Mapping Of High-dimensional Data Research Articles

Dimensionality Reduction and Classification through PCA and LDA

formation explosion has occurred in most of the sciences and researches due to advances in data collection and storage capacity in last few decades. Advance datasets with large number of observations present new challenges in data, mining, analysis and classification. Traditional statistical method breaks down partly because of the increase in the number of variables associated with each observation which is known as high dimensional data. Much of the data is highly redundant which can be ignored to extract features of dataset. The process of mapping of high dimensional data to lower dimensional space in such a way to discard uninformative variance from the dataset or finding subspace in which data can be easily detected is known as Dimensionality Reduction. In this paper, well known techniques of Dimensionality Reduction namely Principle Component Analysis (PCA) and Linear Discriminant Analysis (LDA) are studied. Performance analysis is carried out on high dimensional data set UMIST, COIL and YALE which consists of images of objects and human faces. Classify the objects using knn classifier and naive bayes classifier to compare performance of these techniques. Difference between supervised and unsupervised learning is also inferred using these results. KeywordsDimensionality reduction, KNN, LDA, PCA, naive bayes.

Distance-preserving mapping of patterns to 3-space

The triangulation method is extended to a tetrahedron method for the distance-preserving mapping of high dimensional data points to 3-space. Each point is mapped so that its distances to three already mapped points are preserved. The choices of these points give a set of ways to display both local and global information. Example applications in pattern analysis are discussed.

An interactive-graphic subsystem for pattern analysis

This paper describes an interactive graphics system which is being used in the solution of both pattern recognition and pattern analysis problems. The paper concentrates on a pattern analysis subsystem of the larger On-Line Pattern Analysis and Recognition System (OLPARS), although its relationship to the larger system is discussed. The basic algorithm underlying the subsystem is a non-linear mapping of high dimensional data to a two- or three-dimensional space. Several graphic interactive options are explained along with example applications in the design of a system for the classification of hand printed characters.