all of their corresponding singular vectors are essential. As a real application, we evaluate the performance of our methods on the problem of Riemannian similarity learning between two various image datasets of MNIST and USPS.
Parameter servers (PSs) facilitate the implementation of distributed training for large machine learning tasks. In this paper, we argue that existing PSs are inefficient for tasks that exhibit non-uniform parameter access; their performance may even fall behind that of single node baselines. We identify two major sources of such non-uniform access: skew and sampling. Existing PSs are ill-suited for managing skew because they uniformly apply the same parameter management technique to all parameters. They are inefficient for sampling because the PS is oblivious to the associated randomized accesses and cannot exploit locality. To overcome these performance limitations, we introduce NuPS, a novel PS architecture that (i) integrates multiple management techniques and employs a suitable technique for each parameter and (ii) supports sampling directly via suitable sampling primitives and sampling schemes that allow for a controlled quality--efficiency trade-off. In our experimental study, NuPS outperformed existing PSs by up to one order of magnitude and provided up to linear scalability across multiple machine learning tasks.
This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems. We also provide examples from machine learning, including principal component analysis, kernel supervised principal component analysis, and Fisher discriminant analysis, which result in eigenvalue and generalized eigenvalue problems. Finally, we introduce the solutions to both eigenvalue and generalized eigenvalue problems.
While several matrix factorization (MF) and tensor factorization (TF) models have been proposed for knowledge base (KB) inference, they have rarely been compared across various datasets. Is there a single model that performs well across datasets? If not, what characteristics of a dataset determine the performance of MF and TF models? Is there a joint TF+MF model that performs robustly on all datasets? We perform an extensive evaluation to compare popular KB inference models across popular datasets in the literature. In addition to answering the questions above, we remove a limitation in the standard evaluation protocol for MF models, propose an extension to MF models so that they can better handle out-of-vocabulary (OOV) entity pairs, and develop a novel combination of TF and MF models. We also analyze and explain the results based on models and dataset characteristics. Our best model is robust, and obtains strong results across all datasets.