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"Time Series Analysis": models, code, and papers

Ultrametric Wavelet Regression of Multivariate Time Series: Application to Colombian Conflict Analysis

Feb 16, 2009
Fionn Murtagh, Michael Spagat, Jorge A. Restrepo

We first pursue the study of how hierarchy provides a well-adapted tool for the analysis of change. Then, using a time sequence-constrained hierarchical clustering, we develop the practical aspects of a new approach to wavelet regression. This provides a new way to link hierarchical relationships in a multivariate time series data set with external signals. Violence data from the Colombian conflict in the years 1990 to 2004 is used throughout. We conclude with some proposals for further study on the relationship between social violence and market forces, viz. between the Colombian conflict and the US narcotics market.

* IEEE Transactions on Systems, Man, and Cybernetics - Part A, Systems and Humans, 2011 
* 36 pages, 13 figures 

Sparsification of the Alignment Path Search Space in Dynamic Time Warping

Nov 13, 2017
Saeid Soheily-Khah, Pierre-François Marteau

Temporal data are naturally everywhere, especially in the digital era that sees the advent of big data and internet of things. One major challenge that arises during temporal data analysis and mining is the comparison of time series or sequences, which requires to determine a proper distance or (dis)similarity measure. In this context, the Dynamic Time Warping (DTW) has enjoyed success in many domains, due to its 'temporal elasticity', a property particularly useful when matching temporal data. Unfortunately this dissimilarity measure suffers from a quadratic computational cost, which prohibits its use for large scale applications. This work addresses the sparsification of the alignment path search space for DTW-like measures, essentially to lower their computational cost without loosing on the quality of the measure. As a result of our sparsification approach, two new (dis)similarity measures, namely SP-DTW (Sparsified-Paths search space DTW) and its kernelization SP-K rdtw (Sparsified-Paths search space K rdtw kernel) are proposed for time series comparison. A wide range of public datasets is used to evaluate the efficiency (estimated in term of speed-up ratio and classification accuracy) of the proposed (dis)similarity measures on the 1-Nearest Neighbor (1-NN) and the Support Vector Machine (SVM) classification algorithms. Our experiment shows that our proposed measures provide a significant speed-up without loosing on accuracy. Furthermore, at the cost of a slight reduction of the speedup they significantly outperform on the accuracy criteria the old but well known Sakoe-Chiba approach that reduces the DTW path search space using a symmetric corridor.


Information Preserving Component Analysis: Data Projections for Flow Cytometry Analysis

Apr 17, 2008
Kevin M. Carter, Raviv Raich, William G. Finn, Alfred O. Hero III

Flow cytometry is often used to characterize the malignant cells in leukemia and lymphoma patients, traced to the level of the individual cell. Typically, flow cytometric data analysis is performed through a series of 2-dimensional projections onto the axes of the data set. Through the years, clinicians have determined combinations of different fluorescent markers which generate relatively known expression patterns for specific subtypes of leukemia and lymphoma -- cancers of the hematopoietic system. By only viewing a series of 2-dimensional projections, the high-dimensional nature of the data is rarely exploited. In this paper we present a means of determining a low-dimensional projection which maintains the high-dimensional relationships (i.e. information) between differing oncological data sets. By using machine learning techniques, we allow clinicians to visualize data in a low dimension defined by a linear combination of all of the available markers, rather than just 2 at a time. This provides an aid in diagnosing similar forms of cancer, as well as a means for variable selection in exploratory flow cytometric research. We refer to our method as Information Preserving Component Analysis (IPCA).

* 26 pages 

Video and Accelerometer-Based Motion Analysis for Automated Surgical Skills Assessment

Feb 24, 2017
Aneeq Zia, Yachna Sharma, Vinay Bettadapura, Eric L. Sarin, Irfan Essa

