The Haar Wavelet Transform in the Time Series Similarity Paradigm

Similarity measures play an important role in many data mining algorithms. To allow the use of such algorithms on non-standard databases, such as databases of financial time series, their similarity measure has to be defined. We present a simple and powerful technique which allows for the rapid evaluation of similarity between time series in large data bases. It is based on the orthonormal decomposition of the time series into the Haar basis. We demonstrate that this approach is capable of providing estimates of the local slope of the time series in the sequence of multi-resolution steps. The Haar representation and a number of related represenations derived from it are suitable for direct comparison, e.g. evaluation of the correlation product. We demonstrate that the distance between such representations closely corresponds to the subjective feeling of similarity between the time series. In order to test the validity of subjective criteria, we test the records of currency exchanges, finding convincing levels of correlation

Methods for characterising microphysical processes in plasmas

Advanced spectral and statistical data analysis techniques have greatly contributed to shaping our understanding of microphysical processes in plasmas. We review some of the main techniques that allow for characterising fluctuation phenomena in geospace and in laboratory plasma observations. Special emphasis is given to the commonalities between different disciplines, which have witnessed the development of similar tools, often with differing terminologies. The review is phrased in terms of few important concepts: self-similarity, deviation from self-similarity (i.e. intermittency and coherent structures), wave-turbulence, and anomalous transport.Comment: Space Science Reviews (2013), in pres

Complex Data: Mining using Patterns

There is a growing need to analyse sets of complex data, i.e., data in which the individual data items are (semi-) structured collections of data themselves, such as sets of time-series. To perform such analysis, one has to redefine familiar notions such as similarity on such complex data types. One can do that either on the data items directly, or indi- rectly, based on features or patterns computed from the individual data items. In this paper, we argue that wavelet decomposition is a general tool for the latter approac

Sparsity and Incoherence in Compressive Sampling

We consider the problem of reconstructing a sparse signal $x^0\in\R^n$ from a limited number of linear measurements. Given $m$ randomly selected samples of $U x^0$, where $U$ is an orthonormal matrix, we show that $\ell_1$ minimization recovers $x^0$ exactly when the number of measurements exceeds $$m\geq \mathrm{Const}\cdot\mu^2(U)\cdot S\cdot\log n,$$ where $S$ is the number of nonzero components in $x^0$, and $\mu$ is the largest entry in $U$ properly normalized: $\mu(U) = \sqrt{n} \cdot \max_{k,j} |U_{k,j}|$. The smaller $\mu$, the fewer samples needed. The result holds for ``most'' sparse signals $x^0$ supported on a fixed (but arbitrary) set $T$. Given $T$, if the sign of $x^0$ for each nonzero entry on $T$ and the observed values of $Ux^0$ are drawn at random, the signal is recovered with overwhelming probability. Moreover, there is a sense in which this is nearly optimal since any method succeeding with the same probability would require just about this many samples

Land surface Verification Toolkit (LVT)

LVT is a framework developed to provide an automated, consolidated environment for systematic land surface model evaluation Includes support for a range of in-situ, remote-sensing and other model and reanalysis products. Supports the analysis of outputs from various LIS subsystems, including LIS-DA, LIS-OPT, LIS-UE. Note: The Land Information System Verification Toolkit (LVT) is a NASA software tool designed to enable the evaluation, analysis and comparison of outputs generated by the Land Information System (LIS). The LVT software is released under the terms and conditions of the NASA Open Source Agreement (NOSA) Version 1.1 or later. Land Information System Verification Toolkit (LVT) NOSA

An auditory classifier employing a wavelet neural network implemented in a digital design

This thesis addresses the problem of classifying audio as either voice or music. The goal was to solve this problem by means of digital logic circuit, capable of performing the classification in real time. Since digital audio is essentially a discrete non-periodic timeseries, it was necessary to extract features from the audio which are suitable for classification. The discrete wavelet transform combined with a feature extraction method was found to produce such features. The task of classifying these features was found to be best performed by an artificial neural network. Collectively known as a wavelet neural network, the digital logic design implementation of this architecture was effective in correctly identifying the test data sets. The wavelet neural network was first implemented as a software model, to develop the network architecture and parameters, and to determine ideal results. The unconstrained software simulation was capable of correctly classifying test data sets with greater than 90% accuracy. This model was not feasible as a digital logic design however, as the size of the implementation would have been prohibitive. The size of the resulting hardware model was constrained by reducing the widths of the data paths and storage registers. The hardware implementation of the wavelet processor consisted of a novel pipelined design with a novel data-flow control structure. The neural network training was performed entirely in software by way of a novel training algorithm, and the resulting weights were made to be available to be uploaded to the hardware model. The digital design of the wavelet neural network was modeled in VHDL and was synthesized with Synplicity Synplify, using Actel ProASICPlus APA600 synthesized library cells with a target clock frequency of 11.025 KHz, to match the sampling rate of the digital audio. The results of the synthesis indicated that the design could operate at 15.6 MHz, and required 96,265 logic cells. The resulting constrained wavelet neural network processor was capable of correctly classifying test data sets with greater than 70% accuracy. Additional modeling showed that with a reasonable increase in hardware size, greater than 86% accuracy is attainable. This thesis focused on classifying audio as either voice or music, and future research could readily extend this work to the problem of speaker recognition and multimedia indexing

Multiresolution FIR neural-network-based learning algorithm applied to network traffic prediction

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