Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters). The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exploratory data analysis. However, clustering is a difficult problem combinatorially, and differences in assumptions and contexts in different communities has made the transfer of useful generic concepts and methodologies slow to occur. This paper presents an overview of pattern clustering methods from a statistical pattern recognition perspective, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners. We present a taxonomy of clustering techniques, and identify cross-cutting themes and recent advances. We also describe some important applications of clustering algorithms such as image segmentation, object recognition, and information retrieval.

/pdf/data-clustering-a-review-4c452f5cab.pdf

Data clustering: a review

A general non-parametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure: the mean shift. For discrete data, we prove the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and, thus, its utility in detecting the modes of the density. The relation of the mean shift procedure to the Nadaraya-Watson estimator from kernel regression and the robust M-estimators; of location is also established. Algorithms for two low-level vision tasks discontinuity-preserving smoothing and image segmentation - are described as applications. In these algorithms, the only user-set parameter is the resolution of the analysis, and either gray-level or color images are accepted as input. Extensive experimental results illustrate their excellent performance.

Mean shift: a robust approach toward feature space analysis

The k-means algorithm is well known for its efficiency in clustering large data sets. However, working only on numeric values prohibits it from being used to cluster real world data containing categorical values. In this paper we present two algorithms which extend the k-means algorithm to categorical domains and domains with mixed numeric and categorical values. The k-modes algorithm uses a simple matching dissimilarity measure to deal with categorical objects, replaces the means of clusters with modes, and uses a frequency-based method to update modes in the clustering process to minimise the clustering cost function. With these extensions the k-modes algorithm enables the clustering of categorical data in a fashion similar to k-means. The k-prototypes algorithm, through the definition of a combined dissimilarity measure, further integrates the k-means and k-modes algorithms to allow for clustering objects described by mixed numeric and categorical attributes. We use the well known soybean disease and credit approval data sets to demonstrate the clustering performance of the two algorithms. Our experiments on two real world data sets with half a million objects each show that the two algorithms are efficient when clustering large data sets, which is critical to data mining applications.

/pdf/extensions-to-the-k-means-algorithm-for-clustering-large-1w7dxyjag2.pdf

Extensions to the k-Means Algorithm for Clustering Large Data Sets with Categorical Values

The clustering problem is cast in the framework of possibility theory. The approach differs from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values can be interpreted as degrees of possibility of the points belonging to the classes, i.e., the compatibilities of the points with the class prototypes. An appropriate objective function whose minimum will characterize a good possibilistic partition of the data is constructed, and the membership and prototype update equations are derived from necessary conditions for minimization of the criterion function. The advantages of the resulting family of possibilistic algorithms are illustrated by several examples. >

http://systemaut.persiangig.com/Fuzzy/IEEE_00227387.pdf

A possibilistic approach to clustering

Minimum cross entropy thresholding

A new approach to clustering

A novel approach to the automatic extraction of geological faults from three-dimensional (3-D) seismic data is described, and qualitative and quantitative comparisons of manually and automatically picked fault geometries interpreted from both high and medium quality 3-D seismic datasets are presented. An algorithm has been developed that allows semiautomated identification, extraction, and modeling of fault surfaces imaged in 3-D seismic datasets. Based on a multistage approach, the algorithm operates initially at a small spatial scale, identifying local discontinuities in the seismic horizons, and then gradually considers larger and larger segments of fault surfaces until a set of complete fault surfaces are identified. A large portion of the work involves merging of segments of fault surfaces, performed using a highest confidence first (HCF) stratagem, taking into consideration the context of the resultant fault geometry. We show that results from the automated fault picker compare favorably with a manually labeled set of faults surfaces interpreted from a high-quality dataset. Last, we present an estimate of the savings in human operator time that can be made by using the automated approach, indicating savings of multiple person-days for the multigigabyte datasets that typify the petroleum industry.

Fault surface detection in 3-D seismic data

Segmentation and recognition of Arabic characters by structural classification

A new method for the compression of angiogram video sequences is presented. The method is based on the philosophy that diagnostically significant areas of the image should be allocated the greatest proportion of the total allocated bit budget. The approach uses a three-dimensional wavelet-coder based on the popular set partitioning in hierarchical trees algorithm. Incorporated into this framework are a region-of-interest (ROI) detection stage and a texture-modeling stage. The combined result is an approach that models the high-frequency wavelet coefficients for some diagnostically unimportant regions of the image in an extremely efficient manner. This allows additional bits to be used within the ROI to improve the quality of the diagnostically significant areas. Results are compared for a number of real data sets and evaluated by trained cardiologists.

A wavelet-based region of interest encoder for the compression of angiogram video sequences

This paper presents an approach to the problem of estimating a dense optical flow field. The approach is based on a multiframe, irregularly spaced motion trajectory set, where each trajectory describes the motion of a given point as a function of time. From this motion trajectory set a dense flow field is estimated using a process of interpolation. A set of localized motion models are estimated, with each pixel labeled as belonging to one of the motion models. A Markov random field framework is adopted, allowing the incorporation of contextual constraints to encourage region-like structures. The approach is compared with a number of conventional optical flow estimation algorithms taken over a number of real and synthetic sequences. Results indicate that the method produces more accurate results for sequences with known ground truth flow. Also, applying the method to real sequences with unknown flow results in lower DFD, for all of the sequences tested.

Robust optical flow estimation based on a sparse motion trajectory set

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