Yang Xu

Hang Zhang, Yang Xu, Lei Gong et al.

This paper introduces a new framework for clustering in a distributed network called Distributed Clustering based on Distributional Kernel (K) or KDC that produces the final clusters based on the similarity with respect to the distributions of initial clusters, as measured by K. It is the only framework that satisfies all three of the following properties. First, KDC guarantees that the combined clustering outcome from all sites is equivalent to the clustering outcome of its centralized counterpart from the combined dataset from all sites. Second, the maximum runtime cost of any site in distributed mode is smaller than the runtime cost in centralized mode. Third, it is designed to discover clusters of arbitrary shapes, sizes and densities. To the best of our knowledge, this is the first distributed clustering framework that employs a distributional kernel. The distribution-based clustering leads directly to significantly better clustering outcomes than existing methods of distributed clustering. In addition, we introduce a new clustering algorithm called Kernel Bounded Cluster Cores, which is the best clustering algorithm applied to KDC among existing clustering algorithms. We also show that KDC is a generic framework that enables a quadratic time clustering algorithm to deal with large datasets that would otherwise be impossible.

Zixuan Chen, Lei Shi, Xuandong Liu et al.

Distributed Machine Learning (DML) systems are utilized to enhance the speed of model training in data centers (DCs) and edge nodes. The Parameter Server (PS) communication architecture is commonly employed, but it faces severe long-tail latency caused by many-to-one "incast" traffic patterns, negatively impacting training throughput. To address this challenge, we design the \textbf{L}oss-tolerant \textbf{T}ransmission \textbf{P}rotocol (LTP), which permits partial loss of gradients during synchronization to avoid unneeded retransmission and contributes to faster synchronization per iteration. LTP implements loss-tolerant transmission through \textit{out-of-order transmission} and \textit{out-of-order Acknowledges (ACKs)}. LTP employs \textit{Early Close} to adjust the loss-tolerant threshold based on network conditions and \textit{Bubble Filling} for data correction to maintain training accuracy. LTP is implemented by C++ and integrated into PyTorch. Evaluations on a testbed of 8 worker nodes and one PS node demonstrate that LTP can significantly improve DML training task throughput by up to 30x compared to traditional TCP congestion controls, with no sacrifice to final accuracy.

Kai Ming Ting, Takashi Washio, Ye Zhu et al.

The curse of dimensionality has been studied in different aspects. However, breaking the curse has been elusive. We show for the first time that it is possible to break the curse using the recently introduced Isolation Kernel. We show that only Isolation Kernel performs consistently well in indexed search, spectral & density peaks clustering, SVM classification and t-SNE visualization in both low and high dimensions, compared with distance, Gaussian and linear kernels. This is also supported by our theoretical analyses that Isolation Kernel is the only kernel that has the provable ability to break the curse, compared with existing metric-based Lipschitz continuous kernels.

Le Li, Jianjun Yang, Yang Xu et al.

Nonnegative matrix factorization (NMF) has been successfully applied to many areas for classification and clustering. Commonly-used NMF algorithms mainly target on minimizing the $l_2$ distance or Kullback-Leibler (KL) divergence, which may not be suitable for nonlinear case. In this paper, we propose a new decomposition method by maximizing the correntropy between the original and the product of two low-rank matrices for document clustering. This method also allows us to learn the new basis vectors of the semantic feature space from the data. To our knowledge, we haven't seen any work has been done by maximizing correntropy in NMF to cluster high dimensional document data. Our experiment results show the supremacy of our proposed method over other variants of NMF algorithm on Reuters21578 and TDT2 databasets.

Le Li, Jianjun Yang, Kaili Zhao et al.

Non-negative matrix factorization (NMF) has proved effective in many clustering and classification tasks. The classic ways to measure the errors between the original and the reconstructed matrix are $l_2$ distance or Kullback-Leibler (KL) divergence. However, nonlinear cases are not properly handled when we use these error measures. As a consequence, alternative measures based on nonlinear kernels, such as correntropy, are proposed. However, the current correntropy-based NMF only targets on the low-level features without considering the intrinsic geometrical distribution of data. In this paper, we propose a new NMF algorithm that preserves local invariance by adding graph regularization into the process of max-correntropy-based matrix factorization. Meanwhile, each feature can learn corresponding kernel from the data. The experiment results of Caltech101 and Caltech256 show the benefits of such combination against other NMF algorithms for the unsupervised image clustering.