Hierarchical Neighbors Embedding.

Area of Science:

• Machine Learning
• Data Science
• Dimensionality Reduction

Background:

• Manifold learning excels with nonlinear data but struggles with sparsity.
• Sparse, high-dimensional data present challenges for obtaining satisfactory embeddings.
• Existing methods may fail to capture complex topological structures in sparse datasets.

Purpose of the Study:

• To introduce Hierarchical Neighbors Embedding (HNE) for improved manifold learning.
• To address the limitations of current techniques in handling data sparsity.
• To enhance the quality of embeddings for sparsely sampled high-dimensional data.

Main Methods:

• Proposing Hierarchical Neighbors Embedding (HNE) by hierarchically combining neighbors.
• Developing three HNE implementations based on topological connection and reconstruction analysis.
• Evaluating HNE on synthetic and real-world datasets.

Main Results:

• HNE methods achieve more faithful embeddings with improved topological and geometrical properties.
• HNE demonstrates significant advantages in embedding quality for general data distributions.
• HNE outperforms state-of-the-art manifold learning methods on sparse and weakly connected data.

Conclusions:

• HNE offers a robust solution for manifold learning with sparse data.
• The proposed method enhances local connections for better representation.
• HNE provides superior performance compared to existing techniques, especially for challenging datasets.