# A Statistical Study on Locally Linear Embedding Modified with Different Distance Metrics.

December 2015

## Date of Award

Winter 12-12-2016

## Institute Name (Publisher)

Indian Statistical Institute

## Document Type

Master's Dissertation

## Degree Name

Master of Technology

Computer Science

## Department

Electronics and Communication Sciences Unit (ECSU-Kolkata)

## Supervisor

Das, Swagatam (ECSU-Kolkata; ISI)

## Abstract (Summary of the Work)

High-dimensional data means data with large number of features and samples. Sometimes, the number of features may even be larger than the number of samples. So, it gets very difficult and computationally complex to handle such huge amount of data. High-dimensional data are obtained from different domains like engineering, informatics, biometrics, neuroimaging, etc. These data needs to be processed and classified or clustered while using in pattern recognition, image processing, information retrieval, computer vision, etc. Classifying these data is a difficult problem because of the enormous size of the data. Conventional classification methods can also handle such huge data but takes a lot of computational time which makes many classical techniques impractical. A trivial approach of solving this problem is to apply any dimensionality reduction technique followed by a classification method. There are many linear and non-linear dimensionality reduction techniques. Some of the popular methods are Principal Component Analysis, Linear Discriminant Analysis, Factor Analysis (linear), Sammonâ€™s Mapping, Locally Linear Embedding, Isomap, Local Tangent Space Alignment, Self-Organising Map, Laplacian Eigenmap (non-linear), etc. These dimensionality reduction techniques varies in terms of basic assumptions about data, principles, computational complexity, objectives (preserving local or global properties), etc.

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843064

## Control Number

ISI-DISS-2015-316