Related papers: Adaptive Clustering Using Kernel Density Estimator…
While clustering is ubiquitously used across science and industry, uncertainty in cluster assignments is rarely quantified with rigorous guarantees. We propose a novel conformal inference framework for clustering that returns confidence…
We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual…
In recent years, there has been a growing demand to discern clusters of subjects in datasets characterized by a large set of features. Often, these clusters may be highly variable in size and present partial hierarchical structures. In this…
There has been much progress on efficient algorithms for clustering data points generated by a mixture of $k$ probability distributions under the assumption that the means of the distributions are well-separated, i.e., the distance between…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion…
Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for…
Given a set of points $P\subset \mathbb{R}^{d}$ and a kernel $k$, the Kernel Density Estimate at a point $x\in\mathbb{R}^{d}$ is defined as $\mathrm{KDE}_{P}(x)=\frac{1}{|P|}\sum_{y\in P} k(x,y)$. We study the problem of designing a data…
Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…
Roughly speaking, clustering evolving networks aims at detecting structurally dense subgroups in networks that evolve over time. This implies that the subgroups we seek for also evolve, which results in many additional tasks compared to…
Kernel adaptive filters, a class of adaptive nonlinear time-series models, are known by their ability to learn expressive autoregressive patterns from sequential data. However, for trivial monotonic signals, they struggle to perform…
It is a common practice to evaluate probability density function or matter spatial density function from statistical samples. Kernel density estimation is a frequently used method, but to select an optimal bandwidth of kernel estimation,…
An accurate sea clutter distribution is crucial for decision region determination when detecting sea-surface floating targets. However, traditional parametric models possibly have a considerable gap to the realistic distribution of sea…
Intermittent renewable energy resources like wind and solar pose great uncertainty of multiple time scales, from minutes to years, on the design and operation of power systems. Energy system optimization models have been developed to find…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
The Adaptive Multilevel Splitting algorithm is a very powerful and versatile iterative method to estimate the probability of rare events, based on an interacting particle systems. In an other article, in a so-called idealized setting, the…
Clustering has become an increasingly important task in analysing huge amounts of data. Traditional applications require that all data has to be located at the site where it is scrutinized. Nowadays, large amounts of heterogeneous, complex…
The spectral clustering algorithm is often used as a binary clustering method for unclassified data by applying the principal component analysis. To study theoretical properties of the algorithm, the assumption of conditional…
We propose the segmentation of noisy datasets into Multiple Inlier Structures with a new Robust Estimator (MISRE). The scale of each individual structure is estimated adaptively from the input data and refined by mean shift, without tuning…
Important information concerning a multivariate data set, such as clusters and modal regions, is contained in the derivatives of the probability density function. Despite this importance, nonparametric estimation of higher order derivatives…