Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit

Subspace clustering methods based on $\ell_1$, $\ell_2$ or nuclear norm regularization have become very popular due to their simplicity, theoretical guarantees and empirical success. However, the choice of the regularizer can greatly impact both theory and practice. For instance, $\ell_1$ regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from different subspaces) under broad conditions (e.g., arbitrary subspaces and corrupted data). However, it requires solving a large scale convex optimization problem. On the other hand, $\ell_2$ and nuclear norm regularization provide efficient closed form solutions, but require very strong assumptions to guarantee a subspace-preserving affinity, e.g., independent subspaces and uncorrupted data. In this paper we study a subspace clustering method based on orthogonal matching pursuit. We show that the method is both computationally efficient and guaranteed to give a subspace-preserving affinity under broad conditions. Experiments on synthetic data verify our theoretical analysis, and applications in handwritten digit and face clustering show that our approach achieves the best trade off between accuracy and efficiency.Comment: 13 pages, 1 figure, 2 tables. Accepted to CVPR 2016 as an oral presentatio

One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative 1/p**2 U(1) Gauge Model

This paper carries forward a series of articles describing our enterprise to construct a gauge equivalent for the $\theta$-deformed non-commutative $p^{-2}$ model originally introduced by Gurau et al. arXiv:0802.0791. It is shown that breaking terms of the form used by Vilar et al. arXiv:0902.2956 and ourselves arXiv:0901.1681 to localize the BRST covariant operator $(D^2\theta^2D^2)^{-1}$ lead to difficulties concerning renormalization. The reason is that this dimensionless operator is invariant with respect to any symmetry of the model, and can be inserted to arbitrary power. In the present article we discuss explicit one-loop calculations, and analyze the mechanism the mentioned problems originate from.Comment: v2: minor corrections and references added; v3: published versio

Classification of Italian banks

Caption titleHandwritten on leaf [1]: C/53-10. 143At head of title: Economic Development. Italy. Economics/4. April 10, 1953. M. HigonnetMimeographe

Modelling agricultural policy reforms in the Mediterranean basin - Adjustments of AGRISIM

In recent years the Mediterranean countries encounter a number of changes of the agricultural policy that could influence significantly their agricultural sector and thus their overall economy. They are faced with the ongoing trade liberalisation, the Reform of the Common Agricultural Policy (CAP) of the European Union (EU), since the EU is one of the major trade partners of the Mediterranean countries and the establishment of a Free Trade Area between the EU and the Mediterranean Countries after 2010. The latest is/will be accomplished through the Euro- Mediterranean Association Agreements, was decided in the Summit of Barcelona in 1995 and is particularly up- to date after 2005, 10 years after the establishment of the Barcelona Agreement. These changes are expected above all to influence the trade flows between the EU and the Mediterranean Partner Countries (MPC) and therefore, to have impacts on the production, consumption, domestic and border prices and welfare. Aim of the paper is to discuss methodological issues connected with the modelling of policy changes in the Mediterranean basin and to provide more insights on the modification of the model AGRISIM so as to make it a suitable tool to analyse the trade flows in the Mediterranean basin.MPCs, Euro- Mediterranean Association, Agricultural and Food Policy,

CAP Reform and the Mediterranean EU-Member States

In the previous years the Mediterranean Member States of the EU came across the Reform of the CAP and especially last year faced the second wave of the Reform for three typical Mediterranean products, namely cotton, olive oil and tobacco. In this paper a partial equilibrium model is used to simulate the impacts of decoupling, as a key point of the decided CAP Reform. The second wave of the Reform appears to be of crucial importance for the southern EU countries and although the producer's income is reduced, there are positive welfare effects.decoupling, partial equilibrium model, CAP reform, Greece, Italy, Spain, Agricultural and Food Policy, Q18, Q17, D59,

On protecting farmers' new varieties: new approaches to rights on collective innovations in plant genetic resources

"Current farmers' breeding goes beyond the gradual selection in landraces, and includes development and maintenance of major new farmers' varieties that are rather uniform, in particular in South-East Asia. Modern varieties developed in the formal sector have simply replaced landraces as the source of diversity, but have not abolished farmers' breeding practices. Interpretations of the new international agreements on plant genetic resources should protect the development of modern farmers' varieties. However, ensuring recognition of collective innovation, allowing access to relevant germplasm sources for farmers' breeding activities, keeping materials freely available, and arranging for effective benefit sharing, all form major challenges. This paper proposes a new protective measure: namely “origin recognition rights." Author's AbstractLandraces, Farmers' varieties, Collective rights, Declaration of origin, Origin recognition, Germplasm resources,

Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering

State-of-the-art subspace clustering methods are based on expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with $\ell_1$, $\ell_2$ or nuclear norms. $\ell_1$ regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from different subspaces) under broad theoretical conditions, but the clusters may not be connected. $\ell_2$ and nuclear norm regularization often improve connectivity, but give a subspace-preserving affinity only for independent subspaces. Mixed $\ell_1$, $\ell_2$ and nuclear norm regularizations offer a balance between the subspace-preserving and connectedness properties, but this comes at the cost of increased computational complexity. This paper studies the geometry of the elastic net regularizer (a mixture of the $\ell_1$ and $\ell_2$ norms) and uses it to derive a provably correct and scalable active set method for finding the optimal coefficients. Our geometric analysis also provides a theoretical justification and a geometric interpretation for the balance between the connectedness (due to $\ell_2$ regularization) and subspace-preserving (due to $\ell_1$ regularization) properties for elastic net subspace clustering. Our experiments show that the proposed active set method not only achieves state-of-the-art clustering performance, but also efficiently handles large-scale datasets.Comment: 15 pages, 6 figures, accepted to CVPR 2016 for oral presentatio

Properties of grains derived from IRAS observations of dust

The authors used the results of Infrared Astronomy Satellite (IRAS) observations of diffuse medium dust to develop a theoretical model of the infrared properties of grains. Recent models based entirely on traditional observations of extinction and polarization include only particles whose equilibrium temperatures do not exceed 20 K in the diffuse interstellar medium. These classical grains, for which the authors have adopted the multipopulation model developed by Hong and Greenberg (1980), can explain only the emission in the IRAS 100 micron band. The measurements at shorter wavelengths (12, 25 and 60 microns) require two new particle populations. Vibrational fluorescence from aromatic molecules provides the most likely explanation for the emission observed at 12 microns, with polycyclic aeromatic hydrocarbons (PAHs) containing about 10 percent of cosmic carbon. A simplified model of the emission process shows that PAH molecules can also explain most of the emission measured by IRAS at 25 microns. The authors identified the warm particles responsible for the excess 60 microns emission with small (a approx. equals 0.01 microns) iron grains. A compilation of the available data on the optical properties of iron indicates that the diffuse medium temperature of small iron particles should be close to 50 K and implies that a large, possibly dominant, fraction of cosmic iron must be locked up in metallic particles in order to match the observed 60 microns intensities. The model matches the infrared fluxes typically observed by IRAS in the diffuse medium and can also reproduce the infrared surface brightness distribution in individual clouds. In particular, the combination of iron and classical cool grains can explain the surprising observations of the 60/100 microns flux ratio in clouds, which is either constant or increases slightly towards higher opacities. The presence of metallic grains has significant implications for the physics of the interstellar medium, including catalytic H2 formation, for which iron grains could be the main site; differences in depletion patterns between iron and other refractory elements (Mg, Si); and superparamagnetic behavior of large grains with embedded iron clusters giving rise to the observed high degree of alignment by the galactic magnetic field