Dynamic Time Warping Averaging of Time Series Allows Faster and More Accurate Classification

Recent years have seen significant progress in improving both the efficiency and effectiveness of time series classification. However, because the best solution is typically the Nearest Neighbor algorithm with the relatively expensive Dynamic Time Warping as the distance measure, successful deployments on resource constrained devices remain elusive. Moreover, the recent explosion of interest in wearable devices, which typically have limited computational resources, has created a growing need for very efficient classification algorithms. A commonly used technique to glean the benefits of the Nearest Neighbor algorithm, without inheriting its undesirable time complexity, is to use the Nearest Centroid algorithm. However, because of the unique properties of (most) time series data, the centroid typically does not resemble any of the instances, an unintuitive and underappreciated fact. In this work we show that we can exploit a recent result to allow meaningful averaging of 'warped' times series, and that this result allows us to create ultra-efficient Nearest 'Centroid' classifiers that are at least as accurate as their more lethargic Nearest Neighbor cousins

Faster and more accurate classification of time series by exploiting a novel dynamic time warping averaging algorithm

A concerted research effort over the past two decades has heralded significant improvements in both the efficiency and effectiveness of time series classification. The consensus that has emerged in the community is that the best solution is a surprisingly simple one. In virtually all domains, the most accurate classifier is the nearest neighbor algorithm with dynamic time warping as the distance measure. The time complexity of dynamic time warping means that successful deployments on resource-constrained devices remain elusive. Moreover, the recent explosion of interest in wearable computing devices, which typically have limited computational resources, has greatly increased the need for very efficient classification algorithms. A classic technique to obtain the benefits of the nearest neighbor algorithm, without inheriting its undesirable time and space complexity, is to use the nearest centroid algorithm. Unfortunately, the unique properties of (most) time series data mean that the centroid typically does not resemble any of the instances, an unintuitive and underappreciated fact. In this paper we demonstrate that we can exploit a recent result by Petitjean et al. to allow meaningful averaging of “warped” time series, which then allows us to create super-efficient nearest “centroid” classifiers that are at least as accurate as their more computationally challenged nearest neighbor relatives. We demonstrate empirically the utility of our approach by comparing it to all the appropriate strawmen algorithms on the ubiquitous UCR Benchmarks and with a case study in supporting insect classification on resource-constrained sensors

A new comprehensive set of elemental abundances in DLAs III. Star formation histories

We obtained comprehensive sets of elemental abundances for eleven damped Ly-alpha systems (DLAs) at z_DLA=1.7-2.5. In Paper I of this series, we showed for three DLA galaxies that we can derive their star formation histories and ages from a detailed comparison of their intrinsic abundance patterns with chemical evolution models. We determine in this paper the star formation properties of six additional DLA galaxies. The derived results confirm that no single star formation history explains the diverse sets of abundance patterns in DLAs. We demonstrate that the various star formation histories reproducing the DLA abundance patterns are typical of local irregular, dwarf starburst and quiescent spiral galaxies. Independent of the star formation history, the DLAs have a common characteristic of being weak star forming galaxies; models with high star formation efficiencies are ruled out. All the derived DLA star formation rates per unit area are moderate or low, with values between -3.2 < log SFR < -1.1 M_sol yr^{-1} kpc^{-2}. The DLA abundance patterns require a large spread in ages ranging from 20 Myr up to 3 Gyr. The oldest DLA in our sample is observed at z_DLA=1.864 with an age estimated to more than 3 Gyr; it nicely indicates that galaxies were already forming at z_f>10. But, most of the DLAs show ages much younger than that of the Universe at the epoch of observation. Young galaxies thus seem to populate the high redshift Universe at z>2, suggesting relatively low redshifts of formation (z~3) for most high-redshift galaxies. The DLA star formation properties are compared with those of other high-redshift galaxies identified in deep imaging surveys with the aim of obtaining a global picture of high-redshift objects.Comment: 19 pages, 11 figures, Accepted for publication in A&

Evolution of chemical abundances in Seyfert galaxies

We computed the chemical evolution of spiral bulges hosting Seyfert nuclei, based on updated chemical and spectro-photometrical evolution models for the bulge of our Galaxy, made predictions about other quantities measured in Seyferts, and modeled the photometry of local bulges. The chemical evolution model contains detailed calculations of the Galactic potential and of the feedback from the central supermassive black hole, and the spectro-photometric model covers a wide range of stellar ages and metallicities. We followed the evolution of bulges in the mass range 10^9 - 10^{11} Msun by scaling the star formation efficiency and the bulge scalelength as in the inverse-wind scenario for elliptical galaxies, and considering an Eddington limited accretion onto the central supermassive black hole. We successfully reproduced the observed black hole-host bulge mass relation. The observed nuclear bolometric luminosity is reproduced only at high redshift or for the most massive bulges; in the other cases, at z = 0 a rejuvenation mechanism is necessary. The black hole feedback is in most cases not significant in triggering the galactic wind. The observed high star formation rates and metal overabundances are easily achieved, as well as the constancy of chemical abundances with redshift and the bulge present-day colours. Those results are not affected if we vary the index of the stellar IMF from x=0.95 to x=1.35; a steeper IMF is instead required in order to reproduce the colour-magnitude relation and the present K-band luminosity of the bulge.Comment: 17 pages, 15 figures, 3 tables, accepted for publication in A&