Parameter-Free Shifted Laplacian Reconstruction for Multiple Kernel Clustering

Dear Editor, This letter proposes a parameter-free multiple kernel clustering (MKC) method by using shifted Laplacian reconstruction. Traditional MKC can effectively cluster nonlinear data, but it faces two main challenges: 1) As an unsupervised method, it is up against parameter problems which makes the parameters intractable to tune and is unfeasible in real-life applications; 2) Only considers the clustering information, but ignores the interference of noise within Laplacian. To solve these problems, this letter proposes a parameter-free shifted Laplacian reconstruction (PF-SLR) method for MKC, relying on shifted Laplacian rather than traditional Laplacian. Specifically, we treat each base kernel as an affinity graph, and construct its corresponding shifted Laplacian with only low-frequency components. Then, by convex combination reconstructing a high-quality shifted Laplacian, PF-SLR can preserve the energy information and clustering information on the largest eigenvalues simultaneously. After that, the cluster assignments can be obtained by performing
$k$
-means on the co-product, without any parameters involved throughout the whole process. Compared with eight state-of-the-art methods, the effectiveness and feasibility of our method are verified.