Clustering Binary Data by Application of Combinatorial Optimization Heuristics
University of Costa Rica（哥斯达黎加大学）；Costa Rica Institute of Technology（哥斯达黎加理工学院）
Javier Trejos-Zelaya, Luis Eduardo Amaya-Briceño, Alejandra Jiménez-Romero, Alex Murillo-Fernández, Eduardo Piza-Volio, Mario Villalobos-Arias
备注：
9 pages. Submitted to Springer Series "Studies in Classification, Data Analysis, and Knowledge Organization". Presented in Conference of the International Federation of Classification Societies (IFCS), Thessaloniki, August 2019
We study clustering methods for binary data, first defining aggregation criteria that measure the compactness of clusters. Five new and original methods are introduced, using neighborhoods and population behavior combinatorial optimization metaheuristics: first ones are simulated annealing, threshold accepting and tabu search, and the others are a genetic algorithm and ant colony optimization. The methods are implemented, performing the proper calibration of parameters in the case of heuristics, to ensure good results. From a set of 16 data tables generated by a quasi-Monte Carlo experiment, a comparison is performed for one of the aggregations using L1 dissimilarity, with hierarchical clustering, and a version of k-means: partitioning around medoids or PAM. Simulated annealing perform very well, especially compared to classical methods.
Indian Institute of Technology Delhi（德里印度理工学院）；Northwestern University（西北大学）；University of California Santa Barbara（加州大学圣巴巴拉分校）
There has been an increased interest in discovering heuristics for combinatorial problems on graphs through machine learning. While existing techniques have primarily focused on obtaining high-quality solutions, scalability to billion-sized graphs has not been adequately addressed. In addition, the impact of budget-constraint, which is necessary for many practical scenarios, remains to be studied. In this paper, we propose a framework called GCOMB to bridge these gaps. GCOMB trains a Graph Convolutional Network (GCN) using a novel probabilistic greedy mechanism to predict the quality of a node…
University College Dublin（都柏林大学学院）；Indian Statistical Institute（印度统计研究所）
Clustering algorithms have regained momentum with recent popularity of data mining and knowledge discovery approaches. To obtain good clustering in reasonable amount of time, various meta-heuristic approaches and their hybridization, sometimes with K-Means technique, have been employed. A Kalman Filtering based heuristic approach called Heuristic Kalman Algorithm (HKA) has been proposed a few years ago, which may be used for optimizing an objective function in data/feature space. In this paper at first HKA is employed in partitional data clustering. Then an improved approach named HKA-K is pro…
University of Toyama（富山大学）；Institute of Natural Medicine, University of Toyama, Japan（富山大学自然医学研究所）
This paper proposes a new dimensionality reduction algorithm named branching embedding (BE). It converts a dendrogram to a two-dimensional scatter plot, and visualizes the inherent structures of the original high-dimensional data. Since the conversion part is not computationally demanding, the BE algorithm would be beneficial for the case where hierarchical clustering is already performed. Numerical experiments revealed that the outputs of the algorithm moderately preserve the original hierarchical structures.
UC Berkeley（加州大学伯克利分校）；Facebook AI Research（脸书人工智能研究院）
Search-based methods for hard combinatorial optimization are often guided by heuristics. Tuning heuristics in various conditions and situations is often time-consuming. In this paper, we propose NeuRewriter that learns a policy to pick heuristics and rewrite the local components of the current solution to iteratively improve it until convergence. The policy factorizes into a region-picking and a rule-picking component, each parameterized by a neural network trained with actor-critic methods in reinforcement learning. NeuRewriter captures the general structure of combinatorial problems and show…
IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Spectral clustering has shown a superior performance in analyzing the cluster structure. However, its computational complexity limits its application in analyzing large-scale data. To address this problem, many low-rank matrix approximating algorithms are proposed, including the Nystrom method - an approach with proven approximate error bounds. There are several algorithms that provide recipes to construct Nystrom approximations with variable accuracies and computing times. This paper proposes a scalable Nystrom-based clustering algorithm with a new sampling procedure, Centroid Minimum Sum of …
University of the Basque Country（巴斯克大学）；Lehigh University（理海大学）
This paper presents a framework to tackle constrained combinatorial optimization problems using deep Reinforcement Learning (RL). To this end, we extend the Neural Combinatorial Optimization (NCO) theory in order to deal with constraints in its formulation. Notably, we propose defining constrained combinatorial problems as fully observable Constrained Markov Decision Processes (CMDP). In that context, the solution is iteratively constructed based on interactions with the environment. The model, in addition to the reward signal, relies on penalty signals generated from constraint dissatisfactio…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；Zyfra（兹夫特拉）；Criteo AI Lab（Criteo人工智能实验室）
Many traditional algorithms for solving combinatorial optimization problems involve using hand-crafted heuristics that sequentially construct a solution. Such heuristics are designed by domain experts and may often be suboptimal due to the hard nature of the problems. Reinforcement learning (RL) proposes a good alternative to automate the search of these heuristics by training an agent in a supervised or self-supervised manner. In this survey, we explore the recent advancements of applying RL frameworks to hard combinatorial problems. Our survey provides the necessary background for operations…
University of Toronto（多伦多大学）；Fujitsu Laboratories of America, Inc.（美国富士通研究所）
The emergence of specialized optimization hardware such as CMOS annealers and adiabatic quantum computers carries the promise of solving hard combinatorial optimization problems more efficiently in hardware. Recent work has focused on formulating different combinatorial optimization problems as Ising models, the core mathematical abstraction used by a large number of these hardware platforms, and evaluating the performance of these models when solved on specialized hardware. An interesting area of application is data mining, where combinatorial optimization problems underlie many core tasks. I…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）
