Projection Matrix Optimization for Class Separation
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Solution Overview
Problem
Existing dimensionality reduction methods, such as those described in PTL 1, may not effectively separate classes in high-dimensional data, leading to inadequate separation of data points during processing.
Innovation Solution
An information processing apparatus and method that calculates a projection matrix based on an objective function incorporating both interclass and intraclass dispersion statistics, optimizing the matrix under constraints that prioritize specific class combinations to enhance separation, using techniques like WRLDA and PWRLDA for improved class separation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional dimensionality reduction methods are used, then the processing can be performed, but the class separation is insufficient
Solution Approach 1:
The patent modifies the objective function parameters by introducing a constraint that forces the projection matrix to prioritize separation of a specific class from other classes. This is achieved by changing the optimization parameters to include a class-specific constraint, thereby improving class separation while maintaining dimensionality reduction effectiveness
Solution Approach 2:
The patent applies local quality by focusing the dimensionality reduction on separating a specific class from other classes rather than treating all classes uniformly. The projection matrix is optimized to give special attention to the separation of a predetermined class, thereby improving local class separation quality
2Reliability
If the projection matrix is optimized without constraints, then the calculation is simpler, but the class separation for specific classes is insufficient
Solution Approach 1:
The patent introduces a constraint in the optimization process that gives special attention to separating a specific class from other classes. This constraint ensures that the projection matrix prioritizes the separation of the predetermined class, thereby improving local quality for specific class separation while adding manageable complexity to the optimization process
Data Source
AI summary
There is provided an information processing apparatus including a calculation means for calculating a projection matrix used for dimensionality reduction of a plurality of data based on an objective function. The objective function includes a first function including a first term indicating interclass dispersion of the plurality of data between a first class and a second class included in a plurality of classes and a second function including a second term indicating intraclass dispersion of the plurality of data in at least one of the first class and the second class. The calculation means performs optimization of the objective function under a constraint in which the first class and the second class are selected so that a combination of the first class and the second class includes a specific class.