Exploring Implicit and Explicit Geometrical Structure of Data for Deep Embedded Clustering
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Exploring Implicit and Explicit Geometrical Structure of Data for Deep Embedded Clustering Xiaofei Zhu1
· Khoi Duy Do2 · Jiafeng Guo3 · Jun Xu4 · Stefan Dietze5
Accepted: 9 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Clustering is an essential data analysis technique and has been studied extensively over the last decades. Previous studies have shown that data representation and data structure information are two critical factors for improving clustering performance, and it forms two important lines of research. The first line of research attempts to learn representative features, especially utilizing the deep neural networks, for handling clustering problems. The second concerns exploiting the geometric structure information within data for clustering. Although both of them have achieved promising performance in lots of clustering tasks, few efforts have been dedicated to combine them in a unified deep clustering framework, which is the research gap we aim to bridge in this work. In this paper, we propose a novel approach, Manifold regularized Deep Embedded Clustering (MDEC), to deal with the aforementioned challenge. It simultaneously models data generating distribution, cluster assignment consistency, as well as geometric structure of data in a unified framework. The proposed method can be optimized by performing mini-batch stochastic gradient descent and back-propagation. We evaluate MDEC on three real-world datasets (USPS, REUTERS-10K, and MNIST), where experimental results demonstrate that our model outperforms baseline models and obtains the state-of-the-art performance. Keywords Deep neural networks · Stacked autoencoder · Manifold constraint · Clustering
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Xiaofei Zhu [email protected]
1
College of Computer Science and Engineering, Chongqing University of Technology, Chongqing 400054, China
2
L3S Research Center, Leibniz University of Hannover, 30167 Hannover, Germany
3
Institute of Computing Technology, Chinese Academy of Science, Beijing 100190, China
4
School of Information, Renmin University of China, Beijing 100872, China
5
Knowledge Technologies for the Social Sciences, Leibniz Institute for the Social Sciences, 50667 Cologne, Germany
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X. Zhu et al.
1 Introduction Clustering has attracted much attention from a variety of communities, especially in scenarios where data is easily accessible and effective data analysis techniques are critical in real applications. Conventional clustering methods, such as k-means [3,13], Gaussian mixture models (GMM) [5] , and spectral clustering [27,35], aim at grouping similar patterns based on hand-crafted features. However, when the dimensionality of data is high, these methods would lead to unsatisfactory results. To tackle this issue, a number of dimensionality reduction methods have been proposed, such as Principle Component Analysis (PCA) and Latent Semantic Indexing (LSI) [7]. One shortcoming of these methods is that the reduced representation might be ineffective due to their shallow learning fra
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