Local methods of dimensionality reduction like neighborhood embedding (NE) and t-SNE in particular outperform older global approaches such as stress-based multi-dimensional scaling (MDS).Stochastic neighborhoods are less sensitive than distances to statistical variations between spaces with strongly different dimensionalities, making a match across them very difficult.Here, we take inspiration from those stochastic neighborhoods in order to devise a pseudo-distance that is less prone to concentration than the Euclidean distance.For two points in the high-dimensional data space, it is defined as the symmetrized Kullback-Leibler divergence across the (stochastic) neighborhoods of the two points (SKLAN).Plugging the SKLAN in a method of stress-based MDS, we compare quantitatively t-SNE, MDS with all Euclidean distances, and MDS with SKLAN & Euclidean distances on several data sets.The results show that SKLAN allows MDS to perform competitively with t-SNE.

International audience

As a local method of dimensionality reduction, t-SNE requires careful initialization in order to preserve the data global structure to the best extent.In regular t-SNE, the low-dimensional embedding is initialized either randomly or with PCA; next, gradient descent refines the embedding coordinates in two phases.In the first one, called early exaggeration, attractive forces between points are artificially strengthened to delay any detrimental effect of repulsive forces while points are still poorly organized.In this paper, a novel initialization of t-SNE is proposed.It works by hierarchizing the data points into a space-partitioning binary tree and successive runs of t-SNE with 4, 8, 16, ..., N points.Between two runs, the prototypical point in each tree branch is split into its two children prototypes, with some little random noise, and the embedding is rescaled to account for the increased population.Experimental results show the effectiveness of the method.The proposed method is compatible with any method of neighbor embedding (t-SNE, UMAP, etc.) provided early exaggeration can be disabled and initial coordinates can be fed into.

A decision support system is used by decision makers for a long time. But, in some cases, the originally designed multidimensional schema does not cover the entire needs of decision makers, which can change over time. One such unfulfilled need, is using facts to describe dimension members. In this article, we propose a methodology to transform the constellation schema of a data warehouse by integrating factual data into a dimension. The proposed methodology and algorithms enrich a constellation multidimensional schema with new analytical possibilities for decision makers. This enrichment has repercussions for the entire multidimensional schema that are managed by multidimensional modeling, hierarchy calculation and the hierarchy version. In this article, we present a theoretical view of the proposed methodology supported by a case study, an implemented prototype and a complete evaluation based on a standard benchmark.

The objective of this work is to find the best metric to ignore the variations of soil reflectance induced by the solar-view angles geometry. Differences between spectra measured for the same soil under different observation and illumination configurations can leads to misclassifications. Using ninety two soils of different composition measured under twenty eight solar- view angles geometries, we tested 3 metrics : RMSE, SAM, R2(the coefficient of determination) and we compared their performances. The best metric seems to be the coefficient of determination with 93 % of good classifications.