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235
Survey of clustering algorithms
- IEEE TRANSACTIONS ON NEURAL NETWORKS
, 2005
"... Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the ..."
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Cited by 499 (4 self)
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Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the profusion of options causes confusion. We survey clustering algorithms for data sets appearing in statistics, computer science, and machine learning, and illustrate their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts. Several tightly related topics, proximity measure, and cluster validation, are also discussed.
Unsupervised learning of finite mixture models
- IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2002
"... This paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data. The adjective ªunsupervisedº is justified by two properties of the algorithm: 1) it is capable of selecting the number of components and 2) unlike the standard expectation-maximization (EM) alg ..."
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Cited by 418 (22 self)
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This paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data. The adjective ªunsupervisedº is justified by two properties of the algorithm: 1) it is capable of selecting the number of components and 2) unlike the standard expectation-maximization (EM) algorithm, it does not require careful initialization. The proposed method also avoids another drawback of EM for mixture fitting: the possibility of convergence toward a singular estimate at the boundary of the parameter space. The novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models; instead, we seamlessly integrate estimation and model selection in a single algorithm. Our technique can be applied to any type of parametric mixture model for which it is possible to write an EM algorithm; in this paper, we illustrate it with experiments involving Gaussian mixtures. These experiments testify for the good performance of our approach.
A New Point Matching Algorithm for Non-Rigid Registration
, 2002
"... Feature-based methods for non-rigid registration frequently encounter the correspondence problem. Regardless of whether points, lines, curves or surface parameterizations are used, feature-based non-rigid matching requires us to automatically solve for correspondences between two sets of features. I ..."
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Cited by 356 (3 self)
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Feature-based methods for non-rigid registration frequently encounter the correspondence problem. Regardless of whether points, lines, curves or surface parameterizations are used, feature-based non-rigid matching requires us to automatically solve for correspondences between two sets of features. In addition, there could be many features in either set that have no counterparts in the other. This outlier rejection problem further complicates an already di#cult correspondence problem. We formulate feature-based non-rigid registration as a non-rigid point matching problem. After a careful review of the problem and an in-depth examination of two types of methods previously designed for rigid robust point matching (RPM), we propose a new general framework for non-rigid point matching. We consider it a general framework because it does not depend on any particular form of spatial mapping. We have also developed an algorithm---the TPS-RPM algorithm---with the thin-plate spline (TPS) as the parameterization of the non-rigid spatial mapping and the softassign for the correspondence. The performance of the TPS-RPM algorithm is demonstrated and validated in a series of carefully designed synthetic experiments. In each of these experiments, an empirical comparison with the popular iterated closest point (ICP) algorithm is also provided. Finally, we apply the algorithm to the problem of non-rigid registration of cortical anatomical structures which is required in brain mapping. While these results are somewhat preliminary, they clearly demonstrate the applicability of our approach to real world tasks involving feature-based non-rigid registration.
Deterministic Annealing for Clustering, Compression, Classification, Regression, and Related Optimization Problems
- Proceedings of the IEEE
, 1998
"... this paper. Let us place it within the neural network perspective, and particularly that of learning. The area of neural networks has greatly benefited from its unique position at the crossroads of several diverse scientific and engineering disciplines including statistics and probability theory, ph ..."
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Cited by 321 (20 self)
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this paper. Let us place it within the neural network perspective, and particularly that of learning. The area of neural networks has greatly benefited from its unique position at the crossroads of several diverse scientific and engineering disciplines including statistics and probability theory, physics, biology, control and signal processing, information theory, complexity theory, and psychology (see [45]). Neural networks have provided a fertile soil for the infusion (and occasionally confusion) of ideas, as well as a meeting ground for comparing viewpoints, sharing tools, and renovating approaches. It is within the ill-defined boundaries of the field of neural networks that researchers in traditionally distant fields have come to the realization that they have been attacking fundamentally similar optimization problems.
Data Clustering: 50 Years Beyond K-Means
, 2008
"... Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms into taxonomic ranks: domain, kingdom, phylum, class, etc.). Cluster analysis is the formal study of algorithms and m ..."
