摘要
The task of clustering is to identify classes of similar objects among a set of objects. The definition of similarity varies from one clustering model to another. However, in most of these models the concept of similarity is often based on such metrics as Manhattan distance, Euclidean distance or other Lp distances. In other words, similar objects must have close values in at least a set of dimensions. In this paper, we explore a more general type of similarity. Under the pCluster model we proposed, two objects are similar if they exhibit a coherent pattern on a subset of dimensions. The new similarity concept models a wide range of applications. For instance, in DNA microarray analysis, the expression levels of two genes may rise and fall synchronously in response to a set of environmental stimuli. Although the magnitude of their expression levels may not be close, the patterns they exhibit can be very much alike. Discovery of such clusters of genes is essential in revealing significant connections in gene regulatory networks. E-commerce applications, such as collaborative filtering, can also benefit from the new model, because it is able to capture not only the closeness of values of certain leading indicators but also the closeness of （purchasing, browsing, etc.） patterns exhibited by the customers. In addition to the novel similarity model, this paper also introduces an effective and efficient algorithm to detect such clusters, and we perform tests on several real and synthetic data sets to show its performance.
The task of clustering is to identify classes of similar objects among a set of objects. The definition of similarity varies from one clustering model to another. However, in most of these models the concept of similarity is often based on such metrics as Manhattan distance, Euclidean distance or other Lp distances. In other words, similar objects must have close values in at least a set of dimensions. In this paper, we explore a more general type of similarity. Under the pCluster model we proposed, two objects are similar if they exhibit a coherent pattern on a subset of dimensions. The new similarity concept models a wide range of applications. For instance, in DNA microarray analysis, the expression levels of two genes may rise and fall synchronously in response to a set of environmental stimuli. Although the magnitude of their expression levels may not be close, the patterns they exhibit can be very much alike. Discovery of such clusters of genes is essential in revealing significant connections in gene regulatory networks. E-commerce applications, such as collaborative filtering, can also benefit from the new model, because it is able to capture not only the closeness of values of certain leading indicators but also the closeness of （purchasing, browsing, etc.） patterns exhibited by the customers. In addition to the novel similarity model, this paper also introduces an effective and efficient algorithm to detect such clusters, and we perform tests on several real and synthetic data sets to show its performance.
