Metric Driven Classification: A Non-Parametric Approach Based on the Henze-Penrose Test Statistic

Area of Science:

• Computer Vision and Pattern Recognition
• Machine Learning
• Statistical Analysis

Background:

• Entropy-based divergence measures are effective but computationally expensive for high-dimensional data.
• Resource-limited applications face challenges with direct probability density estimation.
• Need for efficient metrics to assess inter-class separability and guide classification.

Purpose of the Study:

• To investigate the Henze-Penrose test statistic as a non-parametric, distribution-free metric.
• To obtain reliable bounds for k-nearest neighbors (k-NN) classification accuracy.
• To utilize these bounds for evaluating pre-processing techniques and feature selection.

Main Methods:

• Utilized the Henze-Penrose test statistic, a non-parametric metric.
• Applied the metric to estimate bounds for k-NN classification accuracy.
• Conducted simulations to validate the metric's performance and reliability.

Main Results:

• The Henze-Penrose test statistic effectively estimates inter-class separability.
• Simulation results confirm the metric's reliability in bounding k-NN classification accuracy.
• The proposed bounds successfully evaluated pre-processing methods and feature selection efficacy.

Conclusions:

• The Henze-Penrose test statistic offers an efficient alternative to complex divergence measures.
• This metric provides a reliable tool for assessing classification performance in various applications.
• The bounds derived are valuable for optimizing pre-processing and reducing feature dimensionality.