In k-means clustering, we are given a set of n data points in d-dimensional space R/sup d/ and an integer k and the problem is to determine a set of k points in Rd, called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for k-means clustering is Lloyd's (1982) algorithm. We present a simple and efficient implementation of Lloyd's k-means clustering algorithm, which we call the filtering algorithm. This algorithm is easy to implement, requiring a kd-tree as the only major data structure. We establish the practical efficiency of the filtering algorithm in two ways. First, we present a data-sensitive analysis of the algorithm's running time, which shows that the algorithm runs faster as the separation between clusters increases. Second, we present a number of empirical studies both on synthetically generated data and on real data sets from applications in color quantization, data compression, and image segmentation.

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An efficient k-means clustering algorithm: analysis and implementation

In this paper two classes of clustering models are considered: (1) matrix, and (2) integer programming. The relationship between the matrix model, the p-median model and the classical group technology concept is discussed. A generalized group technology concept, based on generation for one part of a number of different process plans, is proposed. This new concept improves the quality of process (part) families and machine cells. A corresponding integer programming model is formulated. The models discussed are illustrated with numerical examples.

The generalized group technology concept

Efficient solving of the group technology problem

Publisher Summary This chapter reviews cluster analysis and related topics or the formal study of classification schemata, whereby objects are grouped, or clustered, according to measured or perceived intrinsic characteristics. The objective of a cluster analysis is to uncover natural groupings, or types, to prod one's creativity and ingenuity, and initiate hypotheses about the phenomenon being studied. Cluster analysis has a heuristic nature that encourages the exploration of data. Taxonomists, social scientists, psychologists, biologists, statisticians, mathematicians, engineers, computer scientists, medical researchers, and others who handle real data have all contributed to clustering methodology. The chapter presents cross-disciplinary communication so that one application area can profit from the experiences of others. The literature of cluster analysis straddles all quantitative, scientific disciplines, as demonstrated by the remarkable variety. Emphasis is on new developments, especially in the verification and validation of clustering results. The intent is to provide an applications-oriented treatment of cluster analysis in the spirit of exploratory data analysis. The chapter focuses on the four operations highlighted by reviewing techniques for assessing the tendency of the data to cluster, performing the clustering itself, and evaluating the validity of the results. Data representation includes recognition of data type and scale, measures of proximity and affinity, normalization, various two-dimensional projections of data, methods of visualizing multidimensional data, techniques for creating scales to describe data, and related matters. The chapter introduces the concept of intrinsic dimensionality that helps determine an appropriate number of factors for representing data. The chapter recommends that a serious data analyst be conversant with as broad a range of data analysis techniques and programs as possible and be aware of the assumptions on which the techniques are based.

Clustering Methodologies in Exploratory Data Analysis

Parts grouping into families can be performed in flexible manufacturing systems (FMSs) to simplify two classes of problems: long horizon planning and short horizon planning. In this paper the emphasis is on the part families problem applicable to the short horizon planning. Traditionally, parts grouping was based on classification and coding systems, some of which are reviewed in this paper. To overcome the drawbacks of the classical approach to parts grouping, two new methodologies are developed. The methodologies presented are very easy to implement because they take advantage of the information already stored in the CAD system. One of the basic elements of this system is the algorithm for solving the part families problem. Some of the existing clustering algorithms for solving this problem are discussed. A new clustering algorithm has been developed. The computational complexity and some of the computational results of solving the part families problem are also discussed.

The part families problem in flexible manufacturing systems

An efficient algorithm for data reorganization and clustering is presented This algorithm has some decided merits over the algorithm of Slagle et al, which provided the immediate stimulus for this work

A. Haupt

Papers

An Efficient Clustering Algorithm