Clustering as Approximation by Constrained Projectors: Theory and Guarantees
Quick summary
arXiv:2608.29102v1 Announce Type: new Abstract: This paper develops a unified theoretical framework showing that a broad family of clustering methods, including k-means, fuzzy c-means, kernel k-means, kernel FCM, and spectral clustering, can all be expressed as structured low-rank projectors acting on a signal-derived matrix. By formulating each method as an instance of min over B in C of ||M - M P_B||_F^2, with different constraint sets C, we establish a common optimization template that clarifies the algebraic links among hard, fuzzy, kernel-induced, and orthonormal projections. Within this
Key takeaways
- arXiv:2608.29102v1 Announce Type: new Abstract: This paper develops a unified theoretical framework showing that a broad family of clustering methods, including k-means, fuzzy c-means, kernel k-means, kernel FCM, and spectral clustering, can all be expressed as structured low-rank projectors acting on a signal-derived matrix.
- By formulating each method as an instance of min over B in C of ||M - M P_B||_F^2, with different constraint sets C, we establish a common optimization template that clarifies the algebraic links among hard, fuzzy, kernel-induced, and orthonormal projections.
Why it matters
The value of this work lies as much in how it was tested as in the claim itself. Sample design, baselines, uncertainty and replication help separate a laboratory result from real-world impact.
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