Exploring Classification of Topological Priors With Machine Learning for Feature Extraction.

Area of Science:

• Data science
• Computer vision
• Computational topology

Background:

• Abstract data representations enhance scientific interpretation.
• Pixel-level segmentation using deep neural networks (e.g., U-Net) is a common approach.
• Topological analysis offers an alternative framework for data segmentation.

Purpose of the Study:

• To develop and demonstrate a novel approach to data segmentation using learnable topological elements.
• To present topological analysis as a viable alternative to traditional pixel-level segmentation methods.
• To evaluate the accuracy, execution time, and data requirements of the proposed method.

Main Methods:

• Creation of learnable topological elements.
• Application of machine learning (ML) techniques for classification based on topological features.
• Utilizing Morse-Smale complexes for encoding gradient flow behavior.
• Comparison with pixel-level classification methods.

Main Results:

• The topological approach demonstrates comparable accuracy to pixel-level classification.
• The proposed method shows improved execution time.
• This approach requires significantly less training data compared to traditional methods.
• Topological elements reduce the learning space and incorporate learnable geometries and connectivity.

Conclusions:

• Learnable topological elements provide a viable and efficient alternative for data segmentation.
• This approach leverages geometric priors and machine learning for robust classification.
• The method is empirically motivated and suitable for various applications requiring segmentation.