Discriminative variable selection for clustering with the sparse Fisher-EM algorithm

The interest in variable selection for clustering has increased recently due to the growing need in clustering high-dimensional data. Variable selection allows in particular to ease both the clustering and the interpretation of the results. Existing approaches have demonstrated the efficiency of variable selection for clustering but turn out to be either very time consuming or not sparse enough in high-dimensional spaces. This work proposes to perform a selection of the discriminative variables by introducing sparsity in the loading matrix of the Fisher-EM algorithm. This clustering method has been recently proposed for the simultaneous visualization and clustering of high-dimensional data. It is based on a latent mixture model which fits the data into a low-dimensional discriminative subspace. Three different approaches are proposed in this work to introduce sparsity in the orientation matrix of the discriminative subspace through $\ell_{1}$-type penalizations. Experimental comparisons with existing approaches on simulated and real-world data sets demonstrate the interest of the proposed methodology. An application to the segmentation of hyperspectral images of the planet Mars is also presented

Cover Crops to Secure Low Herbicide Weed Control Strategies in Maize Grown with Reduced Tillage

As a key-element of conservation agriculture, the occasional or systematic suppression of full-inversion ploughing implies an adaptation of the cropping system. To assess the ability of cover crops to control weeds in a subsequent maize crop grown with reduced tillage, three annual experiments were implemented at the research station of Agroscope Changins, Nyon, Switzerland. Ten non-wintering cover crop (CC) species were sown in mid-summer and compared to a bare soil treatment in strip-plot experiments including different weeding strategies according to integrated weed management rules. In case of a predictable impasse for weed control, an alternative management option was chosen 1) at the end of winter: total herbicide application instead of no herbicide application, 2) at the beginning of May before maize sowing: minimum soil tillage instead of no tillage. The ability of cover crop species to control weed was evaluated at the stage 2-4 leaves of maize. The shoot dry matter yield of maize was measured at harvest at the end of August. At the beginning of November, mean CC dry shoot biomass varied between 1.2 and 11.1 t DM ha-1 depending on experimental year and CC species. On average over the three years, Asteraceae (Helianthusannuus and Guizotiaabyssinica) showed the highest shoot dry matter among the tested species (> 6.0 t DM ha-1). Legume species (Pisumsativum arvense, Trifolium alexandrinum and Vicia sativa) and Brassicaceae species (Brassicacampestrisoleifera and Raphanussativuslongipinnatus) presented the lowest 3-year mean shoot biomass (≤4.0 t DM ha-1) At the end of winter, the three legume species and Avenastrigosa showed the highest plant residue soil cover and Brassicaceae species the lowest one. CC residue soil cover at the end of winter was only slightly positively correlated with CC autumn shoot biomass. In three out of eight cases, the chosen weeding strategy was very efficient in terms of weed control at the stage 2-4 leaves of maize. In the remaining five cases, the weeding strategy did not succeed in preventing weed infestation at the beginning of maize development. A mean weed cover higher than 15% was observed when no total herbicide and/or no tillage was applied before maize sowing. In three out of these five cases, a significant CC effect on weed cover could be observed. CC species able to produce high amounts of biomass in autumn appeared to be useful in terms of weed control. The most efficient CC species varied from year to year: G. abyssinica in 2011, H. annuus in 2012 and A. strigosa in 2014. CC effect on maize yield was significant in a single case, but the effect of CC species tended to be positive compared to the control treatment without CC. Despite only partial efficacy, the use of cover crops is recommended for limiting weed incidence in cropping systems aimed at reducing soil tillage and herbicide use

Theoretical and practical considerations on the convergence properties of the Fisher-EM algorithm

International audienceThe Fisher-EM algorithm has been recently proposed in (Bouveyron2011) for the simultaneous visualization and clustering of high-dimensional data. It is based on a latent mixture model which fits the data into a latent discriminative subspace with a low intrinsic dimension. Although the Fisher-EM algorithm is based on the EM algorithm, it does not respect at a first glance all conditions of the EM convergence theory. Its convergence toward a maximum of the likelihood is therefore questionable. The aim of this work is two folds. Firstly, the convergence of the Fisher-EM algorithm is studied from the theoretical point of view. It is in particular proved that the algorithm converges under weak conditions in the general case. Secondly, the convergence of the Fisher-EM algorithm is considered from the practical point of view. It is shown that the Fisher's criterion can be used as stopping criterion for the algorithm to improve the clustering accuracy. It is also shown that the Fisher-EM algorithm converges faster than both the EM and CEM algorithm

Probabilistic Fisher discriminant analysis: A robust and flexible alternative to Fisher discriminant analysis

