Local-Topology-Based Scaling for Distance Preserving Dimension Reduction Method to Improve Classification of Biomedical Data-Sets

• Main Authors: Karaj Khosla, Indra Prakash Jha, Ajit Kumar, Vibhor Kumar
• Format: Article
• Language: English
• Published: MDPI AG 2020-08-01
• Series: Algorithms
• Subjects: dimension reduction; distance preserving; local topology; multidimensional scaling (MDS)
• Online Access: https://www.mdpi.com/1999-4893/13/8/192

Dimension reduction is often used for several procedures of analysis of high dimensional biomedical data-sets such as classification or outlier detection. To improve the performance of such data-mining steps, preserving both distance information and local topology among data-points could be more useful than giving priority to visualization in low dimension. Therefore, we introduce topology-preserving distance scaling (TPDS) to augment a dimension reduction method meant to reproduce distance information in a higher dimension. Our approach involves distance inflation to preserve local topology to avoid collapse during distance preservation-based optimization. Applying TPDS on diverse biomedical data-sets revealed that besides providing better visualization than typical distance preserving methods, TPDS leads to better classification of data points in reduced dimension. For data-sets with outliers, the approach of TPDS also proves to be useful, even for purely distance-preserving method for achieving better convergence.