# Encyclopedia of Biometrics

Living Edition
| Editors: Stan Z. Li, Anil K. Jain

# Linear Dimension Reduction Techniques

• Wei-Shi Zheng
• Jian-Huang Lai
• Pong C. Yuen
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27733-7_9220-2

## Definition

Linear dimension reduction technique reduces the dimension of biometric data using a linear transform. The linear transform is always learned by optimization of a criterion. Biometric data are then projected onto the range space of this transform. Subsequent processing will then be performed in that lower-dimensional space.

## Introduction

In biometrics, data are always represented in vectors and the dimensionality is always very high. It would be computationally expensive to process them directly by many algorithms. Moreover, it is sometimes desirable to exact robust, informative or discriminative information from the data. For these reasons, a lower-dimensional subspace is always found such that most important information of data is retained for linear representation. Among the techniques for learning a subspace, linear dimension reduction methods are always popular.

Suppose given a set of N data samples { x 1, ⋯ ,  x N}, where \(\mathbf{x}_{i}...

## Keywords

Linear Discriminant Analysis Independent Component Analysis Dimension Reduction Independent Component Analysis Nonnegative Matrix Factorization
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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