We propose a Reinforcement Learning based approach to approximately solve the Tree Decomposition (TD) problem. TD is a combinatorial problem, which is central to the analysis of graph minor structure and computational complexity, as well as in the algorithms of probabilistic inference, register allocation, and other practical tasks. Recently, it has been shown that combinatorial problems can be successively solved by learned heuristics. However, the majority of existing works do not address the question of the generalization of learning-based solutions. Our model is based on the graph convolut…
Spectral clustering algorithms typically require a priori selection of input parameters such as the number of clusters, a scaling parameter for the affinity measure, or ranges of these values for parameter tuning. Despite efforts for automating the process of spectral clustering, the task of grouping data in multi-scale and higher dimensional spaces is yet to be explored. This study presents a spectral clustering heuristic algorithm that obviates the need for an input by estimating the parameters from the data itself. Specifically, it introduces the heuristic of iterative eigengap search with …
Georgia Institute of Technology（佐治亚理工学院）；Ant Financial（蚂蚁金融）
The design of good heuristics or approximation algorithms for NP-hard combinatorial optimization problems often requires significant specialized knowledge and trial-and-error. Can we automate this challenging, tedious process, and learn the algorithms instead? In many real-world applications, it is typically the case that the same optimization problem is solved again and again on a regular basis, maintaining the same problem structure but differing in the data. This provides an opportunity for learning heuristic algorithms that exploit the structure of such recurring problems. In this paper, w…
Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）；Institut Català de la Salut（加泰罗尼亚卫生研究所）
In this paper we present a method for the unsupervised clustering of high-dimensional binary data, with a special focus on electronic healthcare records. We present a robust and efficient heuristic to face this problem using tensor decomposition. We present the reasons why this approach is preferable for tasks such as clustering patient records, to more commonly used distance-based methods. We run the algorithm on two datasets of healthcare records, obtaining clinically meaningful results.
We develop a Bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual. We introduce a combinatorial stochastic process known as the negative binomial process (NBP) as an infinite-dimensional prior appropriate for such problems. We show that the NBP is conjugate to the beta process, and we characterize the posterior distribution under the beta-negative binomial process (BNBP) and hierarchical models based on the BNBP (the HBNBP). We study t…
We study a variant of the variational autoencoder model (VAE) with a Gaussian mixture as a prior distribution, with the goal of performing unsupervised clustering through deep generative models. We observe that the known problem of over-regularisation that has been shown to arise in regular VAEs also manifests itself in our model and leads to cluster degeneracy. We show that a heuristic called minimum information constraint that has been shown to mitigate this effect in VAEs can also be applied to improve unsupervised clustering performance with our model. Furthermore we analyse the effect of …
Georgia Tech（佐治亚理工学院）；MPI for Intelligent Systems（马克斯·普朗克智能系统研究所）
We show that the popular k-means clustering algorithm (Lloyd's heuristic), used for a variety of scientific data, can result in outcomes that are unfavorable to subgroups of data (e.g., demographic groups). Such biased clusterings can have deleterious implications for human-centric applications such as resource allocation. We present a fair k-means objective and algorithm to choose cluster centers that provide equitable costs for different groups. The algorithm, Fair-Lloyd, is a modification of Lloyd's heuristic for k-means, inheriting its simplicity, efficiency, and stability. In comparison w…
The constant growth of the e-commerce industry has rendered the problem of product retrieval particularly important. As more enterprises move their activities on the Web, the volume and the diversity of the product-related information increase quickly. These factors make it difficult for the users to identify and compare the features of their desired products. Recent studies proved that the standard similarity metrics cannot effectively identify identical products, since similar titles often refer to different products and vice-versa. Other studies employed external data sources (search engine…
We present a learning-based approach to computing solutions for certain NP-hard problems. Our approach combines deep learning techniques with useful algorithmic elements from classic heuristics. The central component is a graph convolutional network that is trained to estimate the likelihood, for each vertex in a graph, of whether this vertex is part of the optimal solution. The network is designed and trained to synthesize a diverse set of solutions, which enables rapid exploration of the solution space via tree search. The presented approach is evaluated on four canonical NP-hard problems an…
Min-cut clustering, based on minimizing one of two heuristic cost-functions proposed by Shi and Malik, has spawned tremendous research, both analytic and algorithmic, in the graph partitioning and image segmentation communities over the last decade. It is however unclear if these heuristics can be derived from a more general principle facilitating generalization to new problem settings. Motivated by an existing graph partitioning framework, we derive relationships between optimizing relevance information, as defined in the Information Bottleneck method, and the regularized cut in a K-partition…
We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires optimizing over a combinatorial space of program "architectures". We frame this optimization problem as a search in a weighted graph whose paths encode top-down derivations of program syntax. Our key innovation is to view various classes of neural networks as continuous relaxations over the space of programs, which can then be used to complete any partial program. Th…
We consider clustering problems where the goal is to determine an optimal partition of a given point set in Euclidean space in terms of a collection of affine subspaces. While there is vast literature on heuristics for this kind of problem, such approaches are known to be susceptible to poor initializations and getting trapped in bad local optima. We alleviate these issues by introducing a semidefinite relaxation based on Lasserre's method of moments. While a similiar approach is known for classical Euclidean clustering problems, a generalization to our more general subspace scenario is not st…
