Given a point set S and an unknown metric d on S, we study the problem of efficiently partitioning S into k clusters while querying few distances between the points. In our model we assume that we have access to one versus all queries that given a point s 2 S return the distances between s and all other points. We show that given a natural assumption about the structure of the instance, we can efficiently find an accurate clustering using only O(k) distance queries. We use our algorithm to cluster proteins by sequence similarity. This setting nicely fits our model because we can use a fast sequence database search program to query a sequence against an entire dataset. We conduct an empirical study that shows that even though we query a small fraction of the distances between the points, we produce clusterings that are close to a desired clustering given by manual classification.
Universidade Federal de Pernambuco（伯南布哥联邦大学）；Centro de Informática（信息中心）
The clustering methods have been used in a variety of fields such as image processing, data mining, pattern recognition, and statistical analysis. Generally, the clustering algorithms consider all variables equally relevant or not correlated for the clustering task. Nevertheless, in real situations, some variables can be correlated or may be more or less relevant or even irrelevant for this task. This paper proposes partitioning fuzzy clustering algorithms based on Euclidean, City-block and Mahalanobis distances and entropy regularization. These methods are an iterative three steps algorithms …
Clustering is a fundamental problem in machine learning where distance-based approaches have dominated the field for many decades. This set of problems is often tackled by partitioning the data into K clusters where the number of clusters is chosen apriori. While significant progress has been made on these lines over the years, it is well established that as the number of clusters or dimensions increase, current approaches dwell in local minima resulting in suboptimal solutions. In this work, we propose a new set of distance threshold methods called Theta-based Algorithms (ThetA). Via experime…
Learning Unified Distance Metric for Heterogeneous Attribute Data Clustering
School of Computer Science and Technology（计算机科学与技术学院）；Guangdong University of Technology（广东工业大学）；Key Laboratory of Multimedia Trusted Perception and Efficient Computing, Ministry of Education of China（教育部多媒体可信感知与高效计算重点实验室）；Xiamen University（厦门大学）；Department of Computer Science（计算机科学系）
Unsupervised clustering algorithm can effectively reduce the dimension of high-dimensional unlabeled data, thus reducing the time and space complexity of data processing. However, the traditional clustering algorithm needs to set the upper bound of the number of categories in advance, and the deep learning clustering algorithm will fall into the problem of local optimum. In order to solve these problems, a probabilistic spatial clustering algorithm based on the Self Discipline Learning(SDL) model is proposed. The algorithm is based on the Gaussian probability distribution of the probability sp…
Clustering is spotting pattern in a group of objects and resultantly grouping the similar objects together. Objects have attributes which are not always numerical, sometimes attributes have domain or categories to which they could belong to. Such data is called categorical data. To group categorical data many clustering algorithms are used, among which k- modes algorithm has so far given the most significant results. Nevertheless, there is still a lot which could be improved. Algorithms like k-means, fuzzy-c-means or hierarchical have given far better accuracies with numerical data. In this pa…
Getting a robust time-series clustering with best choice of distance measure and appropriate representation is always a challenge. We propose a novel mechanism to identify the clusters combining learned compact representation of time-series, Auto Encoded Compact Sequence (AECS) and hierarchical clustering approach. Proposed algorithm aims to address the large computing time issue of hierarchical clustering as learned latent representation AECS has a length much less than the original length of time-series and at the same time want to enhance its performance.Our algorithm exploits Recurrent Neu…
Categorical Data Clustering via Value Order Estimated Distance Metric Learning
School of Computer Science and Technology, Guangdong University of Technology, Guangzhou, China（广东技术大学计算机科学与技术学院）；Department of Computer Science, Hong Kong Baptist University, Hong Kong SAR China（香港 Baptist大学计算机科学系）；Guangdong Provincial Key Laboratory of Intelligent Information Processing, College of Electronics and Information Engineering, Shenzhen University, Shenzhen, China（广东省智能信息处理重点实验室，电子与信息工程学院，深圳大学，深圳，中国）；School of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China（计算机科学与软件工程学院，深圳大学，深圳，中国）；School of Informatics, Xiamen University, Xiamen China（信息学院，厦门大学，厦门中国）
Distance metric learning algorithms aim to appropriately measure similarities and distances between data points. In the context of clustering, metric learning is typically applied with the assist of side-information provided by experts, most commonly expressed in the form of cannot-link and must-link constraints. In this setting, distance metric learning algorithms move closer pairs of data points involved in must-link constraints, while pairs of points involved in cannot-link constraints are moved away from each other. For these algorithms to be effective, it is important to use a distance me…