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Cited by 294 (7 self)
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Organizing data into sensible groupings is one of the most fundamental modes of understanding and learning. As an example, a common scheme of scientific classification puts organisms into taxonomic ranks: domain, kingdom, phylum, class, etc.). Cluster analysis is the formal study of algorithms and methods for grouping, or clustering, objects according to measured or perceived intrinsic characteristics or similarity. Cluster analysis does not use category labels that tag objects with prior identifiers, i.e., class labels. The absence of category information distinguishes data clustering (unsupervised learning) from classification or discriminant analysis (supervised learning). The aim of clustering is exploratory in nature to find structure in data. Clustering has a long and rich history in a variety of scientific fields. One of the most popular and simple clustering algorithms, K-means, was first published in 1955. In spite of the fact that K-means was proposed over 50 years ago and thousands of clustering algorithms have been published since then, K-means is still widely used. This speaks to the difficulty of designing a general purpose clustering algorithm and the illposed problem of clustering. We provide a brief overview of clustering, summarize well known clustering methods, discuss the major challenges and key issues in designing clustering algorithms, and point out some of the emerging and useful research directions, including semi-supervised clustering, ensemble clustering, simultaneous feature selection, and data clustering and large scale data clustering.
Flexible Syntactic Matching of Curves and its Application to Automatic Hierarchical Classification of Silhouettes
- IEEE Transactions on Pattern Analysis and Machine Intelligence
"... Curve matching is one instance of the fundamental correspondence problem. Our exible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations. A syntactic representation is constructed for both curves, and an edit transformation which ..."
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Cited by 131 (2 self)
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Curve matching is one instance of the fundamental correspondence problem. Our exible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations. A syntactic representation is constructed for both curves, and an edit transformation which maps one curve to the other is found using dynamic programming. We present extensive...
Semi-supervised Clustering with User Feedback
, 2003
"... We present a new approach to clustering based on the observation that \it is easier to criticize than to construct." Our approach of semi-supervised clustering allows a user to iteratively provide feedback to a clustering algorithm. The feedback is incorporated in the form of constraints w ..."
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Cited by 125 (2 self)
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We present a new approach to clustering based on the observation that \it is easier to criticize than to construct." Our approach of semi-supervised clustering allows a user to iteratively provide feedback to a clustering algorithm. The feedback is incorporated in the form of constraints which the clustering algorithm attempts to satisfy on future iterations. These constraints allow the user to guide the clusterer towards clusterings of the data that the user nds more useful. We demonstrate semi-supervised clustering with a system that learns to cluster news stories from a Reuters data set. Introduction Consider the following problem: you are given 100,000 text documents (e.g., papers, newsgroup articles, or web pages) and asked to group them into classes or into a hierarchy such that related documents are grouped together. You are not told what classes or hierarchy to use or what documents are related; you have some criteria in mind, but may not be able to say exactly w...
Unsupervised Learning from Dyadic Data
, 1998
"... Dyadic data refers to a domain with two finite sets of objects in which observations are made for dyads, i.e., pairs with one element from either set. This includes event co-occurrences, histogram data, and single stimulus preference data as special cases. Dyadic data arises naturally in many applic ..."
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Cited by 122 (11 self)
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Dyadic data refers to a domain with two finite sets of objects in which observations are made for dyads, i.e., pairs with one element from either set. This includes event co-occurrences, histogram data, and single stimulus preference data as special cases. Dyadic data arises naturally in many applications ranging from computational linguistics and information retrieval to preference analysis and computer vision. In this paper, we present a systematic, domain-independent framework for unsupervised learning from dyadic data by statistical mixture models. Our approach covers different models with flat and hierarchical latent class structures and unifies probabilistic modeling and structure discovery. Mixture models provide both, a parsimonious yet flexible parameterization of probability distributions with good generalization performance on sparse data, as well as structural information about data-inherent grouping structure. We propose an annealed version of the standard Expectation Maximization algorithm for model fitting which is empirically evaluated on a variety of data sets from different domains.
Unsupervised Texture Segmentation in a Deterministic Annealing Framework
, 1998
"... We present a novel optimization framework for unsupervised texture segmentation that relies on statistical tests as a measure of homogeneity. Texture segmentation is formulated as a data clustering problem based on sparse proximity data. Dissimilarities of pairs of textured regions are computed from ..."
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Cited by 104 (9 self)
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We present a novel optimization framework for unsupervised texture segmentation that relies on statistical tests as a measure of homogeneity. Texture segmentation is formulated as a data clustering problem based on sparse proximity data. Dissimilarities of pairs of textured regions are computed from a multi-scale Gabor filter image representation. We discuss and compare a class of clustering objective functions which is systematically derived from invariance principles. As a general optimization framework we propose deterministic annealing based on a mean-field approximation. The canonical way to derive clustering algorithms within this framework as well as an efficient implementation of mean-field annealing and the closely related Gibbs sampler are presented. We apply both annealing variants to Brodatz-like micro-texture mixtures and real-word images.
