Data Mining_ Concepts and Techniques - Jiawei Han [292]
A cluster in DENCLUE is a set of density attractors X and a set of input objects C such that each object in C is assigned to a density attractor in X, and there exists a path between every pair of density attractors where the density is above ξ. By using multiple density attractors connected by paths, DENCLUE can find clusters of arbitrary shape.
DENCLUE has several advantages. It can be regarded as a generalization of several well-known clustering methods such as single-linkage approaches and DBSCAN. Moreover, DENCLUE is invariant against noise. The kernel density estimation can effectively reduce the influence of noise by uniformly distributing noise into the input data.
10.5. Grid-Based Methods
The clustering methods discussed so far are data-driven—they partition the set of objects and adapt to the distribution of the objects in the embedding space. Alternatively, a grid-based clustering method takes a space-driven approach by partitioning the embedding space into cells independent of the distribution of the input objects.
The grid-based clustering approach uses a multiresolution grid data structure. It quantizes the object space into a finite number of cells that form a grid structure on which all of the operations for clustering are performed. The main advantage of the approach is its fast processing time, which is typically independent of the number of data objects, yet dependent on only the number of cells in each dimension in the quantized space.
In this section, we illustrate grid-based clustering using two typical examples. STING (Section 10.5.1) explores statistical information stored in the grid cells. CLIQUE (Section 10.5.2) represents a grid- and density-based approach for subspace clustering in a high-dimensional data space.
10.5.1. STING: STatistical INformation Grid
STING is a grid-based multiresolution clustering technique in which the embedding spatial area of the input objects is divided into rectangular cells. The space can be divided in a hierarchical and recursive way. Several levels of such rectangular cells correspond to different levels of resolution and form a hierarchical structure: Each cell at a high level is partitioned to form a number of cells at the next lower level. Statistical information regarding the attributes in each grid cell, such as the mean, maximum, and minimum values, is precomputed and stored as statistical parameters. These statistical parameters are useful for query processing and for other data analysis tasks.
Figure 10.19 shows a hierarchical structure for STING clustering. The statistical parameters of higher-level cells can easily be computed from the parameters of the lower-level cells. These parameters include the following: the attribute-independent parameter, count; and the attribute-dependent parameters, mean, stdev (standard deviation), min (minimum), max (maximum), and the type of distribution that the attribute value in the cell follows such as normal, uniform, exponential, or none (if the distribution is unknown). Here, the attribute is a selected measure for analysis such as price for house objects. When the data are loaded into the database, the parameters count, mean, stdev, min, and max of the bottom-level cells are calculated directly from the data. The value of distribution may either be assigned by the user if the distribution type is known beforehand or obtained by hypothesis tests such as the χ2 test. The type of distribution of a higher-level cell can be computed based on the majority of distribution types of its corresponding lower-level cells in conjunction with a threshold filtering process. If the distributions of the lower-level cells disagree with each other and fail the threshold test, the distribution type of the high-level cell is set to none.
Figure 10.19 Hierarchical structure for STING clustering.
“How is this statistical information useful for query answering?” The statistical parameters can be used