Jean Golay

The Multipoint Morisita Index for the Analysis of Spatial Patterns

In many fields, the spatial clustering of sampled data points has significant consequences. Therefore, several indices have been proposed to assess the degree of clustering affecting datasets (e.g. the Morisita index, Ripley’s K-function and Renyi’s information). The classical Morisita index measures how many times it is more likely to randomly select two sampled points from the same quadrat (the dataset is covered by a regular grid of changing size) than it would be in the case of a random distribution generated from a Poisson process. The multipoint version takes into account m points with m≥2. The present research deals with a new development of the multipoint Morisita index (m-Morisita) which is directly related to multifractality. This relationship to multifractality is first demonstrated and highlighted on a mathematical multifractal set. Then, the new version of the m-Morisita index is adapted to the characterization of environmental monitoring network clustering. And, finally, an additional extension, the functional m-Morisita index, is presented for the detection of structures in monitored phenomena.

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. HighlightsA new estimator of intrinsic dimension is suggested.Comparisons with commonly used estimators of intrinsic dimension are conducted.The suggested estimator turns out to be robust to sample size and noise.The suggested estimator is able to handle large datasets.The suggested estimator is computationally efficient.

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 research introduces a new supervised filter based on the Morisita estimator of intrinsic dimension. It is able to identify relevant features and to distinguish between redundant and irrelevant information. Besides, it does not rely on arbitrary parameters and it can be easily implemented in any programming environment. The suggested algorithm is applied to both synthetic and real data and a comparison with RReliefF is conducted using extreme learning machine.

Comparing seismicity declustering techniques by means of the joint use of Allan Factor and Morisita index

In this paper, we propose to compare different declustering methods on the basis of the time-correlation and the space-clustering of the residual earthquake catalog after the declustering techniques have been applied. To this aim, we applied two point process clustering measures, the Allan Factor and the Morisita Index, for the identification and quantification of temporal correlation and spatial clustering in point processes, respectively. We used our joint space–time approach to study the earthquake space–time point processes of southern California and Switzerland with surrounding area, declustered by using the method of Gardner and Knopoff (with Grünthal and Uhmhammer window) and that of Reasenberg (with different setting parameters). Our results show that the residual declustered catalog is still characterized by time-correlated structures at long timescales; however, the cutoff timescale that is the lowest timescale above which the time-correlation is visible is higher with the Reasenberg method while is smaller with the Gardner and Knopoff method with Grünthal window. The space-clustering analysis performed by means of the Morisita Index suggests that the declustering technique effectively reduces the spatial clustering of the seismicity of Switzerland, but does not change the spatial properties of the residual seismic catalogue of the southern California.

Unsupervised feature selection based on the Morisita estimator of intrinsic dimension

Abstract This paper deals with a new filter algorithm for selecting the smallest subset of features carrying all the information content of a dataset (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.

Multifractal analysis of the time series of daily means of wind speed in complex regions

Abstract In this paper, we applied the multifractal detrended fluctuation analysis to the daily means of wind speed measured by 119 weather stations distributed over the territory of Switzerland. The analysis was focused on the inner time fluctuations of wind speed, which could be linked with the local conditions of the highly varying topography of Switzerland. Our findings point out to a persistent behaviour of almost all measured wind speed series (indicated by a Hurst exponent larger than 0.5), and to a high multifractality degree indicating a relative dominance of the large fluctuations in the dynamics of wind speed, especially on the Swiss Plateau, which is comprised between the Jura and Alps mountain ranges. The study represents a contribution to the understanding of the dynamical mechanisms of wind speed variability in mountainous regions.