International audienceFisher discriminant analysis (FDA) is a popular and powerful method for dimensionality reduction and classification. Unfortunately, the optimality of the dimension reduction provided by FDA is only proved in the homoscedastic case. In addition, FDA is known to have poor performances in the cases of label noise and sparse labeled data. To overcome these limitations, this work proposes a probabilistic framework for FDA which relaxes the homoscedastic assumption on the class covariance matrices and adds a term to explicitly model the non-discriminative information. This allows the proposed method to be robust to label noise and to be used in the semi-supervised context. Experiments on real-world datasets show that the proposed approach works at least as well as FDA in standard situations and outperforms it in the label noise and sparse label cases

On the estimation of the latent discriminative subspace in the Fisher-EM algorithm

International audienceThe Fisher-EM algorithm has been recently proposed in [2] for the simultaneous visualization and clustering of high-dimensional data. It is based on a discriminative latent mixture model which fits the data into a latent discriminative subspace with an intrinsic dimension lower than the dimension of the original space. The Fisher-EM algorithm includes an F-step which estimates the projection matrix whose columns span the discriminative latent space. This matrix is estimated via an optimization problem which is solved using a Gram-Schmidt procedure in the original algorithm. Unfortunately, this procedure suffers in some case from numerical instabilities which may result in a deterioration of the visualization quality or the clustering accuracy. Two alternatives for estimating the latent subspace are proposed to overcome this limitation. The optimization problem of the F-step is first recasted as a regression-type problem and then reformulated such that the solution can be approximated with a SVD. Experiments on simulated and real datasets show the improvement of the proposed alternatives for both the visualization and the clustering of data

On the kinematic cosmic dipole tension

Our motion through the Universe generates a dipole in the temperature anisotropies of the Cosmic Microwave Background (CMB) and also in the angular distribution of sources. If the cosmological principle is valid, these two dipoles are directly linked, such that the amplitude of one determines that of the other. However, it is a longstanding problem that number counts of radio sources and of quasars at low and intermediate redshifts exhibit a dipole that is well aligned with that of the CMB but with about twice the expected amplitude, leading to a tension reaching up to $4.9 \sigma$. In this paper, we revisit the theoretical derivation of the dipole in the sources number counts, explicitly accounting for the redshift evolution of the population of sources. We argue that if the spectral index and magnification bias of the sources vary with redshift, the standard theoretical description of the dipole may be inaccurate. We provide an alternative expression which does not depend on the spectral index, but instead on the time evolution of the population of sources. We then determine the values that this evolution rate should have in order to remove the tension with the CMB dipole.Comment: 11 pages, 8 figures, typo corrected in Eq. (28), (43). Subsequent Eqs. (54), (56), (59), Fig. 7 and 8 adapted with respect to v

A comparison between different methods for the numerical simulation of polycrystalline aggregates

The macroscopic behavior of polycrystalline materials is largely influenced by the shape, the arrangement and the orientation of crystallites. Different methods have thus been developed to determine the effective behavior of such materials as a function of their microstructural features. In this work, which focuses on polycrystalline materials with an elastic-viscoplastic behavior, the self-consistent (SC) method [1], the finite element (FE) method and the spectral (FFT) method [2] are compared. These common methods are used to determine the effective behavior of different 316L polycrystalline aggregates subjected to various loading conditions (uniaxial tension, cyclic tension/compression).(...

Inventory and First Assessment of Oil and Gas Wells Conversion for Geothermal Heat Recovery in France

International audienceThe repurposing of oil and gas wells for geothermal energy production and resource assessment can provide sustainable solutions to meet the objectives of renewable energy balance targeted within 2030 by the French Parliament in the "energy transition law for a green growth" promulgated in August 2015. Approximately 12 500 wells have been drilled in France since the 19th century for hydrocarbon reservoir exploration and exploitation. Most of them are closed and abandoned or nearing the end of production due to the planned end of exploitation of hydrocarbons in France by 2040. Several sustainable cases of conversion for geothermal energy production have been reported in France and abroad, demonstrating the possibility of using former wells for heat extraction from aquifers or coaxial heat exchangers. This paper presents an overview of the wells drilled in France and the methodology proposed to identify and rank them according to the a priori feasibility of open and closed loop conversion. To this purpose, wells data, geological and hydrothermal information acquired by the BRGM (geometry and dynamic aquifer properties from models) and land occupation have been cross-referenced. The quantitative overview should be followed by a detailed analysis of selected wells to assess their conversion potential for geothermal energy production (possible use at surface, well drilling and abandonment reports, hydrodynamic properties of the reservoir, technology to be implemented, etc.)