A PROBABILISTIC ℓ1 METHOD FOR CLUSTERING HIGH-DIMENSIONAL DATA

In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the unreliability of distances in very high-dimensional spaces. We propose a probabilistic, distance-based, iterative method for clustering data in very high-dimensional space, using the ℓ1-metric that is less sensitive to high dimensionality than the Euclidean distance. For K clusters in ℝ n , the problem decomposes to K problems coupled by probabilities, and an iteration reduces to finding Kn weighted medians of points on a line. The complexity of the algorithm is linear in the dimension of the data space, and its performance was observed to improve significantly as the dimension increases.

Improved probabilistic distance based locality preserving projections method to reduce dimensionality in large datasets

<p>In this paper, a dimensionality reduction is achieved in large datasets using the proposed distance based Non-integer Matrix Factorization (NMF) technique, which is intended to solve the data dimensionality problem. Here, NMF and distance measurement aim to resolve the non-orthogonality problem due to increased dataset dimensionality. It initially partitions the datasets, organizes them into a defined geometric structure and it avoids capturing the dataset structure through a distance based similarity measurement. The proposed method is designed to fit the dynamic datasets and it includes the intrinsic structure using data geometry. Therefore, the complexity of data is further avoided using an Improved Distance based Locality Preserving Projection. The proposed method is evaluated against existing methods in terms of accuracy, average accuracy, mutual information and average mutual information.</p>