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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

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Matrix exponential based discriminant locality preserving projections for feature extraction.

Gui-Fu Lu¹, Yong Wang¹, Jian Zou¹

¹School of Computer Science and Information, AnHui Polytechnic University, WuHu, AnHui 241000, China.

Neural Networks : the Official Journal of the International Neural Network Society

|November 3, 2017

Summary

We introduce matrix exponential based discriminant locality preserving projections (MEDLPP) to solve the small sample size problem in feature extraction. Our efficient algorithm improves performance over existing discriminant analysis methods.

Keywords:

Dimensionality reduction Discriminant locality preserving projections Linear discriminant analysis Matrix exponential

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Area of Science:

Machine Learning
Pattern Recognition
Manifold Learning

Background:

Discriminant locality preserving projections (DLPP) is effective for pattern recognition but struggles with the small sample size (SSS) problem.
The SSS problem occurs when the number of samples is less than the dimensionality of the data.

Purpose of the Study:

To propose a novel method, matrix exponential based discriminant locality preserving projections (MEDLPP), to address the SSS problem in DLPP.
To develop an efficient algorithm for solving the MEDLPP problem and generalize the approach.

Main Methods:

Utilized matrix exponential properties to create a positive definite matrix, overcoming the SSS issue.
Developed an efficient algorithm to reduce the high computational complexity associated with MEDLPP.
Generalized the efficient solving strategy for broader application in matrix exponential-based methods.

Main Results:

The proposed MEDLPP method effectively handles the SSS problem.
The efficient algorithm significantly reduces computational complexity.
Experimental results show superior performance compared to state-of-the-art discriminant analysis techniques.

Conclusions:

MEDLPP offers an elegant solution to the SSS problem in feature extraction.
The efficient algorithm makes MEDLPP practical for real-world applications.
This work advances discriminant analysis methods, particularly for datasets with limited samples.