Generalized Haar DWT and transformations between decision trees and neural networks

Area of Science:

• Computer Science
• Machine Learning
• Data Analysis

Background:

• Traditional discrete wavelet transforms (DWT) are limited to numerical data and lower dimensions.
• Transforming multiclass data and high-dimensional domains presents significant computational challenges.
• Existing methods struggle with efficient representation and summarization of complex datasets, particularly decision trees.

Purpose of the Study:

• To introduce a novel three-fold improved Haar discrete wavelet transform (DWT).
• To adapt DWT for efficient transformation of multiclass-valued functions in multidimensional domains.
• To enable the transformation of multiclass-valued decision trees into alternative useful representations.

Main Methods:

• Development of a multidimensional, multiclass Haar discrete wavelet transform (DWT).
• Application of dynamic programming to minimize nontrivial wavelet coefficients for data summarization.
• Implementation of a spatially localized algorithm with linear time complexity post-sorting.

Main Results:

• The new DWT efficiently transforms multiclass functions and decision trees in multidimensional spaces.
• Dynamic programming minimizes the number of coefficients needed to summarize training sets or decision trees.
• The algorithm achieves linear time complexity concerning the number of training samples after sorting.

Conclusions:

• The multidimensional, multiclass DWT offers a powerful tool for data summarization and representation.
• Potential applications include direct learning of decision trees, conversion to neural networks, and creating interpretable E-trees.
• While convergence may degrade in very high dimensions, the method shows promise for complex data analysis and visualization.