Non-Exhaustive, Overlapping Co-Clustering: An Extended Analysis
Sungkyunkwan University（成均馆大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
Joyce Jiyoung Whang, Inderjit S. Dhillon
发表信息：
"Non-Exhaustive, Overlapping Co-Clustering", Proceedings of the 26th ACM Conference on Information and Knowledge Management (CIKM), pages 2367-2370, November 2017
The goal of co-clustering is to simultaneously identify a clustering of rows as well as columns of a two dimensional data matrix. A number of co-clustering techniques have been proposed including information-theoretic co-clustering and the minimum sum-squared residue co-clustering method. However, most existing co-clustering algorithms are designed to find pairwise disjoint and exhaustive co-clusters while many real-world datasets contain not only a large overlap between co-clusters but also outliers which should not belong to any co-cluster. In this paper, we formulate the problem of Non-Exhaustive, Overlapping Co-Clustering where both of the row and column clusters are allowed to overlap with each other and outliers for each dimension of the data matrix are not assigned to any cluster. To solve this problem, we propose intuitive objective functions, and develop an an efficient iterative algorithm which we call the NEO-CC algorithm. We theoretically show that the NEO-CC algorithm monotonically decreases the proposed objective functions. Experimental results show that the NEO-CC algorithm is able to effectively capture the underlying co-clustering structure of real-world data, and thus outperforms state-of-the-art clustering and co-clustering methods. This manuscript includes an extended analysis of [21].
Air Force Research Laboratory（空军研究实验室）；University of Pennsylvania（宾夕法尼亚大学）；Texas A&M University（德克萨斯A&M大学）
We examine overlapping clustering schemes with functorial constraints, in the spirit of Carlsson--Memoli. This avoids issues arising from the chaining required by partition-based methods. Our principal result shows that any clustering functor is naturally constrained to refine single-linkage clusters and be refined by maximal-linkage clusters. We work in the context of metric spaces with non-expansive maps, which is appropriate for modeling data processing which does not increase information content.
Larodec, ISG University of Tunis（突尼斯ISG大学Larodec）；Ceremade, Université Paris-Dauphine（巴黎第九大学Ceremade）
Producing overlapping schemes is a major issue in clustering. Recent proposed overlapping methods relies on the search of an optimal covering and are based on different metrics, such as Euclidean distance and I-Divergence, used to measure closeness between observations. In this paper, we propose the use of another measure for overlapping clustering based on a kernel similarity metric .We also estimate the number of overlapped clusters using the Gram matrix. Experiments on both Iris and EachMovie datasets show the correctness of the estimation of number of clusters and show that measure based o…
Purdue University（普渡大学）；Sungkyunkwan University（成均馆大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
Clustering is one of the most fundamental and important tasks in data mining. Traditional clustering algorithms, such as K-means, assign every data point to exactly one cluster. However, in real-world datasets, the clusters may overlap with each other. Furthermore, often, there are outliers that should not belong to any cluster. We recently proposed the NEO-K-Means (Non-Exhaustive, Overlapping K-Means) objective as a way to address both issues in an integrated fashion. Optimizing this discrete objective is NP-hard, and even though there is a convex relaxation of the objective, straightforward …
Clustering is one of the most universal approaches for understanding complex data. A pivotal aspect of clustering analysis is quantitatively comparing clusterings; clustering comparison is the basis for many tasks such as clustering evaluation, consensus clustering, and tracking the temporal evolution of clusters. In particular, the extrinsic evaluation of clustering methods requires comparing the uncovered clusterings to planted clusterings or known metadata. Yet, as we demonstrate, existing clustering comparison measures have critical biases which undermine their usefulness, and no measure a…
In a standard cluster analysis, such as k-means, in addition to clusters locations and distances between them, it's important to know if they are connected or well separated from each other. The main focus of this paper is discovering the relations between the resulting clusters. We propose a new method which is based on pairwise overlapping k-means clustering, that in addition to means of clusters provides the graph structure of their relations. The proposed method has a set of parameters that can be tuned in order to control the sensitivity of the model and the desired relative size of the p…
People belong to multiple communities, words belong to multiple topics, and books cover multiple genres; overlapping clusters are commonplace. Many existing overlapping clustering methods model each person (or word, or book) as a non-negative weighted combination of "exemplars" who belong solely to one community, with some small noise. Geometrically, each person is a point on a cone whose corners are these exemplars. This basic form encompasses the widely used Mixed Membership Stochastic Blockmodel of networks (Airoldi et al., 2008) and its degree-corrected variants (Jin et al., 2017), as well…
Air Force Research Laboratory（空军研究实验室）；University of Pennsylvania（宾夕法尼亚大学）；Texas A&M University（得克萨斯农工大学）
This work draws inspiration from three important sources of research on dissimilarity-based clustering and intertwines those three threads into a consistent principled functorial theory of clustering. Those three are the overlapping clustering of Jardine and Sibson, the functorial approach of Carlsson and Mémoli to partition-based clustering, and the Isbell/Dress school's study of injective envelopes. Carlsson and Mémoli introduce the idea of viewing clustering methods as functors from a category of metric spaces to a category of clusters, with functoriality subsuming many desirable properties…
