Cluster Analysis

Introduction

Cluster analysis is finding similarities between data according to the characteristics found in the data and grouping similar data objects into clusters. A cluster is a collection of data objects in which objects similar to one another are put within the same cluster and dissimilar to the objects in the other clusters. Clusters analysis falls into the area of unsupervised learning as there are no pre-specified groups or classes. These are used typically as a stand-alone tool to get insight into data distribution or used as a pre-processing step for other algorithm. It is used in Pattern Recognition, Spatial Data Analysis, Image Processing, Market Research, Documents classification on the internet. It helps in City planning, Earth Quake studies, Insurance, stock selection and marketing programs.

A good clustering method produces high intra-class similarity and low inter-class similarity. The quality of a clustering result depends on both similarity measure used by the method and its implementation. Quality is usually expressed in terms of a distance function or metric.

Categorization of Algorithms

Clustering algorithms can be categorized into partitioning method, hierarchical methods, density-based methods, hierarchical methods, density-based methods, grid-based methods and model based methods. The most common among are partitioning method and Hierarchical approach. In partitioning approach, the objects are partition into k clustered on basis of distance (similarity/dissimilarity). This approach is depicted in the below diagram.

Issues with Partitioning Method (K-mean)

The problem with this approach is that number of clusters has to be specified in advance. Secondly it is not able to handle noisy data and outliers. This problem can be easily handled by Hierarchical clustering. In hierarchical clustering distance matrix is used for clustering so it does not required pre-specifying the number of clusters in advance. It only requires the termination conditions. The below diagram depicts the hierarchical clustering formation in an top down (agglomerative) and bottom up approach (divisive).

Dendrogram

Dendrogram shows how the clusters are merged. It decomposes the objects into a several levels of nested partitioning (tree). The clustering of the data objects is obtained by cutting the dendrogram at the desired level and then each connected component forms a cluster. As shown in the below figure, left diagram show two clusters (below the magenta line) while right diagram shows three clusters.

Uses of Hierarchical clustering in Finance

The hierarchical clustering methodology can be applied in stock selection of selected companies. Since the stock returns are likely to be similar in a region due to geography and macroeconomic conditions so identification of similar clusters allows one to track similar returns but different risks. After the identification of a cluster, the investor can used the output (clusters) according to his interest – for instance, he can look for same return stock and then choose to minimize risk or else he can pick a cluster of same risk stocks and high return. In this way the investor can profit (or lose less) using cluster analysis to select stock.

References

1. “Stock selection based on cluster analysis” by Costa, Cunha, Silva.
2. http://people.revoledu.com/kardi/tutorial/Clustering/dendogram.htm
3. http://en.wikipedia.org/wiki/Dendrogram
4. www.gersteinlab.org/courses/545/07-spr/slides/DM_clustering.ppt

Submitted By:

Mrityunjay Kapoor
12147
Group 5
Finance Batch of 2009-11
SIBM Bangalore.