Purpose: Basic surgical skills of suturing and knot tying are an essential part of medical training. Having an automated system for surgical skills assessment could help save experts time and improve training efficiency. There have been some recent attempts at automated surgical skills assessment using either video analysis or acceleration data. In this paper, we present a novel approach for automated assessment of OSATS based surgical skills and provide an analysis of different features on multi-modal data (video and accelerometer data). Methods: We conduct the largest study, to the best of our knowledge, for basic surgical skills assessment on a dataset that contained video and accelerometer data for suturing and knot-tying tasks. We introduce "entropy based" features - Approximate Entropy (ApEn) and Cross-Approximate Entropy (XApEn), which quantify the amount of predictability and regularity of fluctuations in time-series data. The proposed features are compared to existing methods of Sequential Motion Texture (SMT), Discrete Cosine Transform (DCT) and Discrete Fourier Transform (DFT), for surgical skills assessment. Results: We report average performance of different features across all applicable OSATS criteria for suturing and knot tying tasks. Our analysis shows that the proposed entropy based features out-perform previous state-of-the-art methods using video data. For accelerometer data, our method performs better for suturing only. We also show that fusion of video and acceleration features can improve overall performance with the proposed entropy features achieving highest accuracy. Conclusions: Automated surgical skills assessment can be achieved with high accuracy using the proposed entropy features. Such a system can significantly improve the efficiency of surgical training in medical schools and teaching hospitals.


Multifractal analysis of the time series of daily means of wind speed in complex regions

Oct 04, 2017
Mohamed Laib, Jean Golay, Luciano Telesca, Mikhail Kanevski

In this paper, we applied the multifractal detrended fluctuation analysis to the daily means of wind speed measured by 119 weather stations distributed over the territory of Switzerland. The analysis was focused on the inner time fluctuations of wind speed, which could be more linked with the local conditions of the highly varying topography of Switzerland. Our findings point out to a persistent behaviour of all the measured wind speed series (indicated by a Hurst exponent significantly larger than 0.5), and to a high multifractality degree indicating a relative dominance of the large fluctuations in the dynamics of wind speed, especially in the Swiss plateau, which is comprised between the Jura and Alp mountain ranges. The study represents a contribution to the understanding of the dynamical mechanisms of wind speed variability in mountainous regions.


Integrating Novelty Detection Capabilities with MSL Mastcam Operations to Enhance Data Analysis

Mar 23, 2021
Paul Horton, Hannah R. Kerner, Samantha Jacob, Ernest Cisneros, Kiri L. Wagstaff, James Bell

While innovations in scientific instrumentation have pushed the boundaries of Mars rover mission capabilities, the increase in data complexity has pressured Mars Science Laboratory (MSL) and future Mars rover operations staff to quickly analyze complex data sets to meet progressively shorter tactical and strategic planning timelines. MSLWEB is an internal data tracking tool used by operations staff to perform first pass analysis on MSL image sequences, a series of products taken by the Mast camera, Mastcam. Mastcam's multiband multispectral image sequences require more complex analysis compared to standard 3-band RGB images. Typically, these are analyzed using traditional methods to identify unique features within the sequence. Given the short time frame of tactical planning in which downlinked images might need to be analyzed (within 5-10 hours before the next uplink), there exists a need to triage analysis time to focus on the most important sequences and parts of a sequence. We address this need by creating products for MSLWEB that use novelty detection to help operations staff identify unusual data that might be diagnostic of new or atypical compositions or mineralogies detected within an imaging scene. This was achieved in two ways: 1) by creating products for each sequence to identify novel regions in the image, and 2) by assigning multispectral sequences a sortable novelty score. These new products provide colorized heat maps of inferred novelty that operations staff can use to rapidly review downlinked data and focus their efforts on analyzing potentially new kinds of diagnostic multispectral signatures. This approach has the potential to guide scientists to new discoveries by quickly drawing their attention to often subtle variations not detectable with simple color composites.

* 8 pages, 5 figure, accepted and presented at IEEE Aerospace Conference 2021 

A Bayesian method for the analysis of deterministic and stochastic time series

Oct 23, 2012
C. A. L. Bailer-Jones

I introduce a general, Bayesian method for modelling univariate time series data assumed to be drawn from a continuous, stochastic process. The method accommodates arbitrary temporal sampling, and takes into account measurement uncertainties for arbitrary error models (not just Gaussian) on both the time and signal variables. Any model for the deterministic component of the variation of the signal with time is supported, as is any model of the stochastic component on the signal and time variables. Models illustrated here are constant and sinusoidal models for the signal mean combined with a Gaussian stochastic component, as well as a purely stochastic model, the Ornstein-Uhlenbeck process. The posterior probability distribution over model parameters is determined via Monte Carlo sampling. Models are compared using the "cross-validation likelihood", in which the posterior-averaged likelihood for different partitions of the data are combined. In principle this is more robust to changes in the prior than is the evidence (the prior-averaged likelihood). The method is demonstrated by applying it to the light curves of 11 ultra cool dwarf stars, claimed by a previous study to show statistically significant variability. This is reassessed here by calculating the cross-validation likelihood for various time series models, including a null hypothesis of no variability beyond the error bars. 10 of 11 light curves are confirmed as being significantly variable, and one of these seems to be periodic, with two plausible periods identified. Another object is best described by the Ornstein-Uhlenbeck process, a conclusion which is obviously limited to the set of models actually tested.

