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Improving feature selection process resistance to failures caused by curse-of-dimensionality effects

Petr Somol, Jiří Grim, Jana Novovičová, Pavel Pudil (2011)

Kybernetika

The purpose of feature selection in machine learning is at least two-fold - saving measurement acquisition costs and reducing the negative effects of the curse of dimensionality with the aim to improve the accuracy of the models and the classification rate of classifiers with respect to previously unknown data. Yet it has been shown recently that the process of feature selection itself can be negatively affected by the very same curse of dimensionality - feature selection methods may easily over-fit...

Incomplete time series prediction using max-margin classification of data with absent features.

Zhaowei, Shang, Lingfeng, Zhang, Shangjun, Ma, Bin, Fang, Taiping, Zhang (2010)

Mathematical Problems in Engineering

Inference on y >yo by Using a Correlated Variable: A Three Decision Approach.

P. Bauer (1976)

Metrika

Interpretation and optimization of the $k$ -means algorithm

Kristian Sabo, Rudolf Scitovski (2014)

Applications of Mathematics

The paper gives a new interpretation and a possible optimization of the well-known $k$ -means algorithm for searching for a locally optimal partition of the set $𝒜 = {a_{i} \in ℝ^{n} : i = 1, \dots, m}$ which consists of $k$ disjoint nonempty subsets $π_{1}, \dots, π_{k}$ , $1 \leq k \leq m$ . For this purpose, a new divided $k$ -means algorithm was constructed as a limit case of the known smoothed $k$ -means algorithm. It is shown that the algorithm constructed in this way coincides with the $k$ -means algorithm if during the iterative procedure no data points appear in the Voronoi diagram....

Intrinsic dimensionality and small sample properties of classifiers

Šarūnas Raudys (1998)

Kybernetika

Small learning-set properties of the Euclidean distance, the Parzen window, the minimum empirical error and the nonlinear single layer perceptron classifiers depend on an “intrinsic dimensionality” of the data, however the Fisher linear discriminant function is sensitive to all dimensions. There is no unique definition of the “intrinsic dimensionality”. The dimensionality of the subspace where the data points are situated is not a sufficient definition of the “intrinsic dimensionality”. An exact...

Introduction à l'approche symbolique en analyse des données

E. Diday (1989)

RAIRO - Operations Research - Recherche Opérationnelle

Inversions en classification hiérarchique : application à la construction adaptative d'indices d'agrégation

Edwin Diday (1983)

Revue de Statistique Appliquée