A non-parametric k-nearest neighbour based entropy estimator is proposed. It improves on the classical Kozachenko-Leonenko estimator by considering non-uniform probability densities in the region of k-nearest neighbours around each sample point. It aims at improving the classical estimators in three situations: first, when the dimensionality of the random variable is large; second, when near-fu...

Riassunto: L’analisi di dati simbolici generalizza alcuni metodi statistici standard al caso di oggetti simbolici (SO). Questi oggetti, informalmente definiti “dati aggregati”, poiché sintetizzano le informazioni relative ad un gruppo di individui, possono essere confrontati al fine di individuare dei cluster, di classificarli o ordinarli in base al loro grado di generalizzazione. L’articolo pr...

Data quality is a major concern in Machine Learning and other correlated areas such as Knowledge Discovery from Databases (KDD). As most Machine Learning algorithms induce knowledge strictly from data, the quality of the knowledge extracted is largely determined by the quality of the underlying data. One relevant problem in data quality is the presence of missing data. Despite the frequent occu...

The probabilistic nearest neighbour (PNN) method for pattern recognition was introduced to overcome a number of perceived shortcomings of the nearest neighbour (NN) classifiers namely the lack of any probabilistic semantics when making predictions of class membership. In addition the NN method possesses no inherent principled framework for inferring the number of neighbours, K, nor indeed assoc...

Many algorithms have been implemented to the problem of Automatic Text Categorization (ATC). Most of the work in this area has been carried out on English texts, with only a few researchers addressing Arabic texts. We have investigated the use of the K-Nearest Neighbour (K-NN) classifier, with an Inew, cosine, jaccard and dice similarities, in order to enhance Arabic ATC. We represent the datas...

Let P be a Poisson process of intensity one in a square Sn of area n. For a fixed integer k, join every point of P to its k nearest neighbours, creating an undirected random geometric graph Gn,k. We prove that there exists a critical constant ccrit such that for c < ccrit, Gn,⌊c logn⌋ is disconnected with probability tending to 1 as n → ∞, and for c > ccrit, Gn,⌊c logn⌋ is connected with probab...

Many statistical procedures, including goodness-of-fit tests and methods for independent component analysis, rely critically on the estimation of the entropy of a distribution. In this paper, we seek entropy estimators that are efficient in the sense of achieving the local asymptotic minimax lower bound. To this end, we initially study a generalisation of the estimator originally proposed by Ko...

Most exact methods for k-nearest neighbour search suffer from the curse of dimensionality; that is, their query times exhibit exponential dependence on either the ambient or the intrinsic dimensionality. Dynamic Continuous Indexing (DCI) (Li & Malik, 2016) offers a promising way of circumventing the curse by avoiding space partitioning and achieves a query time that grows sublinearly in the int...

Spam mail classification and filtering is a commonly investigated problem, yet there has been little research into the application of nearest neighbour classifiers in this field. This paper examines the possibility of using a nearest neighbour algorithm for simple, word based spam mail classification. This approach is compared to a neural network, and decision-tree along with results published ...