相关论文: A comparison of Gap statistic definitions with and…
As shown in recent research, deep neural networks can perfectly fit randomly labeled data, but with very poor accuracy on held out data. This phenomenon indicates that loss functions such as cross-entropy are not a reliable indicator of…
When scholars suspect units are dependent on each other within clusters but independent of each other across clusters, they employ cluster-robust standard errors (CRSEs). Nevertheless, what to cluster over is sometimes unknown. For…
A commonly used characteristic of statistical dependence of adjacency relations in real networks, the clustering coefficient, evaluates chances that two neighbours of a given vertex are adjacent. An extension is obtained by considering…
In this paper, the method of gaps, a technique for deriving closed-form expressions in terms of information measures for the generalization error of supervised machine learning algorithms is introduced. The method relies on the notion of…
Biometric recognition is used across a variety of applications from cyber security to border security. Recent research has focused on ensuring biometric performance (false negatives and false positives) is fair across demographic groups.…
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…
GAP measures (also known as Scrooge measures) are a natural class of probability distributions on the unit sphere of a Hilbert space that come up in quantum statistical mechanics; for each density matrix $\rho$ there is a unique measure…
Quantifying distributional separation across groups is fundamental in statistical learning and scientific discovery, yet most classical discrepancy measures are tailored to two-group comparisons. We generalize the underlap coefficient…
This paper addresses the statistical significance of structures in random data: Given a set of vectors and a measure of mutual similarity, how likely does a subset of these vectors form a cluster with enhanced similarity among its elements?…
In this paper, we relatively extend the definition of global clustering coefficient to another clustering, which we call it relative clustering coefficient. The idea of this definition is to ignore the edges in the network that the…
The log-normal distribution is used to describe the positive data, that it has skewed distribution with small mean and large variance. This distribution has application in many sciences for example medicine, economics, biology and…
Since its original formulation, Jensen's inequality has played a fundamental role across mathematics, statistics, and machine learning, with its probabilistic version highlighting the nonnegativity of the so-called Jensen's gap, i.e., the…
Data clustering is the process of identifying natural groupings or clusters within multidimensional data based on some similarity measure. Clustering is a fundamental process in many different disciplines. Hence, researchers from different…
The classical $k$-means clustering requires a complete data matrix without missing entries. As a natural extension of the $k$-means clustering for missing data, the $k$-POD clustering has been proposed, which ignores the missing entries in…
We study the order statistics of a random walk (RW) of $n$ steps whose jumps are distributed according to symmetric Erlang densities $f_p(\eta)\sim |\eta|^p \,e^{-|\eta|}$, parametrized by a non-negative integer $p$. Our main focus is on…
We use a cluster ensemble to determine the number of clusters, k, in a group of data. A consensus similarity matrix is formed from the ensemble using multiple algorithms and several values for k. A random walk is induced on the graph…
We consider the problem of estimating the number of clusters (k) in a dataset. We propose a non-parametric approach to the problem that utilizes similarity graphs to construct a robust statistic that effectively captures similarity…
Mapper is an unsupervised machine learning algorithm generalising the notion of clustering to obtain a geometric description of a dataset. The procedure splits the data into possibly overlapping bins which are then clustered. The output of…
Cluster analysis is a popular unsupervised learning tool used in many disciplines to identify heterogeneous sub-populations within a sample. However, validating cluster analysis results and determining the number of clusters in a data set…
We propose a novel method for clustering data which is grounded in information-theoretic principles and requires no parametric assumptions. Previous attempts to use information theory to define clusters in an assumption-free way are based…