Clustering is a common technique for statistical data analysis, Clustering is the process of grouping the data into classes or clusters so that objects within a cluster have high similarity in comparison to one another, but are very dissimilar to objects in other clusters. Dissimilarities are assessed based on the attribute values describing the objects. Often, distance measures are used. Clustering is an unsupervised learning technique, where interesting patterns and structures can be found directly from very large data sets with little or none of the background knowledge. This paper also considers the partitioning of m-dimensional lattice graphs using Fiedler's approach, which requires the determination of the eigenvector belonging to the second smallest Eigenvalue of the Laplacian with K-means partitioning algorithm.
This paper presents the local best model of PSO for partition-based clustering. The proposed model gets rid off the drawbacks of gbest PSO for clustering. The model uses a pre-specified number of clusters K. The LPOSC has K neighborhoods. Each neighborhood represents one of the clusters. The goal of the particles in each neighborhood is optimizing the position of the centroid of the cluster. The performance of the proposed algorithms is measured using adjusted rand index. The results is compared with k-means and global best model of PSO.
North Carolina State University（北卡罗来纳州立大学）；Washington University（华盛顿大学）；College of Charleston（查尔斯顿学院）；Bard College（巴德学院）
We explore the geometrical interpretation of the PCA based clustering algorithm Principal Direction Divisive Partitioning (PDDP). We give several examples where this algorithm breaks down, and suggest a new method, gap partitioning, which takes into account natural gaps in the data between clusters. Geometric features of the PCA space are derived and illustrated and experimental results are given which show our method is comparable on the datasets used in the original paper on PDDP.
Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges across clusters. Algorithmic solutions based on this approach assume that different partitions of a hyperedge incur the same cost. However, this assumption fails to leverage the fact that different subsets of vertices within the same hyperedge may have different structural importance. We hence propose a new hypergraph clustering technique, termed inhomogeneous hy…
University of Illinois at Urbana Champaign（伊利诺伊大学厄巴纳-香槟分校）
Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue decompositions. Several algorithms have been proposed in the recent past to accelerate spectral clustering, however they compromise on the accuracy of the spectral clustering to achieve faster speed. In this paper, we propose a novel spectral clustering algorithm based on a mixing process on a graph. Unlike the existing spectral clustering algorithms, our algorithm doe…
Insight Centre for Data Analytics School of Computer Science University College Dublin（都柏林大学学院计算机科学学院数据洞察中心）；School of Computer Science University College Dublin（都柏林大学学院计算机科学学院）
Clustering techniques are very attractive for extracting and identifying patterns in datasets. However, their application to very large spatial datasets presents numerous challenges such as high-dimensionality data, heterogeneity, and high complexity of some algorithms. For instance, some algorithms may have linear complexity but they require the domain knowledge in order to determine their input parameters. Distributed clustering techniques constitute a very good alternative to the big data challenges (e.g.,Volume, Variety, Veracity, and Velocity). Usually these techniques consist of two phas…
Georgia Institute of Technology（佐治亚理工学院）；University of Bristol（布里斯托大学）
In this paper we study variants of the widely used spectral clustering that partitions a graph into k clusters by (1) embedding the vertices of a graph into a low-dimensional space using the bottom eigenvectors of the Laplacian matrix, and (2) grouping the embedded points into k clusters via k-means algorithms. We show that, for a wide class of graphs, spectral clustering gives a good approximation of the optimal clustering. While this approach was proposed in the early 1990s and has comprehensive applications, prior to our work similar results were known only for graphs generated from stochas…
Many data types arising from data mining applications can be modeled as bipartite graphs, examples include terms and documents in a text corpus, customers and purchasing items in market basket analysis and reviewers and movies in a movie recommender system. In this paper, we propose a new data clustering method based on partitioning the underlying bipartite graph. The partition is constructed by minimizing a normalized sum of edge weights between unmatched pairs of vertices of the bipartite graph. We show that an approximate solution to the minimization problem can be obtained by computing a p…
