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view-specific eigenvectors

View-specific eigenvectors are the mathematical vectors obtained from the spectral decomposition of a similarity graph or Laplacian matrix that represents a single feature set or modality within a multi-view dataset. In multi-view learning and spectral clustering, each view provides an independent representation of the underlying data points, resulting in distinct graph Laplacians and corresponding eigenvectors that capture the geometry and clustering tendencies of that individual representation. Rather than computing a single global embedding directly from fused data, multi-view frameworks derive these individual embeddings to retain view-dependent relationships, subsequently applying alignment or co-regularization techniques across the different views to achieve a consistent and unified clustering structure.

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Co-regularized Multi-view Spectral Clustering

Co-regularized Multi-view Spectral Clustering

Abhishek Kumar, Piyush Rai, Hal Daumé

OrganizationsUniversity of MarylandUniversity of Utah

Why you should read this

Proposes a multi-view spectral clustering framework that co-regularizes graph Laplacians across different data representations to find consistent cluster assignments across diverse views.

In many clustering problems, we have access to multiple views of the data each of which could be individually used for clustering. Exploiting information from multiple views, one can hope to find a clustering that is more accurate than the ones obtained using the individual views. Often these different views admit same underlying clustering of the data, so we can approach this problem by looking for clusterings that are consistent across the views, i.e., corresponding data points in each view should have same cluster membership. We propose a spectral clustering framework that achieves this goal by co-regularizing the clustering hypotheses, and propose two co-regularization schemes to accomplish this. Experimental comparisons with a number of baselines on two synthetic and three real-world datasets establish the efficacy of our proposed approaches.

Added

2026-09-25