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

Support Spinor Machine

Sep 11, 2017
Kabin Kanjamapornkul, Richard Pinčák, Sanphet Chunithpaisan, Erik Bartoš

We generalize a support vector machine to a support spinor machine by using the mathematical structure of wedge product over vector machine in order to extend field from vector field to spinor field. The separated hyperplane is extended to Kolmogorov space in time series data which allow us to extend a structure of support vector machine to a support tensor machine and a support tensor machine moduli space. Our performance test on support spinor machine is done over one class classification of end point in physiology state of time series data after empirical mode analysis and compared with support vector machine test. We implement algorithm of support spinor machine by using Holo-Hilbert amplitude modulation for fully nonlinear and nonstationary time series data analysis.

* Digital Signal Processing 70 (2017) 59-72 
* 18 pages, 12 figures, 6 tables 

Fuzzy Cognitive Maps and Hidden Markov Models: Comparative Analysis of Efficiency within the Confines of the Time Series Classification Task

Apr 28, 2022
Jakub Michał Bilski, Agnieszka Jastrzębska

Time series classification is one of the very popular machine learning tasks. In this paper, we explore the application of Hidden Markov Model (HMM) for time series classification. We distinguish between two modes of HMM application. The first, in which a single model is built for each class. The second, in which one HMM is built for each time series. We then transfer both approaches for classifier construction to the domain of Fuzzy Cognitive Maps. The identified four models, HMM NN (HMM, one per series), HMM 1C (HMM, one per class), FCM NN, and FCM 1C are then studied in a series of experiments. We compare the performance of different models and investigate the impact of their hyperparameters on the time series classification accuracy. The empirical evaluation shows a clear advantage of the one-model-per-series approach. The results show that the choice between HMM and FCM should be dataset-dependent.


Adaptive Visibility Graph Neural Network and its Application in Modulation Classification

Jun 16, 2021
Qi Xuan, Kunfeng Qiu, Jinchao Zhou, Zhuangzhi Chen, Dongwei Xu, Shilian Zheng, Xiaoniu Yang

Our digital world is full of time series and graphs which capture the various aspects of many complex systems. Traditionally, there are respective methods in processing these two different types of data, e.g., Recurrent Neural Network (RNN) and Graph Neural Network (GNN), while in recent years, time series could be mapped to graphs by using the techniques such as Visibility Graph (VG), so that researchers can use graph algorithms to mine the knowledge in time series. Such mapping methods establish a bridge between time series and graphs, and have high potential to facilitate the analysis of various real-world time series. However, the VG method and its variants are just based on fixed rules and thus lack of flexibility, largely limiting their application in reality. In this paper, we propose an Adaptive Visibility Graph (AVG) algorithm that can adaptively map time series into graphs, based on which we further establish an end-to-end classification framework AVGNet, by utilizing GNN model DiffPool as the classifier. We then adopt AVGNet for radio signal modulation classification which is an important task in the field of wireless communication. The simulations validate that AVGNet outperforms a series of advanced deep learning methods, achieving the state-of-the-art performance in this task.


Deep Recurrent Disease Progression Model for Conversion-Time Prediction of Alzheimer's Disease

May 06, 2020
Wonsik Jung, Eunji Jun, Heung-Il Suk

Alzheimer's disease (AD) is known as one of the major causes of dementia and is characterized by slow progression over several years, with no treatments or available medicines. In this regard, there have been efforts to identify the risk of developing AD in its earliest time. While many of the previous works considered cross-sectional analysis, more recent studies have focused on the diagnosis and prognosis of AD with longitudinal or time-series data in a way of disease progression modeling (DPM). Under the same problem settings, in this work, we propose a novel computational framework that forecasts the phenotypic measurements of MRI biomarkers and predicts the clinical statuses at multiple future time points. However, in handling time series data, it generally faces with many unexpected missing observations. In regard to such an unfavorable situation, we define a secondary problem of estimating those missing values and tackle it in a systematic way by taking account of temporal and multivariate relations inherent in time series data. Concretely, we propose a deep recurrent network that jointly tackles the three problems of (i) missing value imputation, (ii) phenotypic measurements forecasting, and (iii) clinical status prediction of a subject based on his/her longitudinal imaging biomarkers. Notably, the learnable model parameters of our network are trained in an end to end manner with our circumspectly defined loss function. In our experiments over TADPOLE challenge cohort, we measured performance for various metrics and compared our method to competing methods in the literature. Exhaustive analyses and ablation studies were also conducted to better confirm the effectiveness of our method.

* 30 pages, 12 figures 

Human activity recognition based on time series analysis using U-Net

Sep 20, 2018
Yong Zhang, Yu Zhang, Zhao Zhang, Jie Bao, Yunpeng Song

Traditional human activity recognition (HAR) based on time series adopts sliding window analysis method. This method faces the multi-class window problem which mistakenly labels different classes of sampling points within a window as a class. In this paper, a HAR algorithm based on U-Net is proposed to perform activity labeling and prediction at each sampling point. The activity data of the triaxial accelerometer is mapped into an image with the single pixel column and multi-channel which is input into the U-Net network for training and recognition. Our proposal can complete the pixel-level gesture recognition function. The method does not need manual feature extraction and can effectively identify short-term behaviors in long-term activity sequences. We collected the Sanitation dataset and tested the proposed scheme with four open data sets. The experimental results show that compared with Support Vector Machine (SVM), k-Nearest Neighbor (kNN), Decision Tree(DT), Quadratic Discriminant Analysis (QDA), Convolutional Neural Network (CNN) and Fully Convolutional Networks (FCN) methods, our proposal has the highest accuracy and F1-socre in each dataset, and has stable performance and high robustness. At the same time, after the U-Net has finished training, our proposal can achieve fast enough recognition speed.

