This paper proposes a novel similarity measure for clustering sequential data. We first construct a common state-space by training a single probabilistic model with all the sequences in order to get a unified representation for the dataset. Then, distances are obtained attending to the transition matrices induced by each sequence in that state-space. This approach solves some of the usual overfitting and scalability issues of the existing semi-parametric techniques, that rely on training a model for each sequence. Empirical studies on both synthetic and real-world datasets illustrate the advantages of the proposed similarity measure for clustering sequences.
Grouping similar objects is a fundamental tool of scientific analysis, ubiquitous in disciplines from biology and chemistry to astronomy and pattern recognition. Inspired by the torque balance that exists in gravitational interactions when galaxies merge, we propose a novel clustering method based on two natural properties of the universe: mass and distance. The concept of torque describing the interactions of mass and distance forms the basis of the proposed parameter-free clustering algorithm, which harnesses torque balance to recognize any cluster, regardless of shape, size, or density. The…
State University of New York at Buffalo（纽约州立大学布法罗分校）；University of California, Irvine（加州大学欧文分校）
Current state-of-the-art nonparametric Bayesian text clustering methods model documents through multinomial distribution on bags of words. Although these methods can effectively utilize the word burstiness representation of documents and achieve decent performance, they do not explore the sequential information of text and relationships among synonyms. In this paper, the documents are modeled as the joint of bags of words, sequential features and word embeddings. We proposed Sequential Embedding induced Dirichlet Process Mixture Model (SiDPMM) to effectively exploit this joint document represe…
Contraction Clustering (RASTER): A Very Fast Big Data Algorithm for Sequential and Parallel Density-Based Clustering in Linear Time, Constant Memory, and a Single Pass
Fraunhofer-Chalmers Research Centre for Industrial Mathematics（弗劳恩霍夫-查尔默斯工业数学研究中心）；Fraunhofer Center for Machine Learning（弗劳恩霍夫机器学习中心）
Qualcomm Institute, University of California, San Diego（加州大学圣地亚哥分校高通研究所）；Ben Gurion University（本·古里安大学）
We study k-median clustering under the sequential no-substitution setting. In this setting, a data stream is sequentially observed, and some of the points are selected by the algorithm as cluster centers. However, a point can be selected as a center only immediately after it is observed, before observing the next point. In addition, a selected center cannot be substituted later. We give the first algorithm for this setting that obtains a constant approximation factor on the optimal risk under a random arrival order, an exponential improvement over previous work. This is also the first constant…
Technical University of Vienna（维也纳技术大学）；Boston University（波士顿大学）；University of Guelph（圭尔夫大学）；Vector Institute for Artificial Intelligence（向量人工智能研究所）；University of Texas, Austin（德克萨斯大学奥斯汀分校）
Interaction graphs, such as those recording emails between individuals or transactions between institutions, tend to be sparse yet structured, and often grow in an unbounded manner. Such behavior can be well-captured by structured, nonparametric edge-exchangeable graphs. However, such exchangeable models necessarily ignore temporal dynamics in the network. We propose a dynamic nonparametric model for interaction graphs that combine the sparsity of the exchangeable models with dynamic clustering patterns that tend to reinforce recent behavioral patterns. We show that our method yields improved …
We study the sample-based k-median clustering objective under a sequential setting without substitutions. In this setting, an i.i.d. sequence of examples is observed. An example can be selected as a center only immediately after it is observed, and it cannot be substituted later. The goal is to select a set of centers with a good k-median cost on the distribution which generated the sequence. We provide an efficient algorithm for this setting, and show that its multiplicative approximation factor is twice the approximation factor of an efficient offline algorithm. In addition, we show that if …
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…
k-medoids algorithm is a partitional, centroid-based clustering algorithm which uses pairwise distances of data points and tries to directly decompose the dataset with $n$ points into a set of $k$ disjoint clusters. However, k-medoids itself requires all distances between data points that are not so easy to get in many applications. In this paper, we introduce a new method which requires only a small proportion of the whole set of distances and makes an effort to estimate an upper-bound for unknown distances using the inquired ones. This algorithm makes use of the triangle inequality to calcul…
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…
South China University of Technology（华南理工大学）；Institute for Infocomm Research（资讯通信研究院）；Peng Cheng Laboratory（鹏城实验室）
