How to Solve Classification and Regression Problems on High-Dimensional Data with a Supervised Extension of Slow Feature Analysis

Supervised learning from high-dimensional data, e.g., multimedia data, is a challenging task. We propose an extension of slow feature analysis (SFA) for supervised dimensionality reduction called graph-based SFA (GSFA). The algorithm extracts a label-predictive low-dimensional set of features that can be post-processed by typical supervised algorithms to generate the final label or class estimation. GSFA is trained with a so-called training graph, in which the vertices are the samples and the edges represent similarities of the corresponding labels. A new weighted SFA optimization problem is introduced, generalizing the notion of slowness from sequences of samples to such training graphs. We show that GSFA computes an optimal solution to this problem in the considered function space, and propose several types of training graphs. For classification, the most straightforward graph yields features equivalent to those of (nonlinear) Fisher discriminant analysis. Emphasis is on regression, where four different graphs were evaluated experimentally with a subproblem of face detection on photographs. The method proposed is promising particularly when linear models are insufficient, as well as when feature selection is difficult

Measuring the Data Efficiency of Deep Learning Methods

In this paper, we propose a new experimental protocol and use it to benchmark the data efficiency --- performance as a function of training set size --- of two deep learning algorithms, convolutional neural networks (CNNs) and hierarchical information-preserving graph-based slow feature analysis (HiGSFA), for tasks in classification and transfer learning scenarios. The algorithms are trained on different-sized subsets of the MNIST and Omniglot data sets. HiGSFA outperforms standard CNN networks when the models are trained on 50 and 200 samples per class for MNIST classification. In other cases, the CNNs perform better. The results suggest that there are cases where greedy, locally optimal bottom-up learning is equally or more powerful than global gradient-based learning.Comment: 8 page

Food habits, selectivity, and foraging modes of the school shark Galeorhinus galeus

The foraging ecology of the school shark Galeorhinus galeus was studied in Anegada Bay, Argentina, during the seasonal occurrence of this species in Argentinean waters (October to April) from 1998 to 2001. Of the 408 individuals examined, 168 (41.2%) had food remains in their stomachs. The proportion of individuals with food remains was negatively correlated with total length. In general, the diet was composed mainly of teleosts (98.5% IRI [index of relative importance]), with invertebrates and chondrichthyans as minor prey. The diet varied ontogenetically and seasonally. Juveniles and adults differed in their consumption of invertebrates, with juveniles preying more on benthic invertebrates, mainly the octopus Octopus tehuelchus, and adults on squid. From December to February, adults preyed mainly on benthic teleosts (almost exclusively the Atlantic midshipman Porichthys porosissimus), while from March to April the consumption of squid increased. A comparison of numbers of prey in stomachs with abundance of prey in the environment in March and April showed that, in these months, juveniles selected invertebrates and demersal teleosts and avoided pelagic teleosts and chondricthyan prey, and adults selected squid and avoided pelagic teleosts. This indicates that, during this period, G. galeus is not an opportunistic predator. The mean size of prey increased with increasing shark length, but even large sharks consumed small prey. All shark sizes consumed prey fragments that were significantly larger than other prey consumed whole. This indicates that G. galeus is able to overcome gape limitation by mutilating prey, and that the ontogenetic diet shift was not due to a change in the ability to seize prey.Facultad de Ciencias Naturales y Muse

Second Order General Slow-Roll Power Spectrum

Recent combined results from the Wilkinson Microwave Anisotropy Probe (WMAP) and Sloan Digital Sky Survey (SDSS) provide a remarkable set of data which requires more accurate and general investigation. Here we derive formulae for the power spectrum P(k) of the density perturbations produced during inflation in the general slow-roll approximation with second order corrections. Also, using the result, we derive the power spectrum in the standard slow-roll picture with previously unknown third order corrections.Comment: 11 pages, 1 figure ; A typo in Eq. (38) is fixed ; References expanded and a note adde