Basic statistics for probabilistic symbolic variables: a novel metric-based approach

In data mining, it is usually to describe a set of individuals using some summaries (means, standard deviations, histograms, confidence intervals) that generalize individual descriptions into a typology description. In this case, data can be described by several values. In this paper, we propose an approach for computing basic statics for such data, and, in particular, for data described by numerical multi-valued variables (interval, histograms, discrete multi-valued descriptions). We propose to treat all numerical multi-valued variables as distributional data, i.e. as individuals described by distributions. To obtain new basic statistics for measuring the variability and the association between such variables, we extend the classic measure of inertia, calculated with the Euclidean distance, using the squared Wasserstein distance defined between probability measures. The distance is a generalization of the Wasserstein distance, that is a distance between quantile functions of two distributions. Some properties of such a distance are shown. Among them, we prove the Huygens theorem of decomposition of the inertia. We show the use of the Wasserstein distance and of the basic statistics presenting a k-means like clustering algorithm, for the clustering of a set of data described by modal numerical variables (distributional variables), on a real data set. Keywords: Wasserstein distance, inertia, dependence, distributional data, modal variables.Comment: 19 pages, 3 figure

Linear regression for numeric symbolic variables: an ordinary least squares approach based on Wasserstein Distance

In this paper we present a linear regression model for modal symbolic data. The observed variables are histogram variables according to the definition given in the framework of Symbolic Data Analysis and the parameters of the model are estimated using the classic Least Squares method. An appropriate metric is introduced in order to measure the error between the observed and the predicted distributions. In particular, the Wasserstein distance is proposed. Some properties of such metric are exploited to predict the response variable as direct linear combination of other independent histogram variables. Measures of goodness of fit are discussed. An application on real data corroborates the proposed method

Cultural Values and Cross-cultural Video Consumption on YouTube

Video-sharing social media like YouTube provide access to diverse cultural products from all over the world, making it possible to test theories that the Web facilitates global cultural convergence. Drawing on a daily listing of YouTube's most popular videos across 58 countries, we investigate the consumption of popular videos in countries that differ in cultural values, language, gross domestic product, and Internet penetration rate. Although online social media facilitate global access to cultural products, we find this technological capability does not result in universal cultural convergence. Instead, consumption of popular videos in culturally different countries appears to be constrained by cultural values. Cross-cultural convergence is more advanced in cosmopolitan countries with cultural values that favor individualism and power inequality

Neural activity classification with machine learning models trained on interspike interval series data

The flow of information through the brain is reflected by the activity patterns of neural cells. Indeed, these firing patterns are widely used as input data to predictive models that relate stimuli and animal behavior to the activity of a population of neurons. However, relatively little attention was paid to single neuron spike trains as predictors of cell or network properties in the brain. In this work, we introduce an approach to neuronal spike train data mining which enables effective classification and clustering of neuron types and network activity states based on single-cell spiking patterns. This approach is centered around applying state-of-the-art time series classification/clustering methods to sequences of interspike intervals recorded from single neurons. We demonstrate good performance of these methods in tasks involving classification of neuron type (e.g. excitatory vs. inhibitory cells) and/or neural circuit activity state (e.g. awake vs. REM sleep vs. nonREM sleep states) on an open-access cortical spiking activity dataset

Measures of Analysis of Time Series (MATS): A MATLAB Toolkit for Computation of Multiple Measures on Time Series Data Bases

In many applications, such as physiology and finance, large time series data bases are to be analyzed requiring the computation of linear, nonlinear and other measures. Such measures have been developed and implemented in commercial and freeware softwares rather selectively and independently. The Measures of Analysis of Time Series ({\tt MATS}) {\tt MATLAB} toolkit is designed to handle an arbitrary large set of scalar time series and compute a large variety of measures on them, allowing for the specification of varying measure parameters as well. The variety of options with added facilities for visualization of the results support different settings of time series analysis, such as the detection of dynamics changes in long data records, resampling (surrogate or bootstrap) tests for independence and linearity with various test statistics, and discrimination power of different measures and for different combinations of their parameters. The basic features of {\tt MATS} are presented and the implemented measures are briefly described. The usefulness of {\tt MATS} is illustrated on some empirical examples along with screenshots.Comment: 25 pages, 9 figures, two tables, the software can be downloaded at http://eeganalysis.web.auth.gr/indexen.ht