Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization.

Area of Science:

• Data Science
• Machine Learning
• Applied Mathematics

Background:

• Tensor clustering is vital for analyzing complex multiarray data.
• Current subspace clustering methods vectorize data, losing structural information.
• Vectorization fails to leverage the full potential of tensor data structures.

Purpose of the Study:

• To develop a subspace clustering algorithm that bypasses data vectorization.
• To propose a novel heterogeneous Tucker decomposition model for tensor clustering.
• To enhance the exploitation of intrinsic structures in tensor datasets.

Main Methods:

• A novel heterogeneous Tucker decomposition model incorporating cluster membership.
• An iterative clustering algorithm alternating between modes of the tensor model.
• Optimization over the multinomial manifold using Riemannian geometry and a trust-region algorithm for the final mode.

Main Results:

• The proposed algorithm effectively clusters tensor data without vectorization.
• Numerical experiments demonstrate competitive performance against state-of-the-art tensor factorization methods.
• The approach preserves and utilizes complete structural information inherent in tensor datasets.

Conclusions:

• The novel tensor clustering algorithm offers an effective alternative to vectorization-based methods.
• The heterogeneous Tucker decomposition model advances subspace clustering for tensor data.
• This research provides a more complete structural analysis of multiarray datasets.