arXiv research

DKLM learns adaptive kernels for robust nonlinear subspace clustering.

Proposes a new method for nonlinear Bayesian updates using ensemble kernel regression.

Adapts manifold structure for better clustering performance.

The development of algorithms for unsupervised pattern recognition by nonlinear clustering is a notable problem in data science. Markov clustering (MCL) is a renowned algorithm that simulates stochastic flows on a network of sample similarities to detect the structural organization of clusters in the data, but it has n…

A recent theoretical analysis shows the equivalence between non-negative matrix factorization (NMF) and spectral clustering based approach to subspace clustering. As NMF and many of its variants are essentially linear, we introduce a nonlinear NMF with explicit orthogonality and derive general kernel-based orthogonal m…

A new method clusters heterogeneous subgroups for accurate causal learning.

Kernel measures similarity of nonlinear causal structures in heterogeneous populations.

Proposes a new K-means method for efficient clustering of nonlinear data.

Robust method learns nonlinear structures robustly to noise.

Kernel methods obtain superb performance in terms of accuracy for various machine learning tasks since they can effectively extract nonlinear relations. However, their time complexity can be rather large especially for clustering tasks. In this paper we define a general class of kernels that can be easily approximated …

A new clustering algorithm inspired by Wittgenstein's philosophy.

Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the incorporation of nonlinearity. However, most existing kernel-based graph learning mechanism…

Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However, similarity measurement is challenging because it is usually impacted by many factors, e.g., the choice of similarity metric, neighborhood size, scale of data, noise an…

Proposes MFPC for cross-manifold clustering.

We study the concentration of random kernel matrices around their mean. We derive nonasymptotic exponential concentration inequalities for Lipschitz kernels assuming that the data points are independent draws from a class of multivariate distributions on $\mathbb R^d$, including the strongly log-concave distributions u…

The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common divergences on distributions such as Kullback-Leibler or Jensen-Shannon, it is (weakly) co…

Traditional plane-based clustering methods measure the cost of within-cluster and between-cluster by quadratic, linear or some other unbounded functions, which may amplify the impact of cost. This letter introduces a ramp cost function into the plane-based clustering to propose a new clustering method, called ramp-base…

Kernel-spectral embedding learns low-dim. structures from noisy data.

We study the use of "sign $α$-stable random projections" (where $0<α\leq 2$) for building basic data processing tools in the context of large-scale machine learning applications (e.g., classification, regression, clustering, and near-neighbor search). After the processing by sign stable random projections, the inner pr…

Kernel and Multiple Kernel Canonical Correlation Analysis (CCA) are employed to classify schizophrenic and healthy patients based on their SNPs, DNA Methylation and fMRI data. Kernel and Multiple Kernel CCA are popular methods for finding nonlinear correlations between high-dimensional datasets. Data was gathered from …

SimpleMKKM improves multi-kernel clustering efficiency.

Study provides guarantees for kernel clustering under non-parametric mixtures.

Kernel clustering algorithm improved for large datasets using incomplete Cholesky factorization.

To cluster data that are not linearly separable in the original feature space, $k$-means clustering was extended to the kernel version. However, the performance of kernel $k$-means clustering largely depends on the choice of kernel function. To mitigate this problem, multiple kernel learning has been introduced into th…

Paper improves clustering risk bounds for kernel k-means.

Most existing approaches address multi-view subspace clustering problem by constructing the affinity matrix on each view separately and afterwards propose how to extend spectral clustering algorithm to handle multi-view data. This paper presents an approach to multi-view subspace clustering that learns a joint subspace…

A new distributed clustering framework using distributional kernel.

Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good kernel has to be chosen. Picking a good kernel is a very challenging problem in its…

Kernel K-means clusters probability distributions.

New clustering method using point-set kernel measures similarity.

Unified analysis for nonlinear parametric models in Bayesian optimization.

Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called robust kernel principal component analysis (RKPCA) to decompose a partially cor…

Kernel $k$-means clustering can correctly identify and extract a far more varied collection of cluster structures than the linear $k$-means clustering algorithm. However, kernel $k$-means clustering is computationally expensive when the non-linear feature map is high-dimensional and there are many input points. Kernel …

Kernel discriminant analysis uses nonlinear embeddings to improve classification.

Paper studies kernel hyperparameters for clustering, proposing an efficient search method.

ABC learns context-aware representations for clustering.

In this paper, we compare 5 different nonlinear kernels: min-max, RBF, fRBF (folded RBF), acos, and acos-$χ^2$, on a wide range of publicly available datasets. The proposed fRBF kernel performs very similarly to the RBF kernel. Both RBF and fRBF kernels require an important tuning parameter ($γ$). Interestingly, for a …

Modern information processing relies on the axiom that high-dimensional data lie near low-dimensional geometric structures. This paper revisits the problem of data-driven learning of these geometric structures and puts forth two new nonlinear geometric models for data describing "related" objects/phenomena. The first o…

The term "CoRE kernel" stands for correlation-resemblance kernel. In many applications (e.g., vision), the data are often high-dimensional, sparse, and non-binary. We propose two types of (nonlinear) CoRE kernels for non-binary sparse data and demonstrate the effectiveness of the new kernels through a classification ex…

Kernelized convex clustering handles non-linear and non-convex data.

Kernel methods are popular in clustering due to their generality and discriminating power. However, we show that many kernel clustering criteria have density biases theoretically explaining some practically significant artifacts empirically observed in the past. For example, we provide conditions and formally prove the…

New method preserves spectral clustering performance under aggressive sparsification and quantization.

Survey of Laplacian-based methods for data dimensionality reduction and embedding.

Kernel VICReg improves SSL in RKHS, capturing nonlinear structures.

Novel algorithm identifies nonlinear Granger causal relationships using kernel ridge regression.

Framework simulates market microstructure with stable Hawkes processes.

Clustering is one of the most important unsupervised problems in machine learning and statistics. Among many existing algorithms, kernel k-means has drawn much research attention due to its ability to find non-linear cluster boundaries and its inherent simplicity. There are two main approaches for kernel k-means: SVD o…

Develops a framework for learning nonlinear operators using Mercer kernels.