5,788 research outputs found
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
Inclusión educativa: Estrategias de aprendizaje implementadas por el personal docente en la UCA en 2020-2022
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
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