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies can be achieved by reducing the input space if a minimal loss of information can be achieved. Clustering algorithms, in general, face two common problems: 1) these converge to different settings with different initial conditions and; 2) the number of clusters has to be arbitrarily decided beforehand. This problem has become critical in the realm of big data…
We propose a novel method to co-cluster the vertices and hyperedges of hypergraphs with edge-dependent vertex weights (EDVWs). In this hypergraph model, the contribution of every vertex to each of its incident hyperedges is represented through an edge-dependent weight, conferring the model higher expressivity than the classical hypergraph. In our method, we leverage random walks with EDVWs to construct a hypergraph Laplacian and use its spectral properties to embed vertices and hyperedges in a common space. We then cluster these embeddings to obtain our proposed co-clustering method, of partic…
A Graph-Partitioning Based Continuous Optimization Approach to Semi-supervised Clustering Problems
Rensselaer Polytechnic Institute（伦斯勒理工学院）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）；Hong Kong Baptist University（香港浸会大学）；Sun Yat-sen University（中山大学）
Univ. Lille（里尔大学）；CNRS（法国国家科学研究中心）；Centrale Lille（里尔中央理工学院）；IMT Nord Europe（欧洲北部高等矿业电信学院）；Institut Mines-Télécom（法国矿业电信学院）；Université Bretagne Sud（南布列塔尼大学）
The particle filter (PF) is a powerful inference tool widely used to estimate the filtering distribution in non-linear and/or non-Gaussian problems. To overcome the curse of dimensionality of PF, the block PF (BPF) inserts a blocking step to partition the state space into several subspaces or blocks of smaller dimension so that the correction and resampling steps can be performed independently on each subspace. Using blocks of small size reduces the variance of the filtering distribution estimate, but in turn the correlation between blocks is broken and a bias is introduced. When the dependenc…
Bangladesh University of Engineering and Technology（孟加拉国工程技术大学）；Monash University（莫纳什大学）
Approximate Nearest Neighbor Search (ANNS) in high dimensional spaces is crucial for many real-life applications (e.g., e-commerce, web, multimedia, etc.) dealing with an abundance of data. This paper proposes an end-to-end learning framework that couples the partitioning (one critical step of ANNS) and learning-to-search steps using a custom loss function. A key advantage of our proposed solution is that it does not require any expensive pre-processing of the dataset, which is one of the critical limitations of the state-of-the-art approach. We achieve the above edge by formulating a multi-ob…
Max-cut, clustering, and many other partitioning problems that are of significant importance to machine learning and other scientific fields are NP-hard, a reality that has motivated researchers to develop a wealth of approximation algorithms and heuristics. Although the best algorithm to use typically depends on the specific application domain, a worst-case analysis is often used to compare algorithms. This may be misleading if worst-case instances occur infrequently, and thus there is a demand for optimization methods which return the algorithm configuration best suited for the given applica…
In this paper, we consider unsupervised partitioning problems, such as clustering, image segmentation, video segmentation and other change-point detection problems. We focus on partitioning problems based explicitly or implicitly on the minimization of Euclidean distortions, which include mean-based change-point detection, K-means, spectral clustering and normalized cuts. Our main goal is to learn a Mahalanobis metric for these unsupervised problems, leading to feature weighting and/or selection. This is done in a supervised way by assuming the availability of several potentially partially lab…
Georgia Institute of Technology（佐治亚理工学院）；Sandia National Laboratories（桑迪亚国家实验室）；Heidelberg University（海德堡大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Humboldt-Universität zu Berlin（柏林洪堡大学）；Apple Inc.（苹果公司）
In recent years, significant advances have been made in the design and evaluation of balanced (hyper)graph partitioning algorithms. We survey trends of the last decade in practical algorithms for balanced (hyper)graph partitioning together with future research directions. Our work serves as an update to a previous survey on the topic. In particular, the survey extends the previous survey by also covering hypergraph partitioning and streaming algorithms, and has an additional focus on parallel algorithms.
