A Novel Data Instance Reduction Technique using Linear Feature Reduction

Abstract

Representation of structurally significant data is indispensable to modern research. The need for dimensionality reduction finds its foray in varied genres viz-a-viz, Structural Bioinformatics, Machine Learning, Robotics, Artificial Intelligence, to name a few. The number of points required to effectively capture the essence of a structure is an intuitive decision. Feature reduction methods like Principal Component Analysis (PCA) have already been explored and proven to be an aid in classification and regression. In this work we present a novel approach that first performs PCA on a data set for reduction of features and then attempts to reduce the number of points itself to get rid of the points that have nothing or very little new to offer. The algorithm was tested on various kinds of data (points representing a spiral, protein coordinates, the Iris dataset prevalent in Machine Learning, face image) and the results agree with the quantitative tests applied. In each case, it turns out that a lot of data instances need not be stored to make any kind of decision. Matlab and R simulations were used to assess the structures with reduced data points. The time complexity of the algorithm is linear in the degrees of freedom of the data if the data is in a natural order.

Characterizing Protein Conformational Spaces using Efficient Data Reduction and Algebraic Topology

“…This algorithm removes data instances that are deemed not to contribute to the variance in the data. More details about the algorithm itself and the results it produced can be found in [53,54]. The result of this step produces a nonredundant representation of the dataset which now has fewer instances but its important properties that account for maximum variance present in it are preserved.…”

Characterizing Protein Conformational Spaces using Dimensionality Reduction and Algebraic Topology

“…Our algorithm removes data instances that are deemed not to contribute to the variance in the data. More details about the algorithm itself and the results it produced can be found in [53], [54]. The result of this step produces a non-redundant representation of the dataset which now has fewer instances but its important properties that account for maximum variance present in it are preserved.…”