1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

The parallel explosions of interest in streaming data, and data mining of time series have had surprisingly little intersection. This is in spite of the fact that time series data are typically streaming data. The main reason for this apparent paradox is the fact that the vast majority of work on streaming data explicitly assumes that the data is discrete, whereas the vast majority of time series data is real valued.Many researchers have also considered transforming real valued time series into symbolic representations, nothing that such representations would potentially allow researchers to avail of the wealth of data structures and algorithms from the text processing and bioinformatics communities, in addition to allowing formerly "batch-only" problems to be tackled by the streaming community. While many symbolic representations of time series have been introduced over the past decades, they all suffer from three fatal flaws. Firstly, the dimensionality of the symbolic representation is the same as the original data, and virtually all data mining algorithms scale poorly with dimensionality. Secondly, although distance measures can be defined on the symbolic approaches, these distance measures have little correlation with distance measures defined on the original time series. Finally, most of these symbolic approaches require one to have access to all the data, before creating the symbolic representation. This last feature explicitly thwarts efforts to use the representations with streaming algorithms.In this work we introduce a new symbolic representation of time series. Our representation is unique in that it allows dimensionality/numerosity reduction, and it also allows distance measures to be defined on the symbolic approach that lower bound corresponding distance measures defined on the original series. As we shall demonstrate, this latter feature is particularly exciting because it allows one to run certain data mining algorithms on the efficiently manipulated symbolic representation, while producing identical results to the algorithms that operate on the original data. Finally, our representation allows the real valued data to be converted in a streaming fashion, with only an infinitesimal time and space overhead.We will demonstrate the utility of our representation on the classic data mining tasks of clustering, classification, query by content and anomaly detection.

/pdf/a-symbolic-representation-of-time-series-with-implications-4bu8lln3kv.pdf

A symbolic representation of time series, with implications for streaming algorithms

Many high level representations of time series have been proposed for data mining, including Fourier transforms, wavelets, eigenwaves, piecewise polynomial models, etc. Many researchers have also considered symbolic representations of time series, noting that such representations would potentiality allow researchers to avail of the wealth of data structures and algorithms from the text processing and bioinformatics communities. While many symbolic representations of time series have been introduced over the past decades, they all suffer from two fatal flaws. First, the dimensionality of the symbolic representation is the same as the original data, and virtually all data mining algorithms scale poorly with dimensionality. Second, although distance measures can be defined on the symbolic approaches, these distance measures have little correlation with distance measures defined on the original time series.

In this work we formulate a new symbolic representation of time series. Our representation is unique in that it allows dimensionality/numerosity reduction, and it also allows distance measures to be defined on the symbolic approach that lower bound corresponding distance measures defined on the original series. As we shall demonstrate, this latter feature is particularly exciting because it allows one to run certain data mining algorithms on the efficiently manipulated symbolic representation, while producing identical results to the algorithms that operate on the original data. In particular, we will demonstrate the utility of our representation on various data mining tasks of clustering, classification, query by content, anomaly detection, motif discovery, and visualization.

/pdf/experiencing-sax-a-novel-symbolic-representation-of-time-58ks4rxhdw.pdf

Experiencing SAX: a novel symbolic representation of time series

Prognostics and health management design for rotary machinery systems—Reviews, methodology and applications

Lectures on Cauchy’s Problem in Linear Partial Differential Equations. By J. Hadamard. Pp. viii+316. 15s.net. 1923. (Per Oxford University Press.)

This paper deals with equation error methods that fit continuous-time transfer function models to discrete-time data recently included in the CONTSID (CONtinuous-Time System IDentification) Matlab toolbox. An overview of the methods is first given where implementation issues are highlighted. The performances of the methods are then evaluated on simulated examples by Monte Carlo simulations. The experiments have been carried out to study the sensitivity of each approach to the design parameters, sampling period, signal-to-noise ratio, noise power spectral density and type of input signal. The effectiveness of the CONTSID toolbox techniques is also briefly compared with indirect methods in which discrete-time models are first estimated and then transformed into continuous-time models. The paper does not consider iterative or recursive algorithms for continuous-time transfer function model identification.

Continuous-time model identification from sampled data: Implementation issues and performance evaluation

A method for analysing gearbox faults using time–frequency representations

Gear crack detection by adaptive amplitude and phase demodulation

Multivariable identification of a winding process by subspace methods for tension control

In this paper, a linear model identification of a winding pilot plant for a tension control application is presented. Such a system is characterised by strong interactions between the tensions, frictions, distorsione, sliding and bending effects which make the tension control difficult to handle. Moreover, most of physical state variables as the radius are not measured. Herein, a black-box identification approach based on subspace methods is developed in order to estimate a nominal state-space model around a given operating point. A Linear Quadratic Gaussian (LQG) controller has been implemented to illustrate the applicability of the estimated model. While the pilot plant is non linear, results of this application show that such an ‘average’ state-space model is enough to obtain interesting tension control performances on the whole winding zone.

Alain Richard

Papers

Continuous-time model identification from sampled data: Implementation issues and performance evaluation

A method for analysing gearbox faults using time–frequency representations

Gear crack detection by adaptive amplitude and phase demodulation

Multivariable identification of a winding process by subspace methods for tension control

Application of subspace methods to the identification of a winding process