High Dimensional Mode Hunting Using Pettiest Components Analysis.

Area of Science:

• Multivariate statistics
• Data dimensionality reduction
• Pattern recognition

Background:

• Principal components analysis (PCA) is a standard technique for dimensionality reduction.
• Traditional PCA focuses on components with the largest variance.
• The importance of low-variance components in specific applications like mode detection is underexplored.

Purpose of the Study:

• To introduce and validate "pettiest component analysis" (PCA) for mode detection.
• To demonstrate the superiority of pettiest components over principal components in specific statistical distributions.
• To show improved information gain and pattern recognition using pettiest components.

Main Methods:

• Theoretical proof for optimal volume boxes with multivariate normal and Laplace distributions.
• Implementation of pettiest component analysis for dimensionality reduction.
• Information gain measurement using active information.
• Application to simulations and handwritten digit recognition (MNIST database).

Main Results:

• Pettiest component analysis yields boxes of optimal volume for mode detection.
• This method achieves greater information gain compared to traditional PCA.
• Pettiest components outperform principal components in recognizing handwritten digits from the MNIST dataset.

Conclusions:

• Pettiest component analysis is a valuable alternative to PCA for mode detection tasks.
• Focusing on low-variance components can lead to significant improvements in data analysis and pattern recognition.
• The findings have implications for various fields requiring accurate mode detection and pattern identification.