Islamic Azad University（伊斯兰阿扎德大学）；Iran University of Science and Technology（伊朗科技大学）
This paper is a comparison study in the context of Topic Detection on COVID-19 data. There are various approaches for Topic Detection, among which the Clustering approach is selected in this paper. Clustering requires distance and calculating distance needs embedding. The aim of this research is to simultaneously study the three factors of embedding methods, distance metrics and clustering methods and their interaction. A dataset including one-month tweets collected with COVID-19-related hashtags is used for this study. Five methods, from earlier to new methods, are selected among the embeddin…
Clustering for high-dimension, low-sample size data using distance vectors
Osaka University（大阪大学）；Graduate School of Engineering Science, Osaka University（大阪大学工学研究科）
在高维低样本量（HDLSS）数据中，两个对象的接近程度并不总是反映隐藏的聚类结构。我们指出了一个重要的事实，它不是接近度，但距离的“值”包含的信息，在高维空间的集群结构。基于这一事实，我们提出了一个有效的和简单的聚类方法，称为距离向量聚类，HDLSS数据。在Hall et al.（2005）的工作中给出的假设下，我们证明了当维数趋于无穷大且样本量固定时，所提出的方法在较温和的条件下提供了真正的聚类标签。通过数值实验和实际数据分析，说明了距离向量聚类方法的有效性。
This paper presents a clustering technique that reduces the susceptibility to data noise by learning and clustering the data-distribution and then assigning the data to the cluster of its distribution. In the process, it reduces the impact of noise on clustering results. This method involves introducing a new distance among distributions, namely the expectation distance (denoted, ED), that goes beyond the state-of-art distribution distance of optimal mass transport (denoted, $W_2$ for $2$-Wasserstein): The latter essentially depends only on the marginal distributions while the former also empl…
Time series forecasting has gained lots of attention recently; this is because many real-world phenomena can be modeled as time series. The massive volume of data and recent advancements in the processing power of the computers enable researchers to develop more sophisticated machine learning algorithms such as neural networks to forecast the time series data. In this paper, we propose various neural network architectures to forecast the time series data using the dynamic measurements; moreover, we introduce various architectures on how to combine static and dynamic measurements for forecastin…
In machine learning, observation features are measured in a metric space to obtain their distance function for optimization. Given similar features that are statistically sufficient as a population, a statistical distance between two probability distributions can be calculated for more precise learning. Provided the observed features are multi-valued, the statistical distance function is still efficient. However, due to its scalar output, it cannot be applied to represent detailed distances between feature elements. To resolve this problem, this paper extends the traditional statistical distan…
Energy companies often implement various demand response (DR) programs to better match electricity demand and supply by offering the consumers incentives to reduce their demand during critical periods. Classifying clients according to their consumption patterns enables targeting specific groups of consumers for DR. Traditional clustering algorithms use standard distance measurement to find the distance between two points. The results produced by clustering algorithms such as K-means, K-medoids, and Gaussian Mixture Models depend on the clustering parameters or initial clusters. In contrast, ou…
Although distance measures are used in many machine learning algorithms, the literature on the context-independent selection and evaluation of distance measures is limited in the sense that prior knowledge is used. In cluster analysis, current studies evaluate the choice of distance measure after applying unsupervised methods based on error probabilities, implicitly setting the goal of reproducing predefined partitions in data. Such studies use clusters of data that are often based on the context of the data as well as the custom goal of the specific study. Depending on the data context, diffe…
Deep Clustering With Intra-class Distance Constraint for Hyperspectral Images
Liaoning Technical University（辽宁工程技术大学）；Haixi Institute, Chinese Academy of Sciences（中国科学院海西研究院）；Technical University of Munich（慕尼黑工业大学）；Hong Kong Polytechnic University（香港理工大学）
Carnegie Mellon University（卡内基梅隆大学）；University of Cambridge（剑桥大学）
Clustering under pairwise constraints is an important knowledge discovery tool that enables the learning of appropriate kernels or distance metrics to improve clustering performance. These pairwise constraints, which come in the form of must-link and cannot-link pairs, arise naturally in many applications and are intuitive for users to provide. However, the common practice of relaxing discrete constraints to a continuous domain to ease optimization when learning kernels or metrics can harm generalization, as information which only encodes linkage is transformed to informing distances. We intro…
Learning a Distance for the Clustering of Patients with Amyotrophic Lateral Sclerosis
Laboratoire LIFAT, Université de Tours（图雷大学LIFAT实验室）；Laboratoire LIFO, Université d'Orléans（奥尔良大学LIFO实验室）；Service de Biochimie et Biologie Moléculaire CHRU de Tours（图雷中心医院生物化学与分子生物学服务）；UMR U1253 iBrain, Université de Tours（图雷大学UMR U1253 iBrain）；Inserm（法国国家医学研究院）
