Cluster membership probabilities from proper motions and multiwavelength photometric catalogues: I. Method and application to the Pleiades cluster

We present a new technique designed to take full advantage of the high dimensionality (photometric, astrometric, temporal) of the DANCe survey to derive self-consistent and robust membership probabilities of the Pleiades cluster. We aim at developing a methodology to infer membership probabilities to the Pleiades cluster from the DANCe multidimensional astro-photometric data set in a consistent way throughout the entire derivation. The determination of the membership probabilities has to be applicable to censored data and must incorporate the measurement uncertainties into the inference procedure. We use Bayes' theorem and a curvilinear forward model for the likelihood of the measurements of cluster members in the colour-magnitude space, to infer posterior membership probabilities. The distribution of the cluster members proper motions and the distribution of contaminants in the full multidimensional astro-photometric space is modelled with a mixture-of-Gaussians likelihood. We analyse several representation spaces composed of the proper motions plus a subset of the available magnitudes and colour indices. We select two prominent representation spaces composed of variables selected using feature relevance determination techniques based in Random Forests, and analyse the resulting samples of high probability candidates. We consistently find lists of high probability (p > 0.9975) candidates with $\approx$ 1000 sources, 4 to 5 times more than obtained in the most recent astro-photometric studies of the cluster. The methodology presented here is ready for application in data sets that include more dimensions, such as radial and/or rotational velocities, spectral indices and variability.Comment: 14 pages, 4 figures, accepted by A&

Efficient Scalable Accurate Regression Queries in In-DBMS Analytics

Recent trends aim to incorporate advanced data analytics capabilities within DBMSs. Linear regression queries are fundamental to exploratory analytics and predictive modeling. However, computing their exact answers leaves a lot to be desired in terms of efficiency and scalability. We contribute a novel predictive analytics model and associated regression query processing algorithms, which are efficient, scalable and accurate. We focus on predicting the answers to two key query types that reveal dependencies between the values of different attributes: (i) mean-value queries and (ii) multivariate linear regression queries, both within specific data subspaces defined based on the values of other attributes. Our algorithms achieve many orders of magnitude improvement in query processing efficiency and nearperfect approximations of the underlying relationships among data attributes

Subset selection in dimension reduction methods

Dimension reduction methods play an important role in multivariate statistical analysis, in particular with high-dimensional data. Linear methods can be seen as a linear mapping from the original feature space to a dimension reduction subspace. The aim is to transform the data so that the essential structure is more easily understood. However, highly correlated variables provide redundant information, whereas some other feature may be irrelevant, and we would like to identify and then discard both of them while pursuing dimension reduction. Here we propose a greedy search algorithm, which avoids the search over all possible subsets, for ranking subsets of variables based on their ability to explain variation in the dimension reduction variates.Dimension reduction methods, Linear mapping, Subset selection, Greedy search

The discriminative functional mixture model for a comparative analysis of bike sharing systems

Bike sharing systems (BSSs) have become a means of sustainable intermodal transport and are now proposed in many cities worldwide. Most BSSs also provide open access to their data, particularly to real-time status reports on their bike stations. The analysis of the mass of data generated by such systems is of particular interest to BSS providers to update system structures and policies. This work was motivated by interest in analyzing and comparing several European BSSs to identify common operating patterns in BSSs and to propose practical solutions to avoid potential issues. Our approach relies on the identification of common patterns between and within systems. To this end, a model-based clustering method, called FunFEM, for time series (or more generally functional data) is developed. It is based on a functional mixture model that allows the clustering of the data in a discriminative functional subspace. This model presents the advantage in this context to be parsimonious and to allow the visualization of the clustered systems. Numerical experiments confirm the good behavior of FunFEM, particularly compared to state-of-the-art methods. The application of FunFEM to BSS data from JCDecaux and the Transport for London Initiative allows us to identify 10 general patterns, including pathological ones, and to propose practical improvement strategies based on the system comparison. The visualization of the clustered data within the discriminative subspace turns out to be particularly informative regarding the system efficiency. The proposed methodology is implemented in a package for the R software, named funFEM, which is available on the CRAN. The package also provides a subset of the data analyzed in this work.Comment: Published at http://dx.doi.org/10.1214/15-AOAS861 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org