Deploying models on target domain data subject to distribution shift requires adaptation. Test-time training (TTT) emerges as a solution to this adaptation under a realistic scenario where access to full source domain data is not available and instant inference on target domain is required. Despite many efforts into TTT, there is a confusion over the experimental settings, thus leading to unfair comparisons. In this work, we first revisit TTT assumptions and categorize TTT protocols by two key factors. Among the multiple protocols, we adopt a realistic sequential test-time training (sTTT) prot…
Co-clustering is a specific type of clustering that addresses the problem of finding groups of objects without necessarily considering all attributes. This technique has shown to have more consistent results in high-dimensional sparse data than traditional clustering. In trajectory co-clustering, the methods found in the literature have two main limitations: first, the space and time dimensions have to be constrained by user-defined thresholds; second, elements (trajectory points) are clustered ignoring the trajectory sequence, assuming that the points are independent among them. To address th…
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…
I2R, A-STAR（A*STAR信息通信研究所）；South China University of Technology（华南理工大学）；Southwest Jiaotong University（西南交通大学）
Deploying models on target domain data subject to distribution shift requires adaptation. Test-time training (TTT) emerges as a solution to this adaptation under a realistic scenario where access to full source domain data is not available, and instant inference on the target domain is required. Despite many efforts into TTT, there is a confusion over the experimental settings, thus leading to unfair comparisons. In this work, we first revisit TTT assumptions and categorize TTT protocols by two key factors. Among the multiple protocols, we adopt a realistic sequential test-time training (sTTT)…
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）
University of Florida（佛罗里达大学）；Duke University（杜克大学）
Model-based clustering is widely-used in a variety of application areas. However, fundamental concerns remain about robustness. In particular, results can be sensitive to the choice of kernel representing the within-cluster data density. Leveraging on properties of pairwise differences between data points, we propose a class of Bayesian distance clustering methods, which rely on modeling the likelihood of the pairwise distances in place of the original data. Although some information in the data is discarded, we gain substantial robustness to modeling assumptions. The proposed approach represe…
Hidden Markov Model (HMM) combined with Gaussian Process (GP) emission can be effectively used to estimate the hidden state with a sequence of complex input-output relational observations. Especially when the spectral mixture (SM) kernel is used for GP emission, we call this model as a hybrid HMM-GPSM. This model can effectively model the sequence of time-series data. However, because of a large number of parameters for the SM kernel, this model can not effectively be trained with a large volume of data having (1) long sequence for state transition and 2) a large number of time-series dataset …
Hanoi University of Science and Technology（河内理工大学）；The Graduate University for Advanced Studies, SOKENDAI（综合研究大学院大学（SOKENDAI））；National Institute of Informatics（国立信息学研究所）
Kernel segmentation aims at partitioning a data sequence into several non-overlapping segments that may have nonlinear and complex structures. In general, it is formulated as a discrete optimization problem with combinatorial constraints. A popular algorithm for optimally solving this problem is dynamic programming (DP), which has quadratic computation and memory requirements. Given that sequences in practice are too long, this algorithm is not a practical approach. Although many heuristic algorithms have been proposed to approximate the optimal segmentation, they have no guarantee on the qual…
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…
Institut FEMTO-ST（FEMTO-ST研究所）；Université Bourgogne Franche-Comté（勃艮第-弗朗什-孔泰大学）；Université de technologie de Compiègne（贡比涅技术大学）；CNRS（法国国家科学研究中心）；Heudiasyc（Heudiasyc实验室）；Institut universitaire de France（法兰西大学研究院）
The interpretation of unlabeled acoustic emission (AE) data classically relies on general-purpose clustering methods. While several external criteria have been used in the past to select the hyperparameters of those algorithms, few studies have paid attention to the development of dedicated objective functions in clustering methods able to cope with the specificities of AE data. We investigate how to explicitly represent clusters onsets in mixture models in general, and in Gaussian Mixture Models (GMM) in particular. By modifying the internal criterion of such models, we propose the first clus…
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…
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 …
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…
The misclassification error distance and the adjusted Rand index are two of the most commonly used criteria to evaluate the performance of clustering algorithms. This paper provides an in-depth comparison of the two criteria, aimed to better understand exactly what they measure, their properties and their differences. Starting from their population origins, the investigation includes many data analysis examples and the study of particular cases in great detail. An exhaustive simulation study allows inspecting the criteria distributions and reveals some previous misconceptions.