* Astronomy & Astrophysics 546, A89 (2012) 
* Published in A&A as free access article. Software and additional information available from 

Unsupervised detection of diachronic word sense evolution

May 30, 2018
Jean-François Delpech

Most words have several senses and connotations which evolve in time due to semantic shift, so that closely related words may gain different or even opposite meanings over the years. This evolution is very relevant to the study of language and of cultural changes, but the tools currently available for diachronic semantic analysis have significant, inherent limitations and are not suitable for real-time analysis. In this article, we demonstrate how the linearity of random vectors techniques enables building time series of congruent word embeddings (or semantic spaces) which can then be compared and combined linearly without loss of precision over any time period to detect diachronic semantic shifts. We show how this approach yields time trajectories of polysemous words such as amazon or apple, enables following semantic drifts and gender bias across time, reveals the shifting instantiations of stable concepts such as hurricane or president. This very fast, linear approach can easily be distributed over many processors to follow in real time streams of social media such as Twitter or Facebook; the resulting, time-dependent semantic spaces can then be combined at will by simple additions or subtractions.

* 10 pages, 1 figure, 10 tables 

Regularized Bilinear Discriminant Analysis for Multivariate Time Series Data

Feb 26, 2022
Jianhua Zhao, Haiye Liang, Shulan Li, Zhiji Yang, Zhen Wang

In recent years, the methods on matrix-based or bilinear discriminant analysis (BLDA) have received much attention. Despite their advantages, it has been reported that the traditional vector-based regularized LDA (RLDA) is still quite competitive and could outperform BLDA on some benchmark datasets. Nevertheless, it is also noted that this finding is mainly limited to image data. In this paper, we propose regularized BLDA (RBLDA) and further explore the comparison between RLDA and RBLDA on another type of matrix data, namely multivariate time series (MTS). Unlike image data, MTS typically consists of multiple variables measured at different time points. Although many methods for MTS data classification exist within the literature, there is relatively little work in exploring the matrix data structure of MTS data. Moreover, the existing BLDA can not be performed when one of its within-class matrices is singular. To address the two problems, we propose RBLDA for MTS data classification, where each of the two within-class matrices is regularized via one parameter. We develop an efficient implementation of RBLDA and an efficient model selection algorithm with which the cross validation procedure for RBLDA can be performed efficiently. Experiments on a number of real MTS data sets are conducted to evaluate the proposed algorithm and compare RBLDA with several closely related methods, including RLDA and BLDA. The results reveal that RBLDA achieves the best overall recognition performance and the proposed model selection algorithm is efficient; Moreover, RBLDA can produce better visualization of MTS data than RLDA.

* 14 pages, 2 figures 

Temporal Attention augmented Bilinear Network for Financial Time-Series Data Analysis

Dec 04, 2017
Dat Thanh Tran, Alexandros Iosifidis, Juho Kanniainen, Moncef Gabbouj

Financial time-series forecasting has long been a challenging problem because of the inherently noisy and stochastic nature of the market. In the High-Frequency Trading (HFT), forecasting for trading purposes is even a more challenging task since an automated inference system is required to be both accurate and fast. In this paper, we propose a neural network layer architecture that incorporates the idea of bilinear projection as well as an attention mechanism that enables the layer to detect and focus on crucial temporal information. The resulting network is highly interpretable, given its ability to highlight the importance and contribution of each temporal instance, thus allowing further analysis on the time instances of interest. Our experiments in a large-scale Limit Order Book (LOB) dataset show that a two-hidden-layer network utilizing our proposed layer outperforms by a large margin all existing state-of-the-art results coming from much deeper architectures while requiring far fewer computations.

* 12 pages, 4 figures, 3 tables