Within the field of process mining, several different trace clustering approaches exist for partitioning traces or process instances into similar groups. Typically, this partitioning is based on certain patterns or similarity between the traces, or driven by the discovery of a process model for each cluster. The main drawback of these techniques, however, is that their solutions are usually hard to evaluate or justify by domain experts. In this paper, we present two constrained trace clustering techniques that are capable to leverage expert knowledge in the form of instance-level constraints. …
Leibniz University Hannover（汉诺威莱布尼茨大学）；Free University of Berlin（柏林自由大学）
Traditionally, clustering algorithms focus on partitioning the data into groups of similar instances. The similarity objective, however, is not sufficient in applications where a fair-representation of the groups in terms of protected attributes like gender or race, is required for each cluster. Moreover, in many applications, to make the clusters useful for the end-user, a balanced cardinality among the clusters is required. Our motivation comes from the education domain where studies indicate that students might learn better in diverse student groups and of course groups of similar cardinali…
In this paper, we provide an approach to clustering relational matrices whose entries correspond to either similarities or dissimilarities between objects. Our approach is based on the value of information, a parameterized, information-theoretic criterion that measures the change in costs associated with changes in information. Optimizing the value of information yields a deterministic annealing style of clustering with many benefits. For instance, investigators avoid needing to a priori specify the number of clusters, as the partitions naturally undergo phase changes, during the annealing pro…
Swiss Federal Institute of Technology, ETH Zurich（苏黎世联邦理工学院）
Model selection in clustering requires (i) to specify a suitable clustering principle and (ii) to control the model order complexity by choosing an appropriate number of clusters depending on the noise level in the data. We advocate an information theoretic perspective where the uncertainty in the measurements quantizes the set of data partitionings and, thereby, induces uncertainty in the solution space of clusterings. A clustering model, which can tolerate a higher level of fluctuations in the measurements than alternative models, is considered to be superior provided that the clustering sol…
Image partitioning, or segmentation without semantics, is the task of decomposing an image into distinct segments, or equivalently to detect closed contours. Most prior work either requires seeds, one per segment; or a threshold; or formulates the task as multicut / correlation clustering, an NP-hard problem. Here, we propose an efficient algorithm for graph partitioning, the "Mutex Watershed''. Unlike seeded watershed, the algorithm can accommodate not only attractive but also repulsive cues, allowing it to find a previously unspecified number of segments without the need for explicit seeds o…
The explosion in the amount of news and journalistic content being generated across the globe, coupled with extended and instantaneous access to information through online media, makes it difficult and time-consuming to monitor news developments and opinion formation in real time. There is an increasing need for tools that can pre-process, analyse and classify raw text to extract interpretable content; specifically, identifying topics and content-driven groupings of articles. We present here such a methodology that brings together powerful vector embeddings from Natural Language Processing wit…
Cluster analysis is one of the essential tasks in data mining and knowledge discovery. Each type of data poses unique challenges in achieving relatively efficient partitioning of the data into homogeneous groups. While the algorithms for numeric data are relatively well studied in the literature, there are still challenges to address in case of categorical data. The main issue is the unordered structure of categorical data, which makes the implementation of the standard concepts of clustering algorithms difficult. For instance, the assessment of distance between objects, the selection of repre…
Infinia ML Inc.（Infinia ML公司）；Duke University（杜克大学）
We propose a scalable Gromov-Wasserstein learning (S-GWL) method and establish a novel and theoretically-supported paradigm for large-scale graph analysis. The proposed method is based on the fact that Gromov-Wasserstein discrepancy is a pseudometric on graphs. Given two graphs, the optimal transport associated with their Gromov-Wasserstein discrepancy provides the correspondence between their nodes and achieves graph matching. When one of the graphs has isolated but self-connected nodes ($i.e.$, a disconnected graph), the optimal transport indicates the clustering structure of the other graph…
The objectives of this paper are to explore ways to analyze breast cancer dataset in the context of unsupervised learning without prior training model. The paper investigates different ways of clustering techniques as well as preprocessing. This in-depth analysis builds the footprint which can further use for designing a most robust and accurate medical prognosis system. This paper also give emphasis on correlations of data points with different standard benchmark techniques. Keywords: Breast cancer dataset, Clustering Technique Hopkins Statistic, K-means Clustering, k-medoids or partitioning …
University of Bath（巴斯大学）；University of Cambridge（剑桥大学）
Glioblastoma is profoundly heterogeneous in regional microstructure and vasculature. Characterizing the spatial heterogeneity of glioblastoma could lead to more precise treatment. With unsupervised learning techniques, glioblastoma MRI-derived radiomic features have been widely utilized for tumor sub-region segmentation and survival prediction. However, the reliability of algorithm outcomes is often challenged by both ambiguous intermediate process and instability introduced by the randomness of clustering algorithms, especially for data from heterogeneous patients. In this paper, we propose a…
A new type of federated clustering: A non-model-sharing approach
Center for Artificial Intelligence Research（人工智能研究中心）；Tsukuba Institute for Advanced Research（茨口高级研究机构）；University of Tsukuba（茨口大学）；Graduate School of Science and Technology（科学与技术研究生院）；Institute of Systems and Information Engineering（系统与信息工程研究所）
We propose an algorithm, HPREF (Hierarchical Partitioning by Repeated Features), that produces a hierarchical partition of a set of clusterings of a fixed dataset, such as sets of clusterings produced by running a clustering algorithm with a range of parameters. This gives geometric structure to such sets of clustering, and can be used to visualize the set of results one obtains by running a clustering algorithm with a range of parameters.