University of California at Berkeley（加州大学伯克利分校）；Monash University（莫纳什大学）
We propose a novel probabilistic approach to multilevel clustering problems based on composite transportation distance, which is a variant of transportation distance where the underlying metric is Kullback-Leibler divergence. Our method involves solving a joint optimization problem over spaces of probability measures to simultaneously discover grouping structures within groups and among groups. By exploiting the connection of our method to the problem of finding composite transportation barycenters, we develop fast and efficient optimization algorithms even for potentially large-scale multilev…
University of Konstanz（康斯坦茨大学）；Univ. of Applied Sciences Wolfsburg（沃尔夫斯堡应用科学大学）
For time series comparisons, it has often been observed that z-score normalized Euclidean distances far outperform the unnormalized variant. In this paper we show that a z-score normalized, squared Euclidean Distance is, in fact, equal to a distance based on Pearson Correlation. This has profound impact on many distance-based classification or clustering methods. In addition to this theoretically sound result we also show that the often used k-Means algorithm formally needs a mod ification to keep the interpretation as Pearson correlation strictly valid. Experimental results demonstrate that i…
Czech Technical University in Prague（布拉格捷克理工大学）；CTU in Prague（布拉格捷克理工大学）；Istituto Italiano di Tecnologia（意大利技术研究院）；Plymouth University（普利茅斯大学）
Humans and animals are constantly exposed to a continuous stream of sensory information from different modalities. At the same time, they form more compressed representations like concepts or symbols. In species that use language, this process is further structured by this interaction, where a mapping between the sensorimotor concepts and linguistic elements needs to be established. There is evidence that children might be learning language by simply disambiguating potential meanings based on multiple exposures to utterances in different contexts (cross-situational learning). In existing model…
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）
The high dimensionality of hyperspectral images often results in the degradation of clustering performance. Due to the powerful ability of deep feature extraction and non-linear feature representation, the clustering algorithm based on deep learning has become a hot research topic in the field of hyperspectral remote sensing. However, most deep clustering algorithms for hyperspectral images utilize deep neural networks as feature extractor without considering prior knowledge constraints that are suitable for clustering. To solve this problem, we propose an intra-class distance constrained deep…
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）
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…
Pemalang District Government（北加浪安区政府）；Universitas Muhammadiyah Semarang（三宝垄穆罕默迪亚大学）
Clustering is one of the major roles in data mining that is widely application in pattern recognition and image segmentation. Fuzzy C-means (FCM) is the most used clustering algorithm that proven efficient, fast and easy to implement, however, FCM uses the Euclidean distance that often leads to clustering errors, especially when handling multidimensional and noisy data. In the last few years, many distances metric have been proposed by researchers to improve the performance of the FCM algorithms, and the majority of researchers propose weighted distance. In this paper, we proposed Canberra Wei…
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…
FISHDBC is a flexible, incremental, scalable, and hierarchical density-based clustering algorithm. It is flexible because it empowers users to work on arbitrary data, skipping the feature extraction step that usually transforms raw data in numeric arrays letting users define an arbitrary distance function instead. It is incremental and scalable: it avoids the $\mathcal O(n^2)$ performance of other approaches in non-metric spaces and requires only lightweight computation to update the clustering when few items are added. It is hierarchical: it produces a "flat" clustering which can be expanded …
University of California, Los Angeles（加州大学洛杉矶分校）；University of Michigan（密歇根大学）
We study the use of power weighted shortest path distance functions for clustering high dimensional Euclidean data, under the assumption that the data is drawn from a collection of disjoint low dimensional manifolds. We argue, theoretically and experimentally, that this leads to higher clustering accuracy. We also present a fast algorithm for computing these distances.
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…
ADAPT Research Centre（ADAPT研究中心）；Technological University Dublin（都柏林理工大学）
In order to build efficient deep recurrent neural architectures, it is essential to analyze the complexityof long distance dependencies (LDDs) of the dataset being modeled. In this paper, we presentdetailed analysis of the dependency decay curve exhibited by various datasets. The datasets sampledfrom a similar process (e.g. natural language, sequential MNIST, Strictlyk-Piecewise languages,etc) display variations in the properties of the dependency decay curve. Our analysis reveal thefactors resulting in these variations; such as (i) number of unique symbols in a dataset, (ii) size ofthe datase…
