Localized Multiple Kernel Learning With Dynamical Clustering and Matrix Regularization

Multi-kernel clustering with tensor fusion on Grassmann manifold for high-dimensional genomic data

The high dimensionality and noise challenges in genomic data make it difficult for traditional clustering methods. Existing multi-kernel clustering methods aim to improve the quality of the affinity matrix by learning a set of base kernels, thereby enhancing clustering performance. However, directly learning from the original base kernels presents challenges in handling errors and redundancies when dealing with high-dimensional data, and there is still a lack of feasible multi-kernel fusion strategies. To address these issues, we propose a Multi-Kernel Clustering method with Tensor fusion on Grassmann manifolds, called MKCTM. Specifically, we maximize the clustering consensus among base kernels by imposing tensor low-rank constraints to eliminate noise and redundancy. Unlike traditional kernel fusion approaches, our method fuses learned base kernels on the Grassmann manifold, resulting in a final consensus matrix for clustering. We integrate tensor learning and fusion processes into a unified optimization model and propose an effective iterative optimization algorithm for solving it. Experimental results on ten datasets, comparing against 12 popular baseline clustering methods, confirm the superiority of our approach. Our code is available at https://github.com/foureverfei/MKCTM.git.

One-Class Classification Using ℓp-Norm Multiple Kernel Fisher Null Approach

We address the one-class classification (OCC) problem and advocate a one-class MKL (multiple kernel learning) approach for this purpose. To this aim, based on the Fisher null-space OCC principle, we present a multiple kernel learning algorithm where an $\ell _{p}$ -norm regularisation ( $p \geq 1$ ) is considered for kernel weight learning. We cast the proposed one-class MKL problem as a min-max saddle point Lagrangian optimisation task and propose an efficient approach to optimise it. An extension of the proposed approach is also considered where several related one-class MKL tasks are learned concurrently by constraining them to share common weights for kernels. An extensive evaluation of the proposed MKL approach on a range of data sets from different application domains confirms its merits against the baseline and several other algorithms.

SVRG-MKL: A Fast and Scalable Multiple Kernel Learning Solution for Features Combination in Multi-Class Classification Problems

In this paper, we present a novel strategy to combine a set of compact descriptors to leverage an associated recognition task. We formulate the problem from a multiple kernel learning (MKL) perspective and solve it following a stochastic variance reduced gradient (SVRG) approach to address its scalability, currently an open issue. MKL models are ideal candidates to jointly learn the optimal combination of features along with its associated predictor. However, they are unable to scale beyond a dozen thousand of samples due to high computational and memory requirements, which severely limits their applicability. We propose SVRG-MKL, an MKL solution with inherent scalability properties that can optimally combine multiple descriptors involving millions of samples. Our solution takes place directly in the primal to avoid Gram matrices computation and memory allocation, whereas the optimization is performed with a proposed algorithm of linear complexity and hence computationally efficient. Our proposition builds upon recent progress in SVRG with the distinction that each kernel is treated differently during optimization, which results in a faster convergence than applying off-the-shelf SVRG into MKL. Extensive experimental validation conducted on several benchmarking data sets confirms a higher accuracy and a significant speedup of our solution. Our technique can be extended to other MKL problems, including visual search and transfer learning, as well as other formulations, such as group-sensitive (GMKL) and localized MKL (LMKL) in convex settings.