Random projections have recently emerged as a powerful method for dimensionality reduction. Theoretical results indicate that the method preserves distances quite nicely; however, empirical results are sparse. We present experimental results on using random projection as a dimensionality reduction tool in a number of cases, where the high dimensionality of the data would otherwise lead to burdensome computations. Our application areas are the processing of both noisy and noiseless images, and information retrieval in text documents. We show that projecting the data onto a random lower-dimensional subspace yields results comparable to conventional dimensionality reduction methods such as principal component analysis: the similarity of data vectors is preserved well under random projection. However, using random projections is computationally significantly less expensive than using, e.g., principal component analysis. We also show experimentally that using a sparse random matrix gives additional computational savings in random projection.

Separation of complex valued signals is a frequently arising problem in signal processing. For example, separation of convolutively mixed source signals involves computations on complex valued signals. In this article, it is assumed that the original, complex valued source signals are mutually statistically independent, and the problem is solved by the independent component analysis (ICA) model. ICA is a statistical method for transforming an observed multidimensional random vector into components that are mutually as independent as possible. In this article, a fast fixed-point type algorithm that is capable of separating complex valued, linearly mixed source signals is presented and its computational efficiency is shown by simulations. Also, the local consistency of the estimator given by the algorithm is proved.

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Do large mammals evolve faster than small mammals or vice versa?Because the answer to this question contributes to our understanding of how life-history affects long-term and large-scale evolutionary patterns, and how microevolutionary rates scale-up to macroevolutionary rates, it has received much attention. A satisfactory or consistent answer to this question is lacking, however. Here, we take a fresh look at this problem using a large fossil dataset of mammals from the Neogene of the Old World (NOW). Controlling for sampling biases, calculating per capita origination and extinction rates of boundary-crossers and estimating survival probabilities using capture-mark-recapture (CMR) methods, we found the recurring pattern that large mammal genera and species have higher origination and extinction rates, and therefore shorter durations. This pattern is surprising in the light of molecular studies, which show that smaller animals, with their shorter generation times and higher metabolic rates, have greater absolute rates of evolution. However, higher molecular rates do not necessarily translate to higher taxon rates because both the biotic and physical environments interact with phenotypic variation, in part fueled by mutations, to affect origination and extinction rates. To explain the observed pattern, we propose that the ability to evolve and maintain behavior such as hibernation, torpor and burrowing, collectively termed ''sleep-orhide'' (SLOH) behavior, serves as a means of environmental buffering during expected and unexpected environmental change. SLOH behavior is more common in some small mammals, and, as a result, SLOH small mammals contribute to higher average survivorship and lower origination probabilities among small mammals.body size ͉ environmental buffering ͉ metabolism ͉ Neogene mammals ͉ turnover E volution operates at different scales of time and levels of the biological hierarchy (1). Body size covaries with many individual and species level traits (2), each of which could influence the tempo of evolution at population, species and clade levels. Multiple studies have shown that smaller sized mammals have higher molecular rates of evolution in absolute time, possibly because of a generation time effect and/or metabolic rate effect (3-8). Higher molecular rates may translate to higher rates of phenotypic changes (9 but see 10, 11) and a greater chance of reproductive isolation, which could ultimately lead to higher speciation rates (12) and higher rates of pseudoextinction, which could be observed as higher extinction rates among fossil taxa. As such, small mammals could be expected to have higher origination and extinction rates as observed in the fossil record. However, empirical studies on historical extinctions show that large mammals are at higher risk of extinction and have been selectively removed (13-17), as is also indicated by the Pleistocene megafauna extinction literature (18,19), even though body size per se may not always be a good predictor of extinction risk (20)(21)(22). Neither ...