Related papers: A clustering tool for nucleotide sequences using L…
In spectral clustering, one defines a similarity matrix for a collection of data points, transforms the matrix to get the Laplacian matrix, finds the eigenvectors of the Laplacian matrix, and obtains a partition of the data using the…
A probabilistic clustering algorithm is proposed for the analysis of forensic DNA mixtures in which individual cells are isolated and short tandem repeats are amplified using the polymerase chain reaction to generate single cell…
This article proposes a first analysis of kernel spectral clustering methods in the regime where the dimension $p$ of the data vectors to be clustered and their number $n$ grow large at the same rate. We demonstrate, under a $k$-class…
Spectral clustering is a novel clustering method which can detect complex shapes of data clusters. However, it requires the eigen decomposition of the graph Laplacian matrix, which is proportion to $O(n^3)$ and thus is not suitable for…
Clustering of data sets is a standard problem in many areas of science and engineering. The method of spectral clustering is based on embedding the data set using a kernel function, and using the top eigenvectors of the normalized Laplacian…
We present clustering methods for multivariate data exploiting the underlying geometry of the graphical structure between variables. As opposed to standard approaches that assume known graph structures, we first estimate the edge structure…
Our previous experiments demonstrated that subsets collections of (short) documents (with several hundred entries) share a common normalized in some way eigenvalue spectrum of combinatorial Laplacian. Based on this insight, we propose a…
The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used for spectral clustering and community detection. However, in real-life applications the number of clusters or…
In clustering we normally output one cluster variable for each datapoint. However it is not necessarily the case that there is only one way to partition a given dataset into cluster components. For example, one could cluster objects by…
The aim of this study was to develop a method that would identify the cluster centroids and the optimal number of clusters for a given sensitivity level and could work equally well for the different sequence datasets. A novel method that…
Generative approaches to clustering provide information on geometric properties of clusters, whereas discriminative approaches provide boundaries between clusters. Ideas from both approaches are incorporated to present a fully unsupervised,…
Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices. We expand upon recent results in spectral analysis for…
Graph learning methods have recently been receiving increasing interest as means to infer structure in datasets. Most of the recent approaches focus on different relationships between a graph and data sample distributions, mostly in…
We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical…
Cluster analysis of biological samples using gene expression measurements is a common task which aids the discovery of heterogeneous biological sub-populations having distinct mRNA profiles. Several model-based clustering algorithms have…
This paper presents a new, parallel implementation of clustering and demonstrates its utility in greatly speeding up the process of identifying homologous proteins. Clustering is a technique to reduce the number of comparison needed to find…
Spectral clustering uses a graph Laplacian spectral embedding to enhance the cluster structure of some data sets. When the embedding is one dimensional, it can be used to sort the items (spectral ordering). A number of empirical results…
Different numerical mappings of the DNA sequences have been studied using a new cluster-scaling method and the well known spectral methods. It is shown, in particular, that the nucleotide sequences in DNA molecules have robust…
3D models are commonly used in computer vision and graphics. With the wider availability of mesh data, an efficient and intrinsic deep learning approach to processing 3D meshes is in great need. Unlike images, 3D meshes have irregular…
This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. Under a generalised random dot product graph, the embedding provides uniformly…