Protocols for the Ecient Dissemination of
01 Jan 2016-
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01 Jan 1967
TL;DR: The k-means algorithm as mentioned in this paper partitions an N-dimensional population into k sets on the basis of a sample, which is a generalization of the ordinary sample mean, and it is shown to give partitions which are reasonably efficient in the sense of within-class variance.
Abstract: The main purpose of this paper is to describe a process for partitioning an N-dimensional population into k sets on the basis of a sample. The process, which is called 'k-means,' appears to give partitions which are reasonably efficient in the sense of within-class variance. That is, if p is the probability mass function for the population, S = {S1, S2, * *, Sk} is a partition of EN, and ui, i = 1, 2, * , k, is the conditional mean of p over the set Si, then W2(S) = ff=ISi f z u42 dp(z) tends to be low for the partitions S generated by the method. We say 'tends to be low,' primarily because of intuitive considerations, corroborated to some extent by mathematical analysis and practical computational experience. Also, the k-means procedure is easily programmed and is computationally economical, so that it is feasible to process very large samples on a digital computer. Possible applications include methods for similarity grouping, nonlinear prediction, approximating multivariate distributions, and nonparametric tests for independence among several variables. In addition to suggesting practical classification methods, the study of k-means has proved to be theoretically interesting. The k-means concept represents a generalization of the ordinary sample mean, and one is naturally led to study the pertinent asymptotic behavior, the object being to establish some sort of law of large numbers for the k-means. This problem is sufficiently interesting, in fact, for us to devote a good portion of this paper to it. The k-means are defined in section 2.1, and the main results which have been obtained on the asymptotic behavior are given there. The rest of section 2 is devoted to the proofs of these results. Section 3 describes several specific possible applications, and reports some preliminary results from computer experiments conducted to explore the possibilities inherent in the k-means idea. The extension to general metric spaces is indicated briefly in section 4. The original point of departure for the work described here was a series of problems in optimal classification (MacQueen [9]) which represented special
24,320 citations
TL;DR: An overview of pattern clustering methods from a statistical pattern recognition perspective is presented, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners.
Abstract: 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.
14,054 citations
Book•
01 Jan 1990TL;DR: An electrical signal transmission system, applicable to the transmission of signals from trackside hot box detector equipment for railroad locomotives and rolling stock, wherein a basic pulse train is transmitted whereof the pulses are of a selected first amplitude and represent a train axle count.
Abstract: 1. Introduction. 2. Partitioning Around Medoids (Program PAM). 3. Clustering large Applications (Program CLARA). 4. Fuzzy Analysis. 5. Agglomerative Nesting (Program AGNES). 6. Divisive Analysis (Program DIANA). 7. Monothetic Analysis (Program MONA). Appendix 1. Implementation and Structure of the Programs. Appendix 2. Running the Programs. Appendix 3. Adapting the Programs to Your Needs. Appendix 4. The Program CLUSPLOT. References. Author Index. Subject Index.
10,537 citations
01 Jan 1998
TL;DR: Integrated circuits will lead to such wonders as home computers or at least terminals connected to a central computer, automatic controls for automobiles, and personal portable communications equipment as mentioned in this paper. But the biggest potential lies in the production of large systems.
Abstract: The future of integrated electronics is the future of electronics itself. The advantages of integration will bring about a proliferation of electronics, pushing this science into many new areas. Integrated circuits will lead to such wonders as home computers—or at least terminals connected to a central computer—automatic controls for automobiles, and personal portable communications equipment. The electronic wristwatch needs only a display to be feasible today. But the biggest potential lies in the production of large systems. In telephone communications, integrated circuits in digital filters will separate channels on multiplex equipment. Integrated circuits will also switch telephone circuits and perform data processing. Computers will be more powerful, and will be organized in completely different ways. For example, memories built of integrated electronics may be distributed throughout the machine instead of being concentrated in a central unit. In addition, the improved reliability made possible by integrated circuits will allow the construction of larger processing units. Machines similar to those in existence today will be built at lower costs and with faster turnaround.
9,647 citations
01 Jan 1990
TL;DR: In this article, an electrical signal transmission system for railway locomotives and rolling stock is proposed, where a basic pulse train is transmitted whereof the pulses are of a selected first amplitude and represent a train axle count, and a spike pulse of greater selected amplitude is transmitted, occurring immediately after the axle count pulse to which it relates, whenever an overheated axle box is detected.
Abstract: An electrical signal transmission system, applicable to the transmission of signals from trackside hot box detector equipment for railroad locomotives and rolling stock, wherein a basic pulse train is transmitted whereof the pulses are of a selected first amplitude and represent a train axle count, and a spike pulse of greater selected amplitude is transmitted, occurring immediately after the axle count pulse to which it relates, whenever an overheated axle box is detected. To enable the signal receiving equipment to determine on which side of a train the overheated box is located, the spike pulses are of two different amplitudes corresponding, respectively, to opposite sides of the train.
9,011 citations