Univ Lyon, UJM-Saint-Etienne, CNRS, Institut d Optique Graduate School, Laboratoire Hubert Curien UMR 5516（里昂大学，圣艾蒂安让·莫奈大学，法国国家科学研究中心，光学研究生院，于贝尔·居里安实验室 UMR 5516）；Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK（格勒诺布尔-阿尔卑斯大学，法国国家科学研究中心，格勒诺布尔理工学院，让·昆兹曼实验室）
In this paper, we introduce and formalize a rank-one partitioning learning paradigm that unifies partitioning methods that proceed by summarizing a data set using a single vector that is further used to derive the final clustering partition. Using this unification as a starting point, we propose a novel algorithmic solution for the partitioning problem based on rank-one matrix factorization and denoising of piecewise constant signals. Finally, we propose an empirical demonstration of our findings and demonstrate the robustness of the proposed denoising step. We believe that our work provides a…
This paper presents a Fast Synchronization Clustering algorithm (FSynC), which is an improved version of SynC algorithm. In order to decrease the time complexity of the original SynC algorithm, we combine grid cell partitioning method and Red-Black tree to construct the near neighbor point set of every point. By simulated experiments of some artificial data sets and several real data sets, we observe that FSynC algorithm can often get less time than SynC algorithm for many kinds of data sets. At last, it gives some research expectations to popularize this algorithm.
In this article, the logic rule ensembles approach to supervised learning is applied to the unsupervised or semi-supervised clustering. Logic rules which were obtained by combining simple conjunctive rules are used to partition the input space and an ensemble of these rules is used to define a similarity matrix. Similarity partitioning is used to partition the data in an hierarchical manner. We have used internal and external measures of cluster validity to evaluate the quality of clusterings or to identify the number of clusters.
Sharif University of Technology（谢里夫理工大学）；Amirkabir University of Technology（阿米尔卡比尔理工大学）
Centroid-based methods including k-means and fuzzy c-means are known as effective and easy-to-implement approaches to clustering purposes in many applications. However, these algorithms cannot be directly applied to supervised tasks. This paper thus presents a generative model extending the centroid-based clustering approach to be applicable to classification and regression tasks. Given an arbitrary loss function, the proposed approach, termed Supervised Fuzzy Partitioning (SFP), incorporates labels information into its objective function through a surrogate term penalizing the empirical risk.…
Stanford University（斯坦福大学）；Florida State University（佛罗里达州立大学）
We establish a bridge between spectral clustering and Gromov-Wasserstein Learning (GWL), a recent optimal transport-based approach to graph partitioning. This connection both explains and improves upon the state-of-the-art performance of GWL. The Gromov-Wasserstein framework provides probabilistic correspondences between nodes of source and target graphs via a quadratic programming relaxation of the node matching problem. Our results utilize and connect the observations that the GW geometric structure remains valid for any rank-2 tensor, in particular the adjacency, distance, and various kerne…
This paper further extends RIn-Close_CVC, a biclustering algorithm capable of performing an efficient, complete, correct and non-redundant enumeration of maximal biclusters with constant values on columns in numerical datasets. By avoiding a priori partitioning and itemization of the dataset, RIn-Close_CVC implements an online partitioning, which is demonstrated here to guide to more informative biclustering results. The improved algorithm is called RIn-Close_CVC3, keeps those attractive properties of RIn-Close_CVC, as formally proved here, and is characterized by: a drastic reduction in memor…
ASIL: Augmented Structural Information Learning for Deep Graph Clustering in Hyperbolic Space
Beijing University of Posts and Telecommunications（北京邮电大学）；North China Electric Power University（华北电力大学）；DiDi Chuxing（滴滴出行）；Beihang University（北航）；University of Illinois at Chicago（伊利诺伊大学香槟分校）
