Optimisation of on-line principal component analysis

Different techniques, used to optimise on-line principal component analysis, are investigated by methods of statistical mechanics. These include local and global optimisation of node-dependent learning-rates which are shown to be very efficient in speeding up the learning process. They are investigated further for gaining insight into the learning rates' time-dependence, which is then employed for devising simple practical methods to improve training performance. Simulations demonstrate the benefit gained from using the new methods.Comment: 10 pages, 5 figure

Hypervelocity gun

A velocity amplifier system which uses both electric and chemical energy for projectile propulsion is provided in a compact hypervelocity gun suitable for laboratory use. A relatively heavy layer of a tamping material such as concrete encloses a loop of an electrically conductive material. An explosive charge at least partially surrounding the loop is adapted to collapse the loop upon detonation of the charge. A source of electricity charges the loop through two leads, and an electric switch which is activated by the charge explosive charge, disconnects the leads from the source of electricity and short circuits them. An opening in the tamping material extends to the loop and forms a barrel. The loop, necked down in the opening, forms the sabot on which the projectile is located. When the loop is electrically charged and the explosive detonated, the loop is short circuited and collapsed thus building up a magnetic field which acts as a sabot catcher. The sabot is detached from the loop and the sabot and projectile are accelerated to hypervelocity

Vegetation and soils field research data base: Experiment summaries

Understanding of the relationships between the optical, spectral characteristics and important biological-physical parameters of earth-surface features can best be obtained by carefully controlled studies over fields and plots where complete data describing the condition of targets are attainable and where frequent, timely spectral measurement can be obtained. Development of a vegetation and soils field research data base was initiated in 1972 at Purdue University's Laboratory for Applications of Remote Sensing and expanded in the fall of 1974 by NASA as part of LACIE. Since then, over 250,000 truck-mounted and helicopter-borne spectrometer/multiband radiometer observations have been obtained of more than 50 soil series and 20 species of crops, grasses, and trees. These data are supplemented by an extensive set of biophysical and meteorological data acquired during each mission. The field research data form one of the most complete and best-documented data sets acquired for agricultural remote sensing research. Thus, they are well-suited to serve as a data base for research to: (1) quantiatively determine the relationships of spectral and biophysical characteristics of vegetation, (2) define future sensor systems, and (3) develop advanced data analysis techniques

Characterization of vegetation by microwave and optical remote sensing

Two series of carefully controlled experiments were conducted. First, plots of important crops (corn, soybeans, and sorghum), prairie grasses (big bluestem, switchgrass, tal fescue, orchardgrass, bromegrass), and forage legumes (alfalfa, red clover, and crown vetch) were manipulated to produce wide ranges of phytomass, leaf area index, and canopy architecture. Second, coniferous forest canopies were simulated using small balsam fir trees grown in large pots of soil and arranged systematically on a large (5 m) platform. Rotating the platform produced many new canopies for frequency and spatial averaging of the backscatter signal. In both series of experiments, backscatter of 5.0 GHz (C-Band) was measured as a function of view angle and polarization. Biophysical measurements included leaf area index, fresh and dry phytomass, water content of canopy elements, canopy height, and soil roughness and moisture content. For a subset of the above plots, additional measurements were acquired to exercise microwave backscatter models. These measurements included size and shape of leaves, stems, and fruit and the probability density function of leaf and stem angles. The relationships of the backscattering coefficients and the biophysical properties of the canopies were evaluated using statistical correlations, analysis of variance, and regression analysis. Results from the corn density and balsam fir experiments are discussed and analyses of data from the other experiments are summarized

Soybean canopy reflectance modeling data sets

Numerous mathematical models of the interaction of radiation with vegetation canopies have been developed over the last two decades. However, data with which to exercise and validate these models are scarce. During three days in the summer of 1980, experiments are conducted with the objective of gaining insight about the effects of solar illumination and view angles on soybean canopy reflectance. In concert with these experiment, extensive measurements of the soybean canopies are obtained. This document is a compilation of the bidirectional reflectance factors, agronomic, characteristics, canopy geometry, and leaf, stem, and pod optical properties of the soybean canopies. These data sets should be suitable for use with most vegetation canopy reflectance models

Dynamics of Learning with Restricted Training Sets I: General Theory

We study the dynamics of supervised learning in layered neural networks, in the regime where the size $p$ of the training set is proportional to the number $N$ of inputs. Here the local fields are no longer described by Gaussian probability distributions and the learning dynamics is of a spin-glass nature, with the composition of the training set playing the role of quenched disorder. We show how dynamical replica theory can be used to predict the evolution of macroscopic observables, including the two relevant performance measures (training error and generalization error), incorporating the old formalism developed for complete training sets in the limit $\alpha=p/N\to\infty$ as a special case. For simplicity we restrict ourselves in this paper to single-layer networks and realizable tasks.Comment: 39 pages, LaTe

Phase transitions in optimal unsupervised learning

We determine the optimal performance of learning the orientation of the symmetry axis of a set of P = alpha N points that are uniformly distributed in all the directions but one on the N-dimensional sphere. The components along the symmetry breaking direction, of unitary vector B, are sampled from a mixture of two gaussians of variable separation and width. The typical optimal performance is measured through the overlap Ropt=B.J* where J* is the optimal guess of the symmetry breaking direction. Within this general scenario, the learning curves Ropt(alpha) may present first order transitions if the clusters are narrow enough. Close to these transitions, high performance states can be obtained through the minimization of the corresponding optimal potential, although these solutions are metastable, and therefore not learnable, within the usual bayesian scenario.Comment: 9 pages, 8 figures, submitted to PRE, This new version of the paper contains one new section, Bayesian versus optimal solutions, where we explain in detail the results supporting our claim that bayesian learning may not be optimal. Figures 4 of the first submission was difficult to understand. We replaced it by two new figures (Figs. 4 and 5 in this new version) containing more detail

A two step algorithm for learning from unspecific reinforcement

We study a simple learning model based on the Hebb rule to cope with "delayed", unspecific reinforcement. In spite of the unspecific nature of the information-feedback, convergence to asymptotically perfect generalization is observed, with a rate depending, however, in a non- universal way on learning parameters. Asymptotic convergence can be as fast as that of Hebbian learning, but may be slower. Moreover, for a certain range of parameter settings, it depends on initial conditions whether the system can reach the regime of asymptotically perfect generalization, or rather approaches a stationary state of poor generalization.Comment: 13 pages LaTeX, 4 figures, note on biologically motivated stochastic variant of the algorithm adde