G²BFNN: Generalized geodesic basis function neural network.

Area of Science:

• Machine Learning
• Data Science
• Computational Geometry

Background:

• Real-world data often resides on low-dimensional manifolds within high-dimensional spaces.
• Effective feature representation requires accurately capturing intrinsic data characteristics on these manifolds.
• Existing methods struggle with extracting robust spatial distribution features from complex manifold structures.

Purpose of the Study:

• To propose a novel neural network architecture, the generalized geodesic basis function neural network (G²BFNN), for enhanced feature extraction on manifolds.
• To develop a generalized geodesic distance metric (G²DM) by learning the manifold structure.
• To introduce a specific implementation, the discriminative local preserving projection-based G²BFNN (DLPP-G²BFNN), for improved data representation.

Main Methods:

• The proposed G²BFNN architecture utilizes generalized geodesic basis functions (G²BF) defined by a learned G²DM.
• The DLPP-G²BFNN comprises a manifold structure learning module (MSLM) and a network mapping module (NMM).
• MSLM employs a supervised adjacency graph to learn manifold structure, preserving local geometry and enhancing feature discriminability.

Main Results:

• The DLPP-G²BFNN effectively extracts spatial distribution features reflecting intrinsic manifold characteristics.
• Experimental results show superior recognition performance compared to Euclidean distance-based methods.
• The proposed network achieved higher recognition rates with fewer kernels than existing approaches.

Conclusions:

• The G²BFNN architecture offers a generalized and scalable approach for manifold data analysis.
• DLPP-G²BFNN demonstrates superior ability in revealing essential spatial structure compared to traditional methods.
• The proposed method provides a powerful tool for feature representation and recognition in manifold learning.