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

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

Bird faunas of the humid montane forests of Mesoamerica: biogeographic patterns and priorities for conservation

The distribution of 335 species of birds in 33 islands of humid montane forest in Mesoamerica is summarized, and patterns of distribution, diversity and endemism are analysed. The montane forests of Costa Rica and western Panama far exceed other habitat islands considered for species-richness, richness of species endemic to Mesoamerica, and richness of species ecologically restricted to humid montane forests. Other regions, such as the Sierra Madre del Sur of Guerrero and Oaxaca, the Los Tuxtlas region of southern Veracruz and the mountains of Chiapas and Guatemala, also hold rich and endemic avifaunas. Based on patterns of similarity of avifaunas, the region can be divided into seven regions holding distinctive avifaunas (Costa Rica and western Panama; northern Central America and northern Chiapas; southern Chiapas; eastern Mexico north of the Isthmus of Tehuantepec; Sierra Madre del Sur; interior Oaxaca; and Transvolcanic Belt and Sierra Madre Occidental), which serve as useful guides for the setting of priorities for conservation action. Se resumen las distribuciones de 335 especies de aves en 33 islas de bosque humedo de montana en Mesoamerica, y se analizan patrones de distribution, diversidad y endemismo. Los bosques montanos de Costa Rica y del oeste de Panama tienen la mas alta riqueza de especies, riqueza de especies endemicas a Mesoamerica, y riqueza de especies ecologicamente restringidas a bosque humedo de montana. Otras regiones, tales como la Sierra Madre del Sur de Guerrero y Oaxaca, la region de Los Tuxtlas y las montanas de Chiapas y Guatemala, tambien tienen avifaunas ricas en especies y en endemicas. Basado en patrones de similitud de avifaunas, se puede dividir Mesoamerica en siete regiones que tienen avifaunas distintas (Costa Rica y el oeste de Panama; el norte de Centroamerica y el norte de Chiapas; el sur de Chiapas; el este de Mexico; la Sierra Madre del Sur; el interior de Oaxaca; y el Eje Neovolcanico y la Sierra Madre Occidental), las cuales pueden servir como guias en el establecimiento de prioridades para la conservation