Reordered $k$-Means: A New Baseline for View-Unaligned Multi-View Clustering

Most current multi-view clustering methods necessitate that a sample's features be view-aligned or at least partially aligned across different views. Regrettably, real-world applications often fail to meet this requirement due to spatial, temporal, or spatiotemporal mismatches, resulting in the view-unaligned issue. To tackle this issue, we conceptualize the view-unaligned problem and demonstrate that it can be transformed into a view-aligned problem through reordering. Building on this concept, we introduce an innovative reorder matrix that realigns view-unaligned features. Utilizing these realigned features, we develop a sophisticated and efficient approach called Reordered <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-means (RKM), which merges NMF with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-means. Unlike traditional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-means, our method converts the binary challenge into an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{0}$</tex-math></inline-formula> problem, confirming the merit of this advancement. Furthermore, RKM's efficacy is affirmed on benchmarks, indicating substantial enhancements in handling the view-unaligned issue and maintaining competitive results with view-aligned problems.