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

Skill Analysis with Time Series Image Data

Jan 21, 2014
Toshiyuki Maeda, Masanori Fujii, Isao Hayashi

We present a skill analysis with time series image data using data mining methods, focused on table tennis. We do not use body model, but use only hi-speed movies, from which time series data are obtained and analyzed using data mining methods such as C4.5 and so on. We identify internal models for technical skills as evaluation skillfulness for the forehand stroke of table tennis, and discuss mono and meta-functional skills for improving skills.

* International Journal of Soft Computing and Software Engineering [JSCSE], Vol. 3, No. 3, pp. 576-580, 2013 
* 5 pages, 6 figures 

Robust multivariate and functional archetypal analysis with application to financial time series analysis

Oct 01, 2018
Jesús Moliner, Irene Epifanio

Archetypal analysis approximates data by means of mixtures of actual extreme cases (archetypoids) or archetypes, which are a convex combination of cases in the data set. Archetypes lie on the boundary of the convex hull. This makes the analysis very sensitive to outliers. A robust methodology by means of M-estimators for classical multivariate and functional data is proposed. This unsupervised methodology allows complex data to be understood even by non-experts. The performance of the new procedure is assessed in a simulation study, where a comparison with a previous methodology for the multivariate case is also carried out, and our proposal obtains favorable results. Finally, robust bivariate functional archetypoid analysis is applied to a set of companies in the S\&P 500 described by two time series of stock quotes. A new graphic representation is also proposed to visualize the results. The analysis shows how the information can be easily interpreted and how even non-experts can gain a qualitative understanding of the data.


Temporal Logistic Neural Bag-of-Features for Financial Time series Forecasting leveraging Limit Order Book Data

Jan 24, 2019
Nikolaos Passalis, Anastasios Tefas, Juho Kanniainen, Moncef Gabbouj, Alexandros Iosifidis

Time series forecasting is a crucial component of many important applications, ranging from forecasting the stock markets to energy load prediction. The high-dimensionality, velocity and variety of the data collected in these applications pose significant and unique challenges that must be carefully addressed for each of them. In this work, a novel Temporal Logistic Neural Bag-of-Features approach, that can be used to tackle these challenges, is proposed. The proposed method can be effectively combined with deep neural networks, leading to powerful deep learning models for time series analysis. However, combining existing BoF formulations with deep feature extractors pose significant challenges: the distribution of the input features is not stationary, tuning the hyper-parameters of the model can be especially difficult and the normalizations involved in the BoF model can cause significant instabilities during the training process. The proposed method is capable of overcoming these limitations by a employing a novel adaptive scaling mechanism and replacing the classical Gaussian-based density estimation involved in the regular BoF model with a logistic kernel. The effectiveness of the proposed approach is demonstrated using extensive experiments on a large-scale financial time series dataset that consists of more than 4 million limit orders.


Topological Machine Learning for Multivariate Time Series

Nov 27, 2019
Chengyuan Wu, Carol Anne Hargreaves

We develop a framework for analyzing multivariate time series using topological data analysis (TDA) methods. The proposed methodology involves converting the multivariate time series to point cloud data, calculating Wasserstein distances between the persistence diagrams and using the $k$-nearest neighbors algorithm ($k$-NN) for supervised machine learning. Two methods (symmetry-breaking and anchor points) are also introduced to enable TDA to better analyze data with heterogeneous features that are sensitive to translation, rotation, or choice of coordinates. We apply our methods to room occupancy detection based on 5 time-dependent variables (temperature, humidity, light, CO2 and humidity ratio). Experimental results show that topological methods are effective in predicting room occupancy during a time window.

* 15 pages 

Period Estimation in Astronomical Time Series Using Slotted Correntropy

Dec 13, 2011
Pablo Huijse, Pablo A. Estévez, Pablo Zegers, José Príncipe, Pavlos Protopapas

In this letter, we propose a method for period estimation in light curves from periodic variable stars using correntropy. Light curves are astronomical time series of stellar brightness over time, and are characterized as being noisy and unevenly sampled. We propose to use slotted time lags in order to estimate correntropy directly from irregularly sampled time series. A new information theoretic metric is proposed for discriminating among the peaks of the correntropy spectral density. The slotted correntropy method outperformed slotted correlation, string length, VarTools (Lomb-Scargle periodogram and Analysis of Variance), and SigSpec applications on a set of light curves drawn from the MACHO survey.

