A parameter free relative density based biclustering method for identifying non-linear feature relations.

The existing biclustering algorithms often depend on assumptions like monotonicity or linearity of feature relations for finding biclusters. Though a few algorithms overcome this problem using density-based methods, they tend to miss out many biclusters because they use global criteria for identifying dense regions. The proposed method, PF-RelDenBi, uses local variations in marginal and joint densities for each pair of features to find the subset of observations, forming the basis of the relation between them. It then finds the set of features connected by a common set of observations using a non-linear feature relation index, resulting in a bicluster. This approach allows us to find biclusters based on feature relations, even if the relations are non-linear or non-monotonous. Additionally, the proposed method does not require the user to provide any parameters, allowing its application to datasets from different domains. To study the behaviour of PF-RelDenBi on datasets with different properties, experiments were carried out on sixteen simulated datasets and the performance has been compared with eleven state-of-the-art algorithms. The proposed method is seen to produce better results for most of the simulated datasets. Experiments were conducted with five benchmark datasets and biclusters were detected using PF-RelDenBi. For the first two datasets, the detected biclusters were used to generate additional features that improved classification performance. For the other three datasets, the performance of PF-RelDenBi was compared with the eleven state-of-the-art methods in terms of accuracy, NMI and ARI. The proposed method is seen to detect biclusters with greater accuracy. The proposed technique has also been applied to the COVID-19 dataset to identify some demographic features that are likely to affect the spread of COVID-19.