Probabilistic Clustering of Time-Evolving Distance Data
Memorial Sloan-Kettering Cancer Center（纪念斯隆-凯特琳癌症中心）；Humboldt University of Berlin（柏林洪堡大学）；University of Basel（巴塞尔大学）；University of Zurich（苏黎世大学）；ETH Zurich（苏黎世联邦理工学院）
University of Sydney（悉尼大学）；TU Eindhoven（埃因霍温理工大学）；Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）
Due to the massively increasing amount of available geospatial data and the need to present it in an understandable way, clustering this data is more important than ever. As clusters might contain a large number of objects, having a representative for each cluster significantly facilitates understanding a clustering. Clustering methods relying on such representatives are called center-based. In this work we consider the problem of center-based clustering of trajectories. In this setting, the representative of a cluster is again a trajectory. To obtain a compact representation of the clusters a…
University of Calcutta（加尔各答大学）；Basanti Devi College（巴桑蒂·德维学院）
A new interpoint distance-based measure is proposed to identify the optimal number of clusters present in a data set. Designed in nonparametric approach, it is independent of the distribution of given data. Interpoint distances between the data members make our cluster validity index applicable to univariate and multivariate data measured on arbitrary scales, or having observations in any dimensional space where the number of study variables can be even larger than the sample size. Our proposed criterion is compatible with any clustering algorithm, and can be used to determine the unknown numb…
Singapore University of Technology and Design (SUTD)（新加坡科技设计大学）
The proliferation of smartphones has accelerated mobility studies by largely increasing the type and volume of mobility data available. One such source of mobility data is from GPS technology, which is becoming increasingly common and helps the research community understand mobility patterns of people. However, there lacks a standardized framework for studying the different mobility patterns created by the non-Work, non-Home locations of Working and Nonworking users on Workdays and Offdays using machine learning methods. We propose a new mobility metric, Daily Characteristic Distance, and use …
Sony Computer Science Laboratories Inc.（索尼计算机科学研究所）；Data61；The Australian National University（澳大利亚国立大学）
Clustering categorical distributions in the finite-dimensional probability simplex is a fundamental task met in many applications dealing with normalized histograms. Traditionally, the differential-geometric structures of the probability simplex have been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the dualistic information-geometric structure induced by a smooth dissimilarity measure, the Kullback-Leibler divergence. In this work, we introduce for clustering tasks a novel computationally-friendly f…
Developing technology and changing lifestyles have made online grocery delivery applications an indispensable part of urban life. Since the beginning of the COVID-19 pandemic, the demand for such applications has dramatically increased, creating new competitors that disrupt the market. An increasing level of competition might prompt companies to frequently restructure their marketing and product pricing strategies. Therefore, identifying the change patterns in product prices and sales volumes would provide a competitive advantage for the companies in the marketplace. In this paper, we investig…
Robust Fuzzy local k-plane clustering with mixture distance of hinge loss and L1 norm
China Electric Power Research Institute（中国电力科学研究院）；Key Laboratory of Measurement and Test of High Voltage and Heavy Current, State Administration for Market Regulation（高压及大电流测量测试关键实验室，国家市场监督管理总局）；School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学学院）；National Center for Applied Mathematics in Hubei, Wuhan University（湖北省应用数学中心，武汉大学）；Hubei Key Laboratory of Computational Science, Wuhan University（湖北省计算科学重点实验室，武汉大学）；Wuhan Institute for Math and AI, Wuhan University（武汉数学与人工智能研究院，武汉大学）
University of Wisconsin–Madison（威斯康星大学麦迪逊分校）；University of Iowa（爱荷华大学）
The topological patterns exhibited by many real-world networks motivate the development of topology-based methods for assessing the similarity of networks. However, extracting topological structure is difficult, especially for large and dense networks whose node degrees range over multiple orders of magnitude. In this paper, we propose a novel and computationally practical topological clustering method that clusters complex networks with intricate topology using principled theory from persistent homology and optimal transport. Such networks are aggregated into clusters through a centroid-based…
School of Electronics and Computer Science, University of Southampton（南安普顿大学电子与计算机科学学院）；School of Computing Sciences, University of East Anglia（东英吉利大学计算科学学院）
Monash University（莫纳什大学）；University of California, Berkeley（加州大学伯克利分校）；University of Michigan（密歇根大学）；IBM Research（IBM研究院）；VinAI Research（VinAI研究院）
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures, which are endowed with Wasserstein distance metrics. We propose several variants of this problem, which admit fast optimization algorithms, by exploiting the connection to the problem of finding Wasserstein barycenters. Consistency properties are establishe…
