The idea of representation has been used in various fields of study from data analysis to political science. In this paper, we define representativeness and describe a method to isolate data points that can represent the entire data set. Also, we show how the minimum set of representative data points can be generated. We use data from GLOBE (a project to study the effects on Land Change based on a set of parameters that include temperature, forest cover, human population, atmospheric parameters and many other variables) to test & validate the algorithm. Principal Component Analysis (PCA) is used to reduce the dimensions of the multivariate data set, so that the representative points can be generated efficiently and its Representativeness has been compared against Random Sampling of points from the data set.
Clustering techniques are of different types and mainly divided into 2 categories:- - These techniques create groups of points which are similar to each other. Once a group is formed, it creates the next level by combining groups that are similar. In this way, a hierarchy of groups is created with all groups merged at the top most level of the hierarchy. The structure is called a dendogram @cite_15 . - These techniques try to create a single partition in the dataset as compared to a dendogram which may have a high computation time. The problem occurs when the size of the dataset is large. Partitional techniques try to optimize a certain function based on which the partition is made. Calculating the optimal set of values for the function could again be computationally expensive. Hence an approximation is calculated by executing the algorithm multiple times on the same dataset until the function reaches a state that is to optimal. For example, using squared error a as function to create partitions @cite_15 . The algorithm is executed until the squared error is reduced to a value that is below a certain pre-determined threshold.
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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 overviewof 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.