* 21 pages 

Deep Discriminative Direct Decoders for High-dimensional Time-series Analysis

May 22, 2022
Mohammad R. Rezaei, Milos R. Popovic, Milad Lankarany, Ali Yousefi

Dynamical latent variable modeling has been significantly invested over the last couple of decades with established solutions encompassing generative processes like the state-space model (SSM) and discriminative processes like a recurrent or a deep neural network (DNN). These solutions are powerful tools with promising results; however, surprisingly they were never put together in a unified model to analyze complex multivariate time-series data. A very recent modeling approach, called the direct discriminative decoder (DDD) model, proposes a principal solution to combine SMM and DNN models, with promising results in decoding underlying latent processes, e.g. rat movement trajectory, through high-dimensional neural recordings. The DDD consists of a) a state transition process, as per the classical dynamical models, and b) a discriminative process, like DNN, in which the conditional distribution of states is defined as a function of the current observations and their recent history. Despite promising results of the DDD model, no training solutions, in the context of DNN, have been utilized for this model. Here, we propose how DNN parameters along with an optimal history term can be simultaneously estimated as a part of the DDD model. We use the D4 abbreviation for a DDD with a DNN as its discriminative process. We showed the D4 decoding performance in both simulation and (relatively) high-dimensional neural data. In both datasets, D4 performance surpasses the state-of-art decoding solutions, including those of SSM and DNNs. The key success of DDD and potentially D4 is efficient utilization of the recent history of observation along with the state-process that carries long-term information, which is not addressed in either SSM or DNN solutions. We argue that D4 can be a powerful tool for the analysis of high-dimensional time-series data.


Physiological Signal Processing in Heart Rate Variability Measurement: A Focus on Spectral Analysis

Aug 02, 2022
Amin Gasmi

Fast Fourier Transform (FFT) relies on the HRV frequency-domain analysis techniques. It requires re-sampling of the inherently unevenly sampled heartbeat time-series (RR tachogram) to produce an evenly sampled time series of the heartbeat. However, re-sampling of the heartbeat time -- series is found to produce a substantial error when estimating an artificial RR tachogram.


Recurrent Auto-Encoder Model for Large-Scale Industrial Sensor Signal Analysis

Jul 10, 2018
Timothy Wong, Zhiyuan Luo

Recurrent auto-encoder model summarises sequential data through an encoder structure into a fixed-length vector and then reconstructs the original sequence through the decoder structure. The summarised vector can be used to represent time series features. In this paper, we propose relaxing the dimensionality of the decoder output so that it performs partial reconstruction. The fixed-length vector therefore represents features in the selected dimensions only. In addition, we propose using rolling fixed window approach to generate training samples from unbounded time series data. The change of time series features over time can be summarised as a smooth trajectory path. The fixed-length vectors are further analysed using additional visualisation and unsupervised clustering techniques. The proposed method can be applied in large-scale industrial processes for sensors signal analysis purpose, where clusters of the vector representations can reflect the operating states of the industrial system.

* E. Pimenidis and C. Jayne (Eds.): EANN 2018, CCIS 893 
* Accepted paper at the 19th International Conference on Engineering Applications of Neural Networks (EANN 2018) 

Temporal Registration in In-Utero Volumetric MRI Time Series

Aug 12, 2016
Ruizhi Liao, Esra Turk, Miaomiao Zhang, Jie Luo, Ellen Grant, Elfar Adalsteinsson, Polina Golland

We present a robust method to correct for motion and deformations for in-utero volumetric MRI time series. Spatio-temporal analysis of dynamic MRI requires robust alignment across time in the presence of substantial and unpredictable motion. We make a Markov assumption on the nature of deformations to take advantage of the temporal structure in the image data. Forward message passing in the corresponding hidden Markov model (HMM) yields an estimation algorithm that only has to account for relatively small motion between consecutive frames. We demonstrate the utility of the temporal model by showing that its use improves the accuracy of the segmentation propagation through temporal registration. Our results suggest that the proposed model captures accurately the temporal dynamics of deformations in in-utero MRI time series.

* to appear in International Conference on Medical Image Computing and Computer Assisted Intervention, 2016 

Modelling stellar activity with Gaussian process regression networks

May 13, 2022
J. D. Camacho, J. P. Faria, P. T. P. Viana

Stellar photospheric activity is known to limit the detection and characterisation of extra-solar planets. In particular, the study of Earth-like planets around Sun-like stars requires data analysis methods that can accurately model the stellar activity phenomena affecting radial velocity (RV) measurements. Gaussian Process Regression Networks (GPRNs) offer a principled approach to the analysis of simultaneous time-series, combining the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian Processes. Using HARPS-N solar spectroscopic observations encompassing three years, we demonstrate that this framework is capable of jointly modelling RV data and traditional stellar activity indicators. Although we consider only the simplest GPRN configuration, we are able to describe the behaviour of solar RV data at least as accurately as previously published methods. We confirm the correlation between the RV and stellar activity time series reaches a maximum at separations of a few days, and find evidence of non-stationary behaviour in the time series, associated with an approaching solar activity minimum.

* 28 pages, 23 figures, submitted to MNRAS