Biclustering is the task of simultaneously clustering the rows and columns of the data matrix into different subgroups such that the rows and columns within a subgroup exhibit similar patterns. In this paper, we consider the case of producing block-diagonal biclusters. We provide a new formulation of the biclustering problem based on the idea of minimizing the empirical clustering risk. We develop and prove a consistency result with respect to the empirical clustering risk. Since the optimization problem is combinatorial in nature, finding the global minimum is computationally intractable. In light of this fact, we propose a simple and novel algorithm that finds a local minimum by alternating the use of an adapted version of the k-means clustering algorithm between columns and rows. We evaluate and compare the performance of our algorithm to other related biclustering methods on both simulated data and real-world gene expression data sets. The results demonstrate that our algorithm is able to detect meaningful structures in the data and outperform other competing biclustering methods in various settings and situations.
Learning the "blocking" structure is a central challenge for high dimensional data (e.g., gene expression data). Recently, a sparse singular value decomposition (SVD) has been used as a biclustering tool to achieve this goal. However, this model ignores the structural information between variables (e.g., gene interaction graph). Although typical graph-regularized norm can incorporate such prior graph information to get accurate discovery and better interpretability, it fails to consider the opposite effect of variables with different signs. Motivated by the development of sparse coding and gra…
University of Pennsylvania（宾夕法尼亚大学）；AGH University of Science and Technology（AGH科技大学）；Ben-Gurion University（本-古里安大学）；Arkansas State University（阿肯色州立大学）
In this paper a novel biclustering algorithm based on artificial intelligence (AI) is introduced. The method called EBIC aims to detect biologically meaningful, order-preserving patterns in complex data. The proposed algorithm is probably the first one capable of discovering with accuracy exceeding 50% multiple complex patterns in real gene expression datasets. It is also one of the very few biclustering methods designed for parallel environments with multiple graphics processing units (GPUs). We demonstrate that EBIC outperforms state-of-the-art biclustering methods, in terms of recovery and …
Silesian University of Technology（西里西亚工业大学）；Pablo de Olavide University（巴勃罗·德·奥拉维德大学）；Universidad Nacional de San Agustín（圣奥古斯丁国立大学）
Biclustering is a powerful approach to search for patterns in data, as it can be driven by a function that measures the quality of diverse types of patterns of interest. However, due to its computational complexity, the exploration of the search space is usually guided by an algorithmic strategy, sometimes introducing random factors that simplify the computational cost (e.g. greedy search or evolutionary computation). Shifting patterns are specially interesting as they account constant fluctuations in data, i.e. they capture situations in which all the values in the pattern move up or down for…
NVE: A Separability and Coverage-Aware Internal Validation Metric for Biclustering
Robert Bosch Center for Cyber-Physical Systems (RBCCPS)（罗伯特博世网络物理系统中心（RBCCPS））；Indian Institute of Science（印度科学学院）；Cisco India（思科印度公司）；University of Melbourne（墨尔本大学）；Centre for Infrastructure, Sustainable Transportation and Urban Planning (CiSTUP)（基础设施、可持续交通与城市规划中心（CiSTUP））
To understand complex biological systems, the research community has produced huge corpus of gene expression data. A large number of clustering approaches have been proposed for the analysis of gene expression data. However, extracting important biological knowledge is still harder. To address this task, clustering techniques are used. In this paper, hybrid Hierarchical k-Means algorithm is used for clustering and biclustering gene expression data is used. To discover both local and global clustering structure biclustering and clustering algorithms are utilized. A validation technique, Figure …
Lehigh University（里海大学）；University of Coimbra（科英布拉大学）
In the application of data clustering to human-centric decision-making systems, such as loan applications and advertisement recommendations, the clustering outcome might discriminate against people across different demographic groups, leading to unfairness. A natural conflict occurs between the cost of clustering (in terms of distance to cluster centers) and the balance representation of all demographic groups across the clusters, leading to a bi-objective optimization problem that is nonconvex and nonsmooth. To determine the complete trade-off between these two competing goals, we design a no…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution parameters are computed using an alternate coordinate minimization. However, the convergence properties of this algorithm remain unclear. In this paper, we show how, by adding an appropriate penalization term, we can guarantee convergence to a critical point, while keeping a closed form update at each step. A convergence rate estimate can also be derived based on…
This paper deals with unsupervised clustering with feature selection. The problem is to estimate both labels and a sparse projection matrix of weights. To address this combinatorial non-convex problem maintaining a strict control on the sparsity of the matrix of weights, we propose an alternating minimization of the Frobenius norm criterion. We provide a new efficient algorithm named K-sparse which alternates k-means with projection-gradient minimization. The projection-gradient step is a method of splitting type, with exact projection on the $\ell^1$ ball to promote sparsity. The convergence …
In this work we propose a clustering framework based on the paradigm of transform learning. In simple terms the representation from transform learning is used for K-means clustering; however, the problem is not solved in such a naïve piecemeal fashion. The K-means clustering loss is embedded into the transform learning framework and the joint problem is solved using the alternating direction method of multipliers. Results on document clustering show that our proposed approach improves over the state-of-the-art.
