**L1-Norm Kernel PCA**

We present the first model and algorithm for L1-norm kernel PCA. While L2-norm kernel PCA has been widely studied, there has been no work on L1-norm kernel PCA. For this non-convex and non-smooth problem, we offer geometric understandings through reformulations and present an efficient algorithm where the kernel trick is applicable. To attest the efficiency of the algorithm, we provide a convergence analysis including linear rate of convergence. Moreover, we prove that the output of our algorithm is a local optimal solution to the L1-norm kernel PCA problem. We also numerically show its robustness when extracting principal components in the presence of influential outliers, as well as its runtime comparability to L2-norm kernel PCA. Lastly, we introduce its application to outlier detection and show that the L1-norm kernel PCA based model outperforms especially for high dimensional data. … **swCaffe**

This paper reports our efforts on swCaffe, a highly efficient parallel framework for accelerating deep neural networks (DNNs) training on Sunway TaihuLight, the current fastest supercomputer in the world that adopts a unique many-core heterogeneous architecture, with 40,960 SW26010 processors connected through a customized communication network. First, we point out some insightful principles to fully exploit the performance of the innovative many-core architecture. Second, we propose a set of optimization strategies for redesigning a variety of neural network layers based on Caffe. Third, we put forward a topology-aware parameter synchronization scheme to scale the synchronous Stochastic Gradient Descent (SGD) method to multiple processors efficiently. We evaluate our framework by training a variety of widely used neural networks with the ImageNet dataset. On a single node, swCaffe can achieve 23\%\~{}119\% overall performance compared with Caffe running on K40m GPU. As compared with the Caffe on CPU, swCaffe runs 3.04\~{}7.84x faster on all the networks. Finally, we present the scalability of swCaffe for the training of ResNet-50 and AlexNet on the scale of 1024 nodes. … **K-Indicators**

The K-means algorithm is arguably the most popular data clustering method, commonly applied to processed datasets in some ‘feature spaces’, as is in spectral clustering. Highly sensitive to initializations, however, K-means encounters a scalability bottleneck with respect to the number of clusters K as this number grows in big data applications. In this work, we promote a closely related model called K-indicators model and construct an efficient, semi-convex-relaxation algorithm that requires no randomized initializations. We present extensive empirical results to show advantages of the new algorithm when K is large. In particular, using the new algorithm to start the K-means algorithm, without any replication, can significantly outperform the standard K-means with a large number of currently state-of-the-art random replications. … **Outline Generation**

In this paper, we introduce and tackle the Outline Generation (OG) task, which aims to unveil the inherent content structure of a multi-paragraph document by identifying its potential sections and generating the corresponding section headings. Without loss of generality, the OG task can be viewed as a novel structured summarization task. To generate a sound outline, an ideal OG model should be able to capture three levels of coherence, namely the coherence between context paragraphs, that between a section and its heading, and that between context headings. The first one is the foundation for section identification, while the latter two are critical for consistent heading generation. In this work, we formulate the OG task as a hierarchical structured prediction problem, i.e., to first predict a sequence of section boundaries and then a sequence of section headings accordingly. We propose a novel hierarchical structured neural generation model, named HiStGen, for the task. Our model attempts to capture the three-level coherence via the following ways. First, we introduce a Markov paragraph dependency mechanism between context paragraphs for section identification. Second, we employ a section-aware attention mechanism to ensure the semantic coherence between a section and its heading. Finally, we leverage a Markov heading dependency mechanism and a review mechanism between context headings to improve the consistency and eliminate duplication between section headings. Besides, we build a novel WIKIOG dataset, a public collection which consists of over 1.75 million document-outline pairs for research on the OG task. Experimental results on our benchmark dataset demonstrate that our model can significantly outperform several state-of-the-art sequential generation models for the OG task. …

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Feb 2021

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