Related papers: Validity of Clusters Produced By kernel-$k$-means …
We consider clustering in group decision making where the opinions are given by pairwise comparison matrices. In particular, the k-medoids model is suggested to classify the matrices since it has a linear programming problem formulation…
We construct a framework for studying clustering algorithms, which includes two key ideas: persistence and functoriality. The first encodes the idea that the output of a clustering scheme should carry a multiresolution structure, the second…
Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…
When solving data analysis problems it is important to integrate prior knowledge and/or structural invariances. This paper contributes by a novel framework for incorporating algebraic invariance structure into kernels. In particular, we…
If the same data is used for both clustering and for testing a null hypothesis that is formulated in terms of the estimated clusters, then the traditional hypothesis testing framework often fails to control the Type I error. Gao et al.…
Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the…
We prove the Berenstein-Zelevinsky conjecture that the quantized coordinate rings of the double Bruhat cells of all finite dimensional simple algebraic groups admit quantum cluster algebra structures with initial seeds as specified by [4].…
Multiple kernel methods based on k-means aims to integrate a group of kernels to improve the performance of kernel k-means clustering. However, we observe that most existing multiple kernel k-means methods exploit the nonlinear relationship…
K-means is one of the most widely used clustering algorithms in various disciplines, especially for large datasets. However the method is known to be highly sensitive to initial seed selection of cluster centers. K-means++ has been proposed…
Kernel-based K-means clustering has gained popularity due to its simplicity and the power of its implicit non-linear representation of the data. A dominant concern is the memory requirement since memory scales as the square of the number of…
Kernel power $k$-means (KPKM) leverages a family of means to mitigate local minima issues in kernel $k$-means. However, KPKM faces two key limitations: (1) the computational burden of the full kernel matrix restricts its use on extensive…
Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density.…
We review some important results by Gross, Hacking, Keel, and Kontsevich on cluster algebra theory, namely, the column sign-coherence of $C$-matrices and the Laurent positivity, both of which were conjectured by Fomin and Zelevinsky. We…
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…
The $k$-Means clustering problem on $n$ points is NP-Hard for any dimension $d\ge 2$, however, for the 1D case there exists exact polynomial time algorithms. Previous literature reported an $O(kn^2)$ time dynamic programming algorithm that…
The number of accidents and health diseases which are increasing at an alarming rate are resulting in a huge increase in the demand for blood. There is a necessity for the organized analysis of the blood donor database or blood banks…
The kernel $k$-means is an effective method for data clustering which extends the commonly-used $k$-means algorithm to work on a similarity matrix over complex data structures. The kernel $k$-means algorithm is however computationally very…
We prove general kernel theorems for operators acting between coorbit spaces. These are Banach spaces associated to an integrable representation of a locally compact group and contain most of the usual function spaces (Besov spaces,…
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, distances between…
The k-means clustering algorithm is a popular algorithm that partitions data into k clusters. There are many improvements to accelerate the standard algorithm. Most current research employs upper and lower bounds on point-to-cluster…