School of Microelectronics and Communication Engineering, Chongqing University（重庆大学微电子与通信工程学院）
The challenge of imbalanced learning lies not only in class imbalance problem, but also in the class overlapping problem which is complex. However, most of the existing algorithms mainly focus on the former. The limitation prevents the existing methods from breaking through. To address this limitation, this paper proposes an ensemble learning algorithm based on dual clustering and stage-wise hybrid sampling (DCSHS). The DCSHS has three parts. Firstly, we design a projection clustering combination framework (PCC) guided by Davies-Bouldin clustering effectiveness index (DBI), which is used to ob…
In the past few years co-clustering has emerged as an important data mining tool for two way data analysis. Co-clustering is more advantageous over traditional one dimensional clustering in many ways such as, ability to find highly correlated sub-groups of rows and columns. However, one of the overlooked benefits of co-clustering is that, it can be used to extract meaningful knowledge for various other knowledge extraction purposes. For example, building predictive models with high dimensional data and heterogeneous population is a non-trivial task. Co-clusters extracted from such data, which …
Learning a better representation with neural networks is a challenging problem, which was tackled extensively from different prospectives in the past few years. In this work, we focus on learning a representation that could be used for a clustering task and introduce two novel loss components that substantially improve the quality of produced clusters, are simple to apply to an arbitrary model and cost function, and do not require a complicated training procedure. We evaluate them on two most common types of models, Recurrent Neural Networks and Convolutional Neural Networks, showing that the …
University of Maryland, College Park（马里兰大学帕克分校）；Johns Hopkins University（约翰斯·霍普金斯大学）；University of Michigan, Ann Arbor（密歇根大学安娜堡分校）
We consider the problem of estimating overlapping community memberships in a network, where each node can belong to multiple communities. More than a few communities per node are difficult to both estimate and interpret, so we focus on sparse node membership vectors. Our algorithm is based on sparse principal subspace estimation with iterative thresholding. The method is computationally efficient, with a computational cost equivalent to estimating the leading eigenvectors of the adjacency matrix, and does not require an additional clustering step, unlike spectral clustering methods. We show th…
Clustering consists of grouping together samples giving their similar properties. The problem of modeling simultaneously groups of samples and features is known as Co-Clustering. This paper introduces ROCCO - a Robust Continuous Co-Clustering algorithm. ROCCO is a scalable, hyperparameter-free, easy and ready to use algorithm to address Co-Clustering problems in practice over massive cross-domain datasets. It operates by learning a graph-based two-sided representation of the input matrix. The underlying proposed optimization problem is non-convex, which assures a flexible pool of solutions. Mo…
LARODEC（拉罗德克实验室）；Institut Supérieur de Gestion de Tunis（突尼斯高等管理学院）；Université de Tunis（突尼斯大学）
Overlapping clustering problem is an important learning issue in which clusters are not mutually exclusive and each object may belongs simultaneously to several clusters. This paper presents a kernel based method that produces overlapping clusters on a high feature space using mercer kernel techniques to improve separability of input patterns. The proposed method, called OKM-K(Overlapping $k$-means based kernel method), extends OKM (Overlapping $k$-means) method to produce overlapping schemes. Experiments are performed on overlapping dataset and empirical results obtained with OKM-K outperform…
DCSI -- An improved measure of cluster separability based on separation and connectedness
Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Machine Learning（慕尼黑机器学习中心）；Institute for Medical Information Processing, Biometry, and Epidemiology（医学信息处理、生物统计学与流行病学研究所）
Identifying mobility behaviors in rich trajectory data is of great economic and social interest to various applications including urban planning, marketing and intelligence. Existing work on trajectory clustering often relies on similarity measurements that utilize raw spatial and/or temporal information of trajectories. These measures are incapable of identifying similar moving behaviors that exhibit varying spatio-temporal scales of movement. In addition, the expense of labeling massive trajectory data is a barrier to supervised learning models. To address these challenges, we propose an uns…
Scripps Institution of Oceanography, UCSD（斯克里普斯海洋研究所，加州大学圣迭戈分校）；Naval Undersea Warfare Center Newport（纽波特海军水下作战中心）
Deep clustering was applied to unlabeled, automatically detected signals in a coral reef soundscape to distinguish fish pulse calls from segments of whale song. Deep embedded clustering (DEC) learned latent features and formed classification clusters using fixed-length power spectrograms of the signals. Handpicked spectral and temporal features were also extracted and clustered with Gaussian mixture models (GMM) and conventional clustering. DEC, GMM, and conventional clustering were tested on simulated datasets of fish pulse calls (fish) and whale song units (whale) with randomized bandwidth, …
Central China Normal University（华中师范大学）；Kharkiv National University of Radio Electronics（哈尔科夫国立无线电电子大学）
A task of clustering data given in the ordinal scale under conditions of overlapping clusters has been considered. It's proposed to use an approach based on memberhsip and likelihood functions sharing. A number of performed experiments proved effectiveness of the proposed method. The proposed method is characterized by robustness to outliers due to a way of ordering values while constructing membership functions.
