arXiv subjects

Mikhail Kanevski

Publications and source records attributed to Mikhail Kanevski.

24 records · Page 2Linked to original sources

arXiv2017

Unsupervised Feature Selection Based on the Morisita Estimator of Intrinsic Dimension

This paper deals with a new filter algorithm for selecting the smallest subset of features carrying all the information content of a data set (i.e. for removing redundant features). It is an advanced version of the fractal dimension reduction technique, and it relies on the recently introduced Morisita estimator of Intrinsic Dimension (ID). Here, the ID is used to quantify dependencies between subsets of features, which allows the effective processing of highly non-linear data. The proposed algorithm is successfully tested on simulated and real world case studies. Different levels of sample size and noise are examined along with the variability of the results. In addition, a comprehensive procedure based on random forests shows that the data dimensionality is significantly reduced by the algorithm without loss of relevant information. And finally, comparisons with benchmark feature selection techniques demonstrate the promising performance of this new filter.

stat.ML↗

arXiv2017

Feature Selection for Regression Problems Based on the Morisita Estimator of Intrinsic Dimension

Data acquisition, storage and management have been improved, while the key factors of many phenomena are not well known. Consequently, irrelevant and redundant features artificially increase the size of datasets, which complicates learning tasks, such as regression. To address this problem, feature selection methods have been proposed. This paper introduces a new supervised filter based on the Morisita estimator of intrinsic dimension. It can identify relevant features and distinguish between redundant and irrelevant information. Besides, it offers a clear graphical representation of the results, and it can be easily implemented in different programming languages. Comprehensive numerical experiments are conducted using simulated datasets characterized by different levels of complexity, sample size and noise. The suggested algorithm is also successfully tested on a selection of real world applications and compared with RReliefF using extreme learning machine. In addition, a new measure of feature relevance is presented and discussed.

stat.ML↗

arXiv2016

Local fractality: the case of forest fires in Portugal

The research deals with a study of local fractality in spatial distribution of forest fires in Portugal using the sandbox method. The general procedure is the following: (a) define a circle centred in each and all events with increasing radius R; (b) count the number of other events located within the circle of radius R, N(R); (c) plot the growth curve which is the functional dependence of N(R) versus R; and (d) estimate the local fractal dimension as the slope on log[N(R)] versus log[R]. The computation is carried out by using the location of every fire event as a centre but without the final averaging over all the fires for a given R, which is usually performed to get a global fractal dimension and to estimate global clustering. Sandbox method is widely used in many applications in physics and other subjects. The local procedure has the ability to provide the most complete information regarding the spatial distribution of clustering and avoiding non-homogeneity and non-stationarity problems. Most of the analysis was performed using the National Mapping Burnt Area (NMBA) database which accounts for 32,156 fires during the 1975 - 2013 period. The results of local analysis are compared with a randomly generated pattern in forest zones (validity domain). The results demonstrate interesting local spatial patterns of clustering. Some results on global measures are reported as well.

physics.soc-ph↗

arXiv2016

Spatial Patterns of Wind Speed Distributions in Switzerland

This paper presents an initial exploration of high frequency records of extreme wind speed in two steps. The first consists in finding the suitable extreme distribution for $120$ measuring stations in Switzerland, by comparing three known distributions: Weibull, Gamma, and Generalized extreme value. This comparison serves as a basis for the second step which applies a spatial modelling by using Extreme Learning Machine. The aim is to model distribution parameters by employing a high dimensional input space of topographical information. The knowledge of probability distribution gives a comprehensive information and a global overview of wind phenomena. Through this study, a flexible and a simple modelling approach is presented, which can be generalized to almost extreme environmental data for risk assessment and to model renewable energy.

physics.data-an↗

arXiv2015

A New Estimator of Intrinsic Dimension Based on the Multipoint Morisita Index

The size of datasets has been increasing rapidly both in terms of number of variables and number of events. As a result, the empty space phenomenon and the curse of dimensionality complicate the extraction of useful information. But, in general, data lie on non-linear manifolds of much lower dimension than that of the spaces in which they are embedded. In many pattern recognition tasks, learning these manifolds is a key issue and it requires the knowledge of their true intrinsic dimension. This paper introduces a new estimator of intrinsic dimension based on the multipoint Morisita index. It is applied to both synthetic and real datasets of varying complexities and comparisons with other existing estimators are carried out. The proposed estimator turns out to be fairly robust to sample size and noise, unaffected by edge effects, able to handle large datasets and computationally efficient.

physics.data-an↗

arXiv2013

Multifractal portrayal of the Swiss population

Fractal geometry is a fundamental approach for describing the complex irregularities of the spatial structure of point patterns. The present research characterizes the spatial structure of the Swiss population distribution in the three Swiss geographical regions (Alps, Plateau and Jura) and at the entire country level. These analyses were carried out using fractal and multifractal measures for point patterns, which enabled the estimation of the spatial degree of clustering of a distribution at different scales. The Swiss population dataset is presented on a grid of points and thus it can be modelled as a "point process" where each point is characterized by its spatial location (geometrical support) and a number of inhabitants (measured variable). The fractal characterization was performed by means of the box-counting dimension and the multifractal analysis was conducted through the Renyi's generalized dimensions and the multifractal spectrum. Results showed that the four population patterns are all multifractals and present different clustering behaviours. Applying multifractal and fractal methods at different geographical regions and at different scales allowed us to quantify and describe the dissimilarities between the four structures and their underlying processes. This paper is the first Swiss geodemographic study applying multifractal methods using high resolution data.

physics.soc-ph↗