Dimensionality reduction plays a vital role in pattern recognition. However, for normalized vector data, existing methods do not utilize the fact that the data is normalized. In this paper, we propose to employ an Angular Decomposition of the normalized vector data which corresponds to embedding them on a unit surface. On graph data for similarity/kernel matrices with constant diagonal elements, we propose the Angular Decomposition of the similarity matrices which corresponds to embedding objects on a unit sphere. In these angular embeddings, the Euclidean distance is equivalent to the cosine similarity. Thus data structures best described in the cosine similarity and data structures best captured by the Euclidean distance can both be effectively detected in our angular embedding. We provide the theoretical analysis, derive the computational algorithm, and evaluate the angular embedding on several datasets. Experiments on data clustering demonstrate that our method can provide a more discriminative subspace.

The paper describes a method of relation extraction, which is based on parsing the input text using a combination of a generic HPSG-based grammar and a highly focused domain- and relation-specific lexicon. We also show a method of unsupervised acquisition of such a lexicon from a large unlabeled corpus. Together, the methods introduce a novel approach to the “Open IE” task, which is superior in accuracy and in quality of relation identification to the existing approaches.

The paper describes a method of relation extraction, which is based on parsing the input text using a combination of a generic HPSG-based grammar and a highly focused domain- and relation-specific lexicon. We also show a method of unsupervised acquisition of such a lexicon from a large unlabeled corpus. Together, the methods introduce a novel approach to the “Open IE” task, which is superior in accuracy and in quality of relation identification to the existing approaches.

The paper describes a method of relation extraction, which is based on parsing the input text using a combination of a generic HPSG-based grammar and a highly focused domain- and relation-specific lexicon. We also show a method of unsupervised acquisition of such a lexicon from a large unlabeled corpus. Together, the methods introduce a novel approach to the “Open IE” task, which is superior in accuracy and in quality of relation identification to the existing approaches.

The paper describes a method of relation extraction, which is based on parsing the input text using a combination of a generic HPSG-based grammar and a highly focused domain- and relation-specific lexicon. We also show a method of unsupervised acquisition of such a lexicon from a large unlabeled corpus. Together, the methods introduce a novel approach to the “Open IE” task, which is superior in accuracy and in quality of relation identification to the existing approaches.

The paper describes a method of relation extraction, which is based on parsing the input text using a combination of a generic HPSG-based grammar and a highly focused domain- and relation-specific lexicon. We also show a method of unsupervised acquisition of such a lexicon from a large unlabeled corpus. Together, the methods introduce a novel approach to the “Open IE” task, which is superior in accuracy and in quality of relation identification to the existing approaches.

The paper describes a method of relation extraction, which is based on parsing the input text using a combination of a generic HPSG-based grammar and a highly focused domain- and relation-specific lexicon. We also show a method of unsupervised acquisition of such a lexicon from a large unlabeled corpus. Together, the methods introduce a novel approach to the “Open IE” task, which is superior in accuracy and in quality of relation identification to the existing approaches.

With the availability of the huge amounts of data produced by current and future large multi-band photometric surveys, photometric redshifts have become a crucial tool for extragalactic astronomy and cosmology. In this paper we present a novel method, called Weak Gated Experts (WGE), which allows to derive photometric redshifts through a combination of data mining techniques. \noindent The WGE, like many other machine learning techniques, is based on the exploitation of a spectroscopic knowledge base composed by sources for which a spectroscopic value of the redshift is available. This method achieves a variance \sigma^2(\Delta z)=2.3x10^{-4} (\sigma^2(\Delta z) =0.08), where \Delta z = z_{phot} - z_{spec}) for the reconstruction of the photometric redshifts for the optical galaxies from the SDSS and for the optical quasars respectively, while the Root Mean Square (RMS) of the \Delta z variable distributions for the two experiments is respectively equal to 0.021 and 0.35. The WGE provides also a mechanism for the estimation of the accuracy of each photometric redshift. We also present and discuss the catalogs obtained for the optical SDSS galaxies, for the optical candidate quasars extracted from the DR7 SDSS photometric dataset {The sample of SDSS sources on which the accuracy of the reconstruction has been assessed is composed of bright sources, for a subset of which spectroscopic redshifts have been measured.}, and for optical SDSS candidate quasars observed by GALEX in the UV range. The WGE method exploits the new technological paradigm provided by the Virtual Observatory and the emerging field of Astroinformatics.

In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an $\epsilon$-accurate solution with probability at least $1-\rho$ in at most $O(\tfrac{n}{\epsilon} \log \tfrac{1}{\rho})$ iterations, where $n$ is the number of blocks. For strongly convex functions the method converges linearly. This extends recent results of Nesterov [Efficiency of coordinate descent methods on huge-scale optimization problems, CORE Discussion Paper #2010/2], which cover the smooth case, to composite minimization, while at the same time improving the complexity by the factor of 4 and removing $\epsilon$ from the logarithmic term. More importantly, in contrast with the aforementioned work in which the author achieves the results by applying the method to a regularized version of the objective function with an unknown scaling factor, we show that this is not necessary, thus achieving true iteration complexity bounds. In the smooth case we also allow for arbitrary probability vectors and non-Euclidean norms. Finally, we demonstrate numerically that the algorithm is able to solve huge-scale $\ell_1$-regularized least squares and support vector machine problems with a billion variables.

In this paper, we give a new sharp generalization bound of lp-MKL which is a generalized framework of multiple kernel learning (MKL) and imposes lp-mixed-norm regularization instead of l1-mixed-norm regularization. We utilize localization techniques to obtain the sharp learning rate. The bound is characterized by the decay rate of the eigenvalues of the associated kernels. A larger decay rate gives a faster convergence rate. Furthermore, we give the minimax learning rate on the ball characterized by lp-mixed-norm in the product space. Then we show that our derived learning rate of lp-MKL achieves the minimax optimal rate on the lp-mixed-norm ball.