Classification of histogram-valued data with support histogram machines.

Area of Science:

• Data Science
• Machine Learning
• Statistical Classification

Background:

• Advanced technologies generate complex data types, including histogram-valued data.
• Conventional classification methods struggle with histogram data as they require vector inputs.
• Existing methods often lose crucial distributional information by converting histograms to summary statistics.

Purpose of the Study:

• To propose a novel margin-based classifier, the support histogram machine (SHM), specifically for histogram-valued data.
• To address the limitations of conventional methods in preserving distributional information from histograms.
• To develop an effective classification approach for complex histogram-valued datasets.

Main Methods:

• Utilizing the support vector machine (SVM) framework for classification.
• Employing the Wasserstein-Kantorovich metric to accurately measure distances between histograms.
• Solving the proposed optimization problem through a dual approach for computational efficiency.

Main Results:

• The support histogram machine (SHM) was tested using both simulated and real-world datasets.
• SHM demonstrated superior performance compared to traditional methods relying on summary values.
• The proposed method effectively leverages the full distributional information within histograms.

Conclusions:

• The support histogram machine (SHM) offers a significant advancement in classifying histogram-valued data.
• SHM preserves and utilizes the rich distributional information inherent in histogram data.
• This approach provides a more accurate and robust classification solution for complex data structures.