Clustering Using Grid-based Method, Lecture notes of Data Mining

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A presentation on

STING: Statistical Information

Grid (Grid–Based Methods )

By:

Binko Toure

Favour Iwoni

Tara Chandra

Shrestha

Grid-Based Clustering Methods

• (^) The clustering methods discussed so far are data driven: they partition the set of objects and adopt to the distribution of the objects in the embedding space.
• (^) Algorithms are query dependent. They are built for one query and generally no use for other query. We need a separate scan for each query, hence computation complexity at least O(n).
• (^) This method takes a space-driven approach by partitioning the embedding space into cells independent of the distribution of the input objects.
• (^) Uses multi-resolution grid data structure
• (^) Quantizes the object space into a finite number of cells that form a grid structure on which all of the operation for clustering are performed.
• (^) Develop hierarchical structure out of a given data and answer various queries efficiently. Every level of Hierarchy consists of cells.

Features & Challenges of a typical grid-based algorithm

• (^) Efficiency & Scalability : # of cells << # of data points
• (^) Uniformity: Uniform, hard to handle highly irregular data distributions
• (^) Locality: Limited by predefined cell sizes, borders, and the density threshold
• (^) Curse of dimensionality: Hard to cluster high-dimensional data

Advantages of Grid-based Clustering Algorithms

• (^) Fast:  (^) No distance computations  (^) Clustering is performed on summaries and not individual objects; complexity is usually O(#- populated-grid-cells) and not O(# data objects)  (^) Easy to determine which clusters are neighboring
• (^) Shapes are limited to union of grid-cells 5

STING: Algorithm (2) 7 The summarized pseudocodes for the STING algorithm are as follows:

STING: Query Processing(3) Used a top-down approach to answer spatial data queries

1. Start from a pre-selected layer—typically with a small number of cells
2. From the pre-selected layer until you reach the bottom layer do the following:

• (^) For each cell in the current level compute the

confidence interval indicating a cell’s relevance to a

given query;

• (^) If it is relevant, include the cell in a cluster
• (^) If it irrelevant, remove cell from further consideration
• (^) otherwise, look for relevant cells at the next lower layer

3. Combine relevant cells into relevant regions (based on grid-neighborhood) and return the so obtained clusters as your answers.