SSRSC

SSRSC applies a Scaled Simplex Representation to subspace clustering by leveraging the self-expressive property to produce non-negative coefficient matrices with coefficient vectors summing to a scalar for improved subspace identification.

Key Features:

• Self-Expressive Property: Exploits that each data point can be linearly represented by other points within the same subspace.
• Scaled Simplex Representation (SSR): Constrains the coefficient matrix to non-negative entries and enforces each coefficient vector to sum to a scalar value.
• Linear Equality-Constrained Problem: Reformulates subspace clustering as a linear equality-constrained optimization problem.
• ADMM Optimization: Solves the equality-constrained optimization under the alternating direction method of multipliers (ADMM) framework.
• Preservation of Data Correlations: Avoids exponentiation or absolute symmetrization of coefficient entries to maintain inherent data correlations.
• Flexible Constraints: Replaces affine constraints with more flexible conditions suited to practical datasets.

Scientific Applications:

• Bioinformatics: Enables precise subspace clustering of high-dimensional biological data.
• Image Processing: Supports segmentation and clustering tasks in high-dimensional image feature spaces.
• Signal Analysis: Facilitates identification of underlying subspaces in complex signal datasets.

Methodology:

Formulates subspace clustering as a linear equality-constrained optimization with non-negative, sum-to-scalar coefficient vectors based on the self-expressive property and solves it using the alternating direction method of multipliers (ADMM).