* IEEE Signal Processing Letters, vol. 18, no. 6, pp. 371-374, year 2011 

Power Data Classification: A Hybrid of a Novel Local Time Warping and LSTM

Jun 07, 2017
Yuanlong Li, Han Hu, Yonggang Wen, Jun Zhang

In this paper, for the purpose of data centre energy consumption monitoring and analysis, we propose to detect the running programs in a server by classifying the observed power consumption series. Time series classification problem has been extensively studied with various distance measurements developed; also recently the deep learning based sequence models have been proved to be promising. In this paper, we propose a novel distance measurement and build a time series classification algorithm hybridizing nearest neighbour and long short term memory (LSTM) neural network. More specifically, first we propose a new distance measurement termed as Local Time Warping (LTW), which utilizes a user-specified set for local warping, and is designed to be non-commutative and non-dynamic programming. Second we hybridize the 1NN-LTW and LSTM together. In particular, we combine the prediction probability vector of 1NN-LTW and LSTM to determine the label of the test cases. Finally, using the power consumption data from a real data center, we show that the proposed LTW can improve the classification accuracy of DTW from about 84% to 90%. Our experimental results prove that the proposed LTW is competitive on our data set compared with existed DTW variants and its non-commutative feature is indeed beneficial. We also test a linear version of LTW and it can significantly outperform existed linear runtime lower bound methods like LB_Keogh. Furthermore, with the hybrid algorithm, for the power series classification task we achieve an accuracy up to about 93%. Our research can inspire more studies on time series distance measurement and the hybrid of the deep learning models with other traditional models.


Training Robust Deep Models for Time-Series Domain: Novel Algorithms and Theoretical Analysis

Jul 13, 2022
Taha Belkhouja, Yan Yan, Janardhan Rao Doppa

Despite the success of deep neural networks (DNNs) for real-world applications over time-series data such as mobile health, little is known about how to train robust DNNs for time-series domain due to its unique characteristics compared to images and text data. In this paper, we propose a novel algorithmic framework referred as RObust Training for Time-Series (RO-TS) to create robust DNNs for time-series classification tasks. Specifically, we formulate a min-max optimization problem over the model parameters by explicitly reasoning about the robustness criteria in terms of additive perturbations to time-series inputs measured by the global alignment kernel (GAK) based distance. We also show the generality and advantages of our formulation using the summation structure over time-series alignments by relating both GAK and dynamic time warping (DTW). This problem is an instance of a family of compositional min-max optimization problems, which are challenging and open with unclear theoretical guarantee. We propose a principled stochastic compositional alternating gradient descent ascent (SCAGDA) algorithm for this family of optimization problems. Unlike traditional methods for time-series that require approximate computation of distance measures, SCAGDA approximates the GAK based distance on-the-fly using a moving average approach. We theoretically analyze the convergence rate of SCAGDA and provide strong theoretical support for the estimation of GAK based distance. Our experiments on real-world benchmarks demonstrate that RO-TS creates more robust DNNs when compared to adversarial training using prior methods that rely on data augmentation or new definitions of loss functions. We also demonstrate the importance of GAK for time-series data over the Euclidean distance. The source code of RO-TS algorithms is available at

* Proceedings of the AAAI Conference on Artificial Intelligence, 36(6), 6055-6063, 2022 
* Published AAAI 2022 

Discovering shared and individual latent structure in multiple time series

Aug 12, 2010
Suchi Saria, Daphne Koller, Anna Penn

This paper proposes a nonparametric Bayesian method for exploratory data analysis and feature construction in continuous time series. Our method focuses on understanding shared features in a set of time series that exhibit significant individual variability. Our method builds on the framework of latent Diricihlet allocation (LDA) and its extension to hierarchical Dirichlet processes, which allows us to characterize each series as switching between latent ``topics'', where each topic is characterized as a distribution over ``words'' that specify the series dynamics. However, unlike standard applications of LDA, we discover the words as we learn the model. We apply this model to the task of tracking the physiological signals of premature infants; our model obtains clinically significant insights as well as useful features for supervised learning tasks.

* Additional supplementary section in tex file 


Jun 05, 2018
Jonathan Mei, José M. F. Moura

In many applications, the interdependencies among a set of $N$ time series $\{ x_{nk}, k>0 \}_{n=1}^{N}$ are well captured by a graph or network $G$. The network itself may change over time as well (i.e., as $G_k$). We expect the network changes to be at a much slower rate than that of the time series. This paper introduces eigennetworks, networks that are building blocks to compose the actual networks $G_k$ capturing the dependencies among the time series. These eigennetworks can be estimated by first learning the time series of graphs $G_k$ from the data, followed by a Principal Network Analysis procedure. Algorithms for learning both the original time series of graphs and the eigennetworks are presented and discussed. Experiments on simulated and real time series data demonstrate the performance of the learning and the interpretation of the eigennetworks.


Geometric feature performance under downsampling for EEG classification tasks

Feb 15, 2021
Bryan Bischof, Eric Bunch

We experimentally investigate a collection of feature engineering pipelines for use with a CNN for classifying eyes-open or eyes-closed from electroencephalogram (EEG) time-series from the Bonn dataset. Using the Takens' embedding--a geometric representation of time-series--we construct simplicial complexes from EEG data. We then compare $\epsilon$-series of Betti-numbers and $\epsilon$-series of graph spectra (a novel construction)--two topological invariants of the latent geometry from these complexes--to raw time series of the EEG to fill in a gap in the literature for benchmarking. These methods, inspired by Topological Data Analysis, are used for feature engineering to capture local geometry of the time-series. Additionally, we test these feature pipelines' robustness to downsampling and data reduction. This paper seeks to establish clearer expectations for both time-series classification via geometric features, and how CNNs for time-series respond to data of degraded resolution.

* 10 pages