Proprties of biclustering algorithms and a novel biclustering technique based on relative density

Biclustering is found to be useful in areas like data mining and bioinformatics. The term biclustering involves searching subsets of observations and features forming coherent structure. This can be interpreted in different ways like spatial closeness, relation between features for selected observations etc. This paper discusses different properties, objectives and approaches of biclustering algorithms. We also present an algorithm which detects feature relation based biclusters using density based techniques. Here we use relative density of regions to identify biclusters embedded in the data. Properties of this algorithm are discussed and demonstrated using artificial datasets. Proposed method is seen to give better results on these datasets using paired right tailed t test. Usefulness of proposed method is also demonstrated using real life datasets.

A new estimate of mutual information based measure of dependence between two variables: properties and fast implementation

This article proposes a new method to estimate an existing mutual information based dependence measure using histogram density estimates. Finding a suitable bin length for histogram is an open problem. We propose a new way of computing the bin length for histogram using a function of maximum separation between points. The chosen bin length leads to consistent density estimates for histogram method. The values of density thus obtained are used to calculate an estimate of an existing dependence measure. The proposed estimate is named as Mutual Information Based Dependence Index (MIDI). Some important properties of MIDI have also been stated. The performance of the proposed method has been compared to generally accepted measures like Distance Correlation (dcor), Maximal Information Coefficient (MINE) in terms of accuracy and computational complexity with the help of several artificial data sets with different amounts of noise. The proposed method is able to detect many types of relationships between variables, without making any assumption about the functional form of the relationship. The power statistics of proposed method illustrate their effectiveness in detecting non linear relationship. Thus, it is able to achieve generality without a high rate of false positive cases. MIDI is found to work better on a real life data set than competing methods. The proposed method is found to overcome some of the limitations which occur with dcor and MINE. Computationally, MIDI is found to be better than dcor and MINE, in terms of time and memory, making it suitable for large data sets.