Home

# Multivariate time series PCA

A PCA-based Similarity Measure for Multivariate Time Series∗ Kiyoung Yang and Cyrus Shahabi Computer Science Department University of Southern Californi Principal Component Analysis (PCA) is one of the most popular dimensionality reduction methods which transforms the data by projecting it to a set of orthogonal axes. It works by finding the..

. It is called a univariate time series (UTS) whennis equal to 1, and a multivariate time series (MTS) whennis equal to, or greater than 2. A UTS data is usually repre-sented in a vector of sizem, while each MTS item is typ-ically stored in anm×nmatrix, wheremis the numberof observations andnis the number of variables (e.g., sen-sors)

Principal component analysis (PCA) of multivariate time series is a statistical technique used for explaining the variance‐covariance matrix of a set of m‐dimensional variables through a few linear combinations of these variables 1. I have a dataset which contains multivariate time series and I would try applying PCA on it, but I'm not sure how to do it. Consider the following scenario - you are monitoring N parameters of some machine during some time (M samples) and you save this test as an observation. You have Q such tests and you would like to learn something about. Multivariate Time Series PCA. 0. I have many multivariate time series each with similar time length window and variables recorded. Example: one time series plot. one time series Data: I am able to extract prin. components for individual time series. But, I am chocked on how to extract Prin. components taking into account all the time series. between several multivariate time series regression methods to provide guidance on when to use what method, and how to implement it in SAS, R, or Matlab. Analysis of multivariate time series. Multivariate time series Vector AutoRegressive (VAR) PCA interpretation. VAR(p) The periodic components embedded in a set of concurrent time-series can be isolated by Principal Component Analysis (PCA), to uncover any abnormal activity hidden in them.¹ This is putting the same math commonly used to reduce feature sets to a different purpose

### Dimensionality Reduction using PCA on multivariate

1. This said, the easiest solution is to ignore that you have a time series and just concatenate the information to perform the PCA analysis with all. import numpy as np from sklearn.decomposition import PCA data = np.random.randn (1000, 300, 20) # n_instances, n_steps, n_features # combine the features and the steps, then # you perform PCA for.
2. The repository provides a synthetic multivariate time series data generator. The implementation is an extention of the cylinder-bell-funnel time series data generator. The scipt enables synthetic data generation of different length, dimensions and samples. timeseries-data synthetic-data multivariate-timeseries timeseriesclassificatio
3. In PCA, the matrix consists of a single variable observed at multiple locations (a multivariate time series dataset, where the variables are different spatial locations) and the resuling components are termed spatial principal components
4. It is called a univariate time series when n is equal to 1, and a multivariate time series (MTS) when n is equal to, or greater than 2.MTS datasets are common in various fields, such as in multimedia, medicine and finance
5. Multivariate time series (MTS) datasets are common in various multimedia, medical and financial applications. We propose a similarity measure for MTS datasets, <i>Eros</i> <i>E</i>xtended F<i>ro</i>beniu<i>s</i> norm), which is based on Principal Component Analysis (PCA). <i>Eros</i> applies PCA to MTS datasets represented as matrices to generate principal components and associated eigenvalues
6. To link to the entire object, paste this link in email, IM or document To embed the entire object, paste this HTML in website To link to this page, paste this link in email, IM or document To embed this page, paste this HTML in websit
7. My leads are the following : classify the series for each dimension (using KNN algorithm and DWT), reduce the dimensionality with PCA and use a final classifier along the multidimensions categories. Being relatively new to ML, I don't know if I am totally wrong. classification time-series pca. Share

### PCA in case of multivariate time series - Cross Validate

• An approach on the use of DTW with multivariate time-series (the paper actual refers to classification but you might want to use the idea and adjust it for clustering) A paper on clustering of time-series. A PCA-based similarity measure for multivariate time-series. A review on feature extraction and pattern recognition methods in time-series dat
• ing techniques without substantially affecting the quality of the obtained results. Our approach includes a representation based on principal component analysis (PCA) in order to reduce the intrinsically.
• Multivariate time series with intrinsic features such as high dimensionality and similarity measure makes the clustering progress more complex than univariate time series. Principal component analysis (PCA) is a common method to transform MTS into a new coordinate space to find the major features
• It is called a univariate time series (UTS) when n is equal to 1, and a multivariate time series (MTS) when n is equal to, or greater than 2
• ing has attracted much interest in recent years due to the increasing number of fields requiring the capability to manage and process large collections of MTS
• This Multivariate Time Series Clustering project follows the development of a Long Short-Term Memory (LSTM), as part of T-DAB's Innovation Sandbox, to predict the rudder movements that a sailor would make during a race

