Change points detection in crime-related time series: an on-line fuzzy approach based on a shape space representation

The extension of traditional data mining methods to time series has been effectively applied to a wide range of domains such as finance, econometrics, biology, security, and medicine. Many existing mining methods deal with the task of change points detection, but very few provide a flexible approach. Querying specific change points with linguistic variables is particularly useful in crime analysis, where intuitive, understandable, and appropriate detection of changes can significantly improve the allocation of resources for timely and concise operations. In this paper, we propose an on-line method for detecting and querying change points in crime-related time series with the use of a meaningful representation and a fuzzy inference system. Change points detection is based on a shape space representation, and linguistic terms describing geometric properties of the change points are used to express queries, offering the advantage of intuitiveness and flexibility. An empirical evaluation is first conducted on a crime data set to confirm the validity of the proposed method and then on a financial data set to test its general applicability. A comparison to a similar change-point detection algorithm and a sensitivity analysis are also conducted. Results show that the method is able to accurately detect change points at very low computational costs. More broadly, the detection of specific change points within time series of virtually any domain is made more intuitive and more understandable, even for experts not related to data mining.

Parameter identification in time series models

Time series analysis can be categorized into three different approaches: classical, Box-Jenkins, and State space. Classical approach makes a basement for the analysis and Box-Jenkins approach is an improvement of the classical approach and deals with stationary time series. State space approach allows time variant factors and covers up a broader area of time series analysis. This thesis focuses on parameter identifiablity of different parameter estimation methods such as LSQ, Yule-Walker, MLE which are used in the above time series analysis approaches. Also the Kalman filter method and smoothing techniques are integrated with the state space approach and MLE method to estimate parameters allowing them to change over time. Parameter estimation is carried out by repeating estimation and integrating with MCMC and inspect how well different estimation methods can identify the optimal model parameters. Identification is performed in probabilistic and general senses and compare the results in order to study and represent identifiability more informative way.

Recurrence Quantification Analysis of System Signals for Detecting Tool and Chatter in Turning

In this thesis, the applications of the recurrence quantification analysis in metal cutting operation in a lathe, with specific objective to detect tool wear and chatter, are presented.This study is based on the discovery that process dynamics in a lathe is low dimensional chaotic. It implies that the machine dynamics is controllable using principles of chaos theory. This understanding is to revolutionize the feature extraction methodologies used in condition monitoring systems as conventional linear methods or models are incapable of capturing the critical and strange behaviors associated with the metal cutting process.As sensor based approaches provide an automated and cost effective way to monitor and control, an efficient feature extraction methodology based on nonlinear time series analysis is much more demanding. The task here is more complex when the information has to be deduced solely from sensor signals since traditional methods do not address the issue of how to treat noise present in real-world processes and its non-stationarity. In an effort to get over these two issues to the maximum possible, this thesis adopts the recurrence quantification analysis methodology in the study since this feature extraction technique is found to be robust against noise and stationarity in the signals.The work consists of two different sets of experiments in a lathe; set-I and set-2. The experiment, set-I, study the influence of tool wear on the RQA variables whereas the set-2 is carried out to identify the sensitive RQA variables to machine tool chatter followed by its validation in actual cutting. To obtain the bounds of the spectrum of the significant RQA variable values, in set-i, a fresh tool and a worn tool are used for cutting. The first part of the set-2 experiments uses a stepped shaft in order to create chatter at a known location. And the second part uses a conical section having a uniform taper along the axis for creating chatter to onset at some distance from the smaller end by gradually increasing the depth of cut while keeping the spindle speed and feed rate constant.The study concludes by revealing the dependence of certain RQA variables; percent determinism, percent recurrence and entropy, to tool wear and chatter unambiguously. The performances of the results establish this methodology to be viable for detection of tool wear and chatter in metal cutting operation in a lathe. The key reason is that the dynamics of the system under study have been nonlinear and the recurrence quantification analysis can characterize them adequately.This work establishes that principles and practice of machining can be considerably benefited and advanced from using nonlinear dynamics and chaos theory.

Analysis of System Signals Based on Cross Recurrence Method for System Dynamics Characterization

Natural systems are inherently non linear. Recurrent behaviours are typical of natural systems. Recurrence is a fundamental property of non linear dynamical systems which can be exploited to characterize the system behaviour effectively. Cross recurrence based analysis of sensor signals from non linear dynamical system is presented in this thesis. The mutual dependency among relatively independent components of a system is referred as coupling. The analysis is done for a mechanically coupled system specifically designed for conducting experiment. Further, cross recurrence method is extended to the actual machining process in a lathe to characterize the chatter during turning. The result is verified by permutation entropy method. Conventional linear methods or models are incapable of capturing the critical and strange behaviours associated with the dynamical process. Hence any effective feature extraction methodologies should invariably gather information thorough nonlinear time series analysis. The sensor signals from the dynamical system normally contain noise and non stationarity. In an effort to get over these two issues to the maximum possible extent, this work adopts the cross recurrence quantification analysis (CRQA) methodology since it is found to be robust against noise and stationarity in the signals. The study reveals that the CRQA is capable of characterizing even weak coupling among system signals. It also divulges the dependence of certain CRQA variables like percent determinism, percent recurrence and entropy to chatter unambiguously. The surrogate data test shows that the results obtained by CRQA are the true properties of the temporal evolution of the dynamics and contain a degree of deterministic structure. The results are verified using permutation entropy (PE) to detect the onset of chatter from the time series. The present study ascertains that this CRP based methodology is capable of recognizing the transition from regular cutting to the chatter cutting irrespective of the machining parameters or work piece material. The results establish this methodology to be feasible for detection of chatter in metal cutting operation in a lathe.