National University of Defense Technology（国防科技大学）；Beihang University（北京航空航天大学）；Imperial College London（帝国理工学院）；University of Modena and Reggio Emilia (UNIMORE)（摩德纳-雷焦艾米利亚大学（UNIMORE））
In this paper, we propose a novel solution for non-convex problems of multiple variables, especially for those typically solved by an alternating minimization (AM) strategy that splits the original optimization problem into a set of sub-problems corresponding to each variable, and then iteratively optimize each sub-problem using a fixed updating rule. However, due to the intrinsic non-convexity of the original optimization problem, the optimization can usually be trapped into spurious local minimum even when each sub-problem can be optimally solved at each iteration. Meanwhile, learning-based …
University of Edinburgh（爱丁堡大学）；University of Surrey（萨里大学）；Samsung AI Centre（三星人工智能中心）
We address the problem of simultaneously learning a k-means clustering and deep feature representation from unlabelled data, which is of interest due to the potential of deep k-means to outperform traditional two-step feature extraction and shallow-clustering strategies. We achieve this by developing a gradient-estimator for the non-differentiable k-means objective via the Gumbel-Softmax reparameterisation trick. In contrast to previous attempts at deep clustering, our concrete k-means model can be optimised with respect to the canonical k-means objective and is easily trained end-to-end witho…
Sun Yat-Sen University（中山大学）；University of Science and Technology of China（中国科学技术大学）；Pazhou Lab（琶洲实验室）
This paper aims to solve a distributed learning problem under Byzantine attacks. In the underlying distributed system, a number of unknown but malicious workers (termed as Byzantine workers) can send arbitrary messages to the master and bias the learning process, due to data corruptions, computation errors or malicious attacks. Prior work has considered a total variation (TV) norm-penalized approximation formulation to handle the Byzantine attacks, where the TV norm penalty forces the regular workers' local variables to be close, and meanwhile, tolerates the outliers sent by the Byzantine work…
Mirror Descent-Ascent for mean-field min-max problems
Center for Advanced Intelligence Project, RIKEN（日本东京RIKEN先进智能项目中心）；School of Mathematical and Computer Sciences, Heriot-Watt University（赫里奥特-瓦特大学数学与计算机科学学院）；Maxwell Institute for Mathematical Sciences, Edinburgh, UK（爱丁堡数学科学研究所）；School of Mathematics, University of Edinburgh（爱丁堡大学数学学院）；The Alan Turing Institute（艾伦·图灵研究所）
Sun Yat-sen University（中山大学）；South China Normal University（华南师范大学）
Multi-task learning (MTL) aims to improve the generalization performance of multiple tasks by exploiting the shared factors among them. Various metrics (e.g., F-score, Area Under the ROC Curve) are used to evaluate the performances of MTL methods. Most existing MTL methods try to minimize either the misclassified errors for classification or the mean squared errors for regression. In this paper, we propose a method to directly optimize the evaluation metrics for a large family of MTL problems. The formulation of MTL that directly optimizes evaluation metrics is the combination of two parts: (1…
National University of Singapore（新加坡国立大学）；Peking University（北京大学）；Shanghai Jiao Tong University（上海交通大学）；AI Institute（360人工智能研究院）
Spectral Clustering (SC) is a widely used data clustering method which first learns a low-dimensional embedding $U$ of data by computing the eigenvectors of the normalized Laplacian matrix, and then performs k-means on $U^\top$ to get the final clustering result. The Sparse Spectral Clustering (SSC) method extends SC with a sparse regularization on $UU^\top$ by using the block diagonal structure prior of $UU^\top$ in the ideal case. However, encouraging $UU^\top$ to be sparse leads to a heavily nonconvex problem which is challenging to solve and the work (Lu, Yan, and Lin 2016) proposes a conv…
Laboratory of Physics of the \'Ecole Normale Sup\'erieure, CNRS UMR 8023 \& PSL Research, Sorbonne Universit\'e, 24 rue Lhomond, 75005 Paris, France
Restricted Boltzmann Machines (RBM) are bi-layer neural networks used for the unsupervised learning of model distributions from data. The bipartite architecture of RBM naturally defines an elegant sampling procedure, called Alternating Gibbs Sampling (AGS), where the configurations of the latent-variable layer are sampled conditional to the data-variable layer, and vice versa. We study here the performance of AGS on several analytically tractable models borrowed from statistical mechanics. We show that standard AGS is not more efficient than classical Metropolis-Hastings (MH) sampling of the e…
