Related papers: Application of optimal data-based binning method t…
Histograms are convenient non-parametric density estimators, which continue to be used ubiquitously. Summary quantities estimated from histogram-based probability density models depend on the choice of the number of bins. We introduce a…
The problem of estimating the number of clusters (say k) is one of the major challenges for the partitional clustering. This paper proposes an algorithm named k-SCC to estimate the optimal k in categorical data clustering. For the…
Clustering is a critical component of decision-making in todays data-driven environments. It has been widely used in a variety of fields such as bioinformatics, social network analysis, and image processing. However, clustering accuracy…
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,…
We consider the problem of determining the optimal block (or subsample) size for a spatial subsampling method for spatial processes observed on regular grids. We derive expansions for the mean square error of the subsampling variance…
In this work, we investigate the statistical computation of the Boltzmann entropy of statistical samples. For this purpose, we use both histogram and kernel function to estimate the probability density function of statistical samples. We…
Averaging amplitudes over consecutive time samples within a time-window is widely used to calculate the amplitude of an event-related potential (ERP) for cognitive neuroscience. Objective determination of the time-window is critical for…
A theoretical framework is developed to estimate the optimal binning of X-ray spectra. We derived expressions for the optimal bin size for model spectra as well as for observed data using different levels of sophistication. It is shown that…
We study the problem of optimal estimation of the density cluster tree under various assumptions on the underlying density. Building up from the seminal work of Chaudhuri et al. [2014], we formulate a new notion of clustering consistency…
In several environmental applications data are functions of time, essentially con- tinuous, observed and recorded discretely, and spatially correlated. Most of the methods for analyzing such data are extensions of spatial statistical tools…
Clustering algorithms are among the most widely used data mining methods due to their exploratory power and being an initial preprocessing step that paves the way for other techniques. But the problem of calculating the optimal number of…
Single-level density-based approach has long been widely acknowledged to be a conceptually and mathematically convincing clustering method. In this paper, we propose an algorithm called "best-scored clustering forest" that can obtain the…
We consider the detection of multivariate spatial clusters in the Bernoulli model with $N$ locations, where the design distribution has weakly dependent marginals. The locations are scanned with a rectangular window with sides parallel to…
The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…
Survival analysis is a widely-used technique for analyzing time-to-event data in the presence of censoring. In recent years, numerous survival analysis methods have emerged which scale to large datasets and relax traditional assumptions…
Rapid growth of genetic databases means huge savings from improvements in their data compression, what requires better inexpensive statistical models. This article proposes automatized optimizations e.g. of Markov-like models, especially…
Small-Angle Neutron Scattering (SANS) data analysis often relies on fixed-width binning schemes that overlook variations in signal strength and structural complexity. We introduce a statistically grounded approach based on the…
Accurate approximation of the sampling distribution of nonparametric kernel density estimators is crucial for many statistical inference problems. Since these estimators have complex asymptotic distributions, bootstrap methods are often…
A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimension ($N_{_{D}}>3$). The data set is first reduced to a smaller set of partitions (multi-dimensional bins). Multiple clustering…
The reconstruction of smooth density fields from scattered data points is a procedure that has multiple applications in a variety of disciplines, including Lagrangian (particle-based) models of solute transport in fluids. In random walk…