This paper proposes an efficient technique for partitioning large biometric database during identification. In this technique feature vector which comprises of global and local descriptors extracted from offline signature are used by fuzzy clustering technique to partition the database. As biometric features posses no natural order of sorting, thus it is difficult to index them alphabetically or numerically. Hence, some supervised criteria is required to partition the search space. At the time of identification the fuzziness criterion is introduced to find the nearest clusters for declaring th…
Graph partitioning is the problem of dividing the nodes of a graph into balanced partitions while minimizing the edge cut across the partitions. Due to its combinatorial nature, many approximate solutions have been developed, including variants of multi-level methods and spectral clustering. We propose GAP, a Generalizable Approximate Partitioning framework that takes a deep learning approach to graph partitioning. We define a differentiable loss function that represents the partitioning objective and use backpropagation to optimize the network parameters. Unlike baselines that redo the optimi…
In a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present paper continues the same line of study, where we focus on partitioning weighted uniform hypergraphs---a problem often encountered in computer vision. This work is motivated by two issues that arise when a hypergraph partitioning approach is used to tackle computer vision problems: (i) The uniform hypergraphs constructed for higher-order learning contain all edges, but most have negligible weights. Thus, the adjacency t…
A Clustering Method with Graph Maximum Decoding Information
University of Chinese Academy of Sciences（中国科学院大学）；Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；Advanced Institute of Big Data (Beijing)（北京大数据研究院）
Long-Term EEG Partitioning for Seizure Onset Detection
SANKEN, Osaka University（大阪大学 SANKEN）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Carle Illinois College of Medicine, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校卡尔伊利诺伊医学院）
A new algorithm based on bayesian inference for learning local graph conductance based on Gaussian Process(GP) is given that uses advanced MCMC convergence ideas to create a scalable and fast algorithm for convergence to stationary distribution which is provided to learn the bahavior of conductance when traversing the indirected weighted graph. First metric embedding is used to represent the vertices of the graph. Then, uniform induced conductance is calculated for training points. Finally, in the learning step, a gaussian process is used to approximate the uniform induced conductance. MCMC is…
Despite the widespread use of Clustering, there is distressingly little general theory of clustering available. Questions like "What distinguishes a clustering of data from other data partitioning?", "Are there any principles governing all clustering paradigms?", "How should a user choose an appropriate clustering algorithm for a particular task?", etc. are almost completely unanswered by the existing body of clustering literature. We consider an axiomatic approach to the theory of Clustering. We adopt the framework of Kleinberg, [Kle03]. By relaxing one of Kleinberg's clustering axioms, we si…
International University of Business Agriculture and Technology（国际商业农业与技术大学）；Mississippi State University（密西西比州立大学）；Rajshahi College（拉杰沙希学院）
In this paper, several two-dimensional clustering scenarios are given. In those scenarios, soft partitioning clustering algorithms (Fuzzy C-means (FCM) and Possibilistic c-means (PCM)) are applied. Afterward, VAT is used to investigate the clustering tendency visually, and then in order of checking cluster validation, three types of indices (e.g., PC, DI, and DBI) were used. After observing the clustering algorithms, it was evident that each of them has its limitations; however, PCM is more robust to noise than FCM as in case of FCM a noise point has to be considered as a member of any of the …
Missouri University of Science and Technology（密苏里科技大学）；CAPES Foundation（巴西高等教育人员素质提升协调局）
Validation is one of the most important aspects of clustering, but most approaches have been batch methods. Recently, interest has grown in providing incremental alternatives. This paper extends the incremental cluster validity index (iCVI) family to include incremental versions of Calinski-Harabasz (iCH), I index and Pakhira-Bandyopadhyay-Maulik (iI and iPBM), Silhouette (iSIL), Negentropy Increment (iNI), Representative Cross Information Potential (irCIP) and Representative Cross Entropy (irH), and Conn_Index (iConn_Index). Additionally, the effect of under- and over-partitioning on the beha…