" Nonlinear Signal Processing of Electroencephalogram .' Application in the Study of Neurodynamics. "

Interfacings of various subjects generate new field ofstudy and research that help in advancing human knowledge. One of the latest of such fields is Neurotechnology, which is an effective amalgamation of neuroscience, physics, biomedical engineering and computational methods. Neurotechnology provides a platform to interact physicist; neurologist and engineers to break methodology and terminology related barriers. Advancements in Computational capability, wider scope of applications in nonlinear dynamics and chaos in complex systems enhanced study of neurodynamics. However there is a need for an effective dialogue among physicists, neurologists and engineers. Application of computer based technology in the field of medicine through signal and image processing, creation of clinical databases for helping clinicians etc are widely acknowledged. Such synergic effects between widely separated disciplines may help in enhancing the effectiveness of existing diagnostic methods. One of the recent methods in this direction is analysis of electroencephalogram with the help of methods in nonlinear dynamics. This thesis is an effort to understand the functional aspects of human brain by studying electroencephalogram. The algorithms and other related methods developed in the present work can be interfaced with a digital EEG machine to unfold the information hidden in the signal. Ultimately this can be used as a diagnostic tool.

Space-time cluster analysis of American visceral leishmaniasis in Bauru, Sao Paulo State, Brazil

A space-time analysis of American visceral leishmaniasis (AVL) in humans in the city of Bauru, Sao Paulo State, Brazil was carried out based on 239 cases diagnosed between June 2003 and October 2008. Spatial analysis of the disease showed that cases occurred especially in the city's urban areas. AVL annual incidence rates were calculated, demonstrating that the highest rate occurred in 2006 (19.55/100,000 inhabitants). This finding was confirmed by the time series analysis, which also showed a positive tendency over the period analyzed. The present study allows us to conclude that the disease was clustered in the Southwest side of the city in 2006, suggesting that this area may require special attention with regard to control and prevention measures.

Space-time cluster analysis of American visceral leishmaniasis in Bauru, São Paulo State, Brazil

A space-time analysis of American visceral leishmaniasis (AVL) in humans in the city of Bauru, São Paulo State, Brazil was carried out based on 239 cases diagnosed between June 2003 and October 2008. Spatial analysis of the disease showed that cases occurred especially in the city's urban areas. AVL annual incidence rates were calculated, demonstrating that the highest rate occurred in 2006 (19.55/100,000 inhabitants). This finding was confirmed by the time series analysis, which also showed a positive tendency over the period analyzed. The present study allows us to conclude that the disease was clustered in the Southwest side of the city in 2006, suggesting that this area may require special attention with regard to control and prevention measures.

Local Trigonometric Methods for Time Series Smoothing.

The thesis is concerned with local trigonometric regression methods. The aim was to develop a method for extraction of cyclical components in time series. The main results of the thesis are the following. First, a generalization of the filter proposed by Christiano and Fitzgerald is furnished for the smoothing of ARIMA(p,d,q) process. Second, a local trigonometric filter is built, with its statistical properties. Third, they are discussed the convergence properties of trigonometric estimators, and the problem of choosing the order of the model. A large scale simulation experiment has been designed in order to assess the performance of the proposed models and methods. The results show that local trigonometric regression may be a useful tool for periodic time series analysis.

Time series forecasting and prediction : a bibliography with abstracts.

Includes indexes.

Manual for the pattern description of time series /

Bibliography: p. 61-69.

Multivariate analyses of variance and covariance for simulation studies involving normal time series

Photocopy.

Extrapolation, interpolation, and smoothing of stationary time series, with engineering applications.

"First published during the war as a classified report to Section D2, National Defense Research Committee."

Causality detection on US mutual fund movements using evolutionary subset time-series

In this paper we develop an evolutionary kernel-based time update algorithm to recursively estimate subset discrete lag models (including fullorder models) with a forgetting factor and a constant term, using the exactwindowed case. The algorithm applies to causality detection when the true relationship occurs with a continuous or a random delay. We then demonstrate the use of the proposed evolutionary algorithm to study the monthly mutual fund data, which come from the 'CRSP Survivor-bias free US Mutual Fund Database'. The results show that the NAV is an influential player on the international stage of global bond and stock markets.

Structural change in macroeconomic time series: A complex systems perspective

We demonstrate that the process of generating smooth transitions Call be viewed as a natural result of the filtering operations implied in the generation of discrete-time series observations from the sampling of data from an underlying continuous time process that has undergone a process of structural change. In order to focus discussion, we utilize the problem of estimating the location of abrupt shifts in some simple time series models. This approach will permit its to address salient issues relating to distortions induced by the inherent aggregation associated with discrete-time sampling of continuous time processes experiencing structural change, We also address the issue of how time irreversible structures may be generated within the smooth transition processes. (c) 2005 Elsevier Inc. All rights reserved.

Using intervention time series analyses to assess the effects of imperfectly identifiable natural events: A general method and example

BACKGROUND: Intervention time series analysis (ITSA) is an important method for analysing the effect of sudden events on time series data. ITSA methods are quasi-experimental in nature and the validity of modelling with these methods depends upon assumptions about the timing of the intervention and the response of the process to it. METHOD: This paper describes how to apply ITSA to analyse the impact of unplanned events on time series when the timing of the event is not accurately known, and so the problems of ITSA methods are magnified by uncertainty in the point of onset of the unplanned intervention. RESULTS: The methods are illustrated using the example of the Australian Heroin Shortage of 2001, which provided an opportunity to study the health and social consequences of an abrupt change in heroin availability in an environment of widespread harm reduction measures. CONCLUSION: Application of these methods enables valuable insights about the consequences of unplanned and poorly identified interventions while minimising the risk of spurious results.