Low-Rank Representation (LRR) highly suffers from discarding the locality information of data points in subspace clustering, as it may not incorporate the data structure nonlinearity and the non-uniform distribution of observations over the ambient space. Thus, the information of the observational density is lost by the state-of-art LRR models, as they take a constant number of adjacent neighbors into account. This, as a result, degrades the subspace clustering accuracy in such situations. To cope with deficiency, in this paper, we propose to consider a hypergraph model to facilitate having a …
This paper presents a novel pairwise constraint propagation approach by decomposing the challenging constraint propagation problem into a set of independent semi-supervised learning subproblems which can be solved in quadratic time using label propagation based on k-nearest neighbor graphs. Considering that this time cost is proportional to the number of all possible pairwise constraints, our approach actually provides an efficient solution for exhaustively propagating pairwise constraints throughout the entire dataset. The resulting exhaustive set of propagated pairwise constraints are furthe…
University of Central Florida（中佛罗里达大学）；Purdue University（普渡大学）
Classification and clustering have been studied separately in machine learning and computer vision. Inspired by the recent success of deep learning models in solving various vision problems (e.g., object recognition, semantic segmentation) and the fact that humans serve as the gold standard in assessing clustering algorithms, here, we advocate for a unified treatment of the two problems and suggest that hierarchical frameworks that progressively build complex patterns on top of the simpler ones (e.g., convolutional neural networks) offer a promising solution. We do not dwell much on the learni…
North Carolina A & T State University（北卡罗来纳农工州立大学）；Clark Altanta University（克拉克亚特兰大大学）
In this paper, we proposed a new clustering-based active learning framework, namely Active Learning using a Clustering-based Sampling (ALCS), to address the shortage of labeled data. ALCS employs a density-based clustering approach to explore the cluster structure from the data without requiring exhaustive parameter tuning. A bi-cluster boundary-based sample query procedure is introduced to improve the learning performance for classifying highly overlapped classes. Additionally, we developed an effective diversity exploration strategy to address the redundancy among queried samples. Our experi…
How to characterize imprecision in multi-view clustering?
East China Normal University（华东师范大学）；Institute de Recherche en Informatique et Systèmes Aléatoires（计算机与随机系统研究所）；University of Rennes 1（雷恩第一大学）；Hainan University（海南大学）；Nantong University（南通大学）
Discovering Operational Patterns Using Image-Based Convolutional Clustering and Composite Evaluation: A Case Study in Foundry Melting Processes
SDU Center for Energy Informatics, The Maersk Mc-Kinney Moller Institute, Faculty of Engineering, University of Southern Denmark（南丹麦大学工程学院马士基麦克-金尼·穆勒研究所SDU能源信息学中心）
School of Electronic Engineering, Xidian University（西安电子科技大学电子工程学院）
Bi-clustering refers to the task of finding sub-matrices (indexed by a group of columns and a group of rows) within a matrix of data such that the elements of each sub-matrix (data and features) are related in a particular way, for instance, that they are similar with respect to some metric. In this paper, after analyzing the well-known Cheng and Church (CC) bi-clustering algorithm which has been proved to be an effective tool for mining co-expressed genes. However, Cheng and Church bi-clustering algorithm and summarizing its limitations (such as interference of random numbers in the greedy st…
In high dimensional regression, feature clustering by their effects on outcomes is often as important as feature selection. For that purpose, clustered Lasso and octagonal shrinkage and clustering algorithm for regression (OSCAR) are used to make feature groups automatically by pairwise $L_1$ norm and pairwise $L_\infty$ norm, respectively. This paper proposes efficient path algorithms for clustered Lasso and OSCAR to construct solution paths with respect to their regularization parameters. Despite too many terms in exhaustive pairwise regularization, their computational costs are reduced by u…
Biclustering involves the simultaneous clustering of objects and their attributes, thus defining local two-way clustering models. Recently, efficient algorithms were conceived to enumerate all biclusters in real-valued datasets. In this case, the solution composes a complete set of maximal and non-redundant biclusters. However, the ability to enumerate biclusters revealed a challenging scenario: in noisy datasets, each true bicluster may become highly fragmented and with a high degree of overlapping. It prevents a direct analysis of the obtained results. To revert the fragmentation, we propose…
Louisiana State University（路易斯安那州立大学）；Los Alamos National Lab（洛斯阿拉莫斯国家实验室）
We present a new clustering algorithm that is based on searching for natural gaps in the components of the lowest energy eigenvectors of the Laplacian of a graph. In comparing the performance of the proposed method with a set of other popular methods (KMEANS, spectral-KMEANS, and an agglomerative method) in the context of the Lancichinetti-Fortunato-Radicchi (LFR) Benchmark for undirected weighted overlapping networks, we find that the new method outperforms the other spectral methods considered in certain parameter regimes. Finally, in an application to climate data involving one of the most …
Clustering is a crucial component of many data mining systems involving the analysis and exploration of various data. Data diversity calls for clustering algorithms to be accurate while providing stable (i.e., deterministic and robust) results on arbitrary input networks. Moreover, modern systems often operate with large datasets, which implicitly constrains the complexity of the clustering algorithm. Existing clustering techniques are only partially stable, however, as they guarantee either determinism or robustness. To address this issue, we introduce DAOC, a Deterministic and Agglomerative …
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；University of Chinese Academy of Sciences（中国科学院大学）
Seeding then expanding is a commonly used scheme to discover overlapping communities in a network. Most seeding methods are either too complex to scale to large networks or too simple to select high-quality seeds, and the non-principled functions used by most expanding methods lead to poor performance when applied to diverse networks. This paper proposes a new method that transforms a network into a corpus where each edge is treated as a document, and all nodes of the network are treated as terms of the corpus. An effective seeding method is also proposed that selects seeds as a training set, …
We study approximation algorithms for the socially fair $(\ell_p, k)$-clustering problem with $m$ groups, whose special cases include the socially fair $k$-median ($p=1$) and socially fair $k$-means ($p=2$) problems. We present (1) a polynomial-time $(5+2\sqrt{6})^p$-approximation with at most $k+m$ centers (2) a $(5+2\sqrt{6}+ε)^p$-approximation with $k$ centers in time $n^{2^{O(p)}\cdot m^2}$, and (3) a $(15+6\sqrt{6})^p$ approximation with $k$ centers in time $k^{m}\cdot\text{poly}(n)$. The first result is obtained via a refinement of the iterative rounding method using a sequence of linear…
Sorted $L_1$ penalization estimator (SLOPE) is a regularization technique for sorted absolute coefficients in high-dimensional regression. By arbitrarily setting its regularization weights $λ$ under the monotonicity constraint, SLOPE can have various feature selection and clustering properties. On weight tuning, the selected features and their clusters are very sensitive to the tuning parameters. Moreover, the exhaustive tracking of their changes is difficult using grid search methods. This study presents a solution path algorithm that provides the complete and exact path of solutions for SLOP…
Federated Incomplete Multi-View Clustering with Heterogeneous Graph Neural Networks
Guangdong University of Foreign Studies（广东外语外贸大学）；School of Engineering, Westlake University（西湖大学工程学院）；East China University of Science and Technology（华东理工大学）
University of Hyderabad（海得拉巴大学）；University of Delhi（德里大学）；Mahindra University（马恒达大学）
Recommender systems based on collaborative filtering play a vital role in many E-commerce applications as they guide the user in finding their items of interest based on the user's past transactions and feedback of other similar customers. Data Sparsity is one of the major drawbacks with collaborative filtering technique arising due to the less number of transactions and feedback data. In order to reduce the sparsity problem, techniques called transfer learning/cross-domain recommendation has emerged. In transfer learning methods, the data from other dense domain(s) (source) is considered in o…