This paper proposes a cluster-based method to analyze the evolution of multivariate time series and applies this to the COVID-19 pandemic. On each day, we partition countries into clusters according to both their cases and death counts. The total number of clusters and individual countries' cluster An essential guide on high dimensional multivariate time series including all the latest topics from one of the leading experts in the field Following the highly successful and much lauded book, Time Series AnalysisUnivariate and Multivariate Methods, this new work by William W.S. Wei focuses on high dimensional multivariate time series, and is illustrated with numerous high dimensional empirical time series 1. I am trying to write a multivariate Singular Spectrum Analysis with Monte Carlo test. To this extent I am working on a code piece that can reconstruct the input series using the lagged trajectory matrix and projection base (ST-PCs) that result from the pca/ssa decomposition of the input series. The attached code piece works for a lagged. Due to the high dimensionality of multivariate time series and most of the previous work concentrating on univariate time series clustering, a novel method which is based on common principal component analysis, is proposed to achieve multivariate time series clustering more fast and accurately [1] Multivariate Time Series Analysis with R and Financial Applications by Ruey S. Tsay (2014), Wiley: ISBN: 978-1118617908. [2] Modeling financial time series with S-Plus®, by E. Zivot, and Wang, J. (2007), Springer Science & Business Media

### Multivariate Time Series PCA - Cross Validate

For example, a model for time series regression (use a series to predict an output value) can be re-used for a time series forecasting task (the predicted output value is a future value). Mission statement : sktime enables understandable and composable machine learning with time series Multivariate Data Format. Usually, you load response and predictor data sets into the MATLAB Workspace as numeric arrays, MATLAB tables, or MATLAB timetables. However, multivariate time series object functions accept 2-D or 3-D numeric arrays only, and you must specify the response and predictor data as separate inputs There is a book available in the Use R! series on using R for multivariate analyses, An Introduction to Applied Multivariate Analysis with R by Everitt and Hothorn. Acknowledgements ¶ Many of the examples in this booklet are inspired by examples in the excellent Open University book, Multivariate Analysis (product code M249/03.

A beginner's explanation for PCA on a multivariate time series. Ask Question Asked 1 year ago. Active 9 months ago. Viewed 51 times 1 $\begingroup$ This is very much a beginner's question. Say you have a 10 dimensional vector for every day in a time series of 100 days. I was reading about using PCA to reduce this to a one dimensional time. In this paper, we study sparse PCA for weakly sta-tionary VAR time series. By treating the transition matrix A as a nuisance parameter, we directly apply sparse PCA on the multivariate time series x 1;:::;x T to estimate the leading eigenvector u 1 as if the data are i.i.d. generated. Let $$u 1;ub 1) be the angle be-tween ub 1 and u 1, an Multivariate time series (MTS) data sets are common in various multimedia, medical and financial application domains. These applications perform several data-analysis operations on large number of MTS data sets such as similarity searches, feature-subset-selection, cluster ing and classification. Inherently, an MTS item has a large number of dimensions ### The PCA Trick with Time-Series I am running PCA on a multivariate time-series dataset using observations across time (i.e. w/out time as an explicit variable) as the design matrix. Given this setup, I've found that it is difficult for me to interpret the covariance matrix derived from such a design matrix. For instance, if two variables (e.g. signal A & signal B) positively. PCA and RT. The ICA paradigm is introduced in sec- tion 3 and in section 3.3, a particular algorithmic im- plementation of ICA is presented for the linear case. An application to geophysical data series is discussed in section 4 using the time series of tropical sea surface temperature variability. 2. Classical Component Extraction Technique Principal component analysis (PCA) computes a new set of uncorrelated multivariate (vector) time series by a transform of coordinate rotation from original correlated multivariate time series. This VI performs PCA according to the following steps: 1. Calculates the covariance/correlation coefficient matrix. This VI calculates the covariance. Jim Ferry's answer is an excellent motivator to one way to look at Fourier analysis (not to mention PCA.) However, there's another way to look at dimension reduction in terms of time series, and that is through multiple signal or series. What a lo.. The Time Series Analysis Tools also provide methods for analyzing multivariate time series, such as covariance matrix, independent component analysis (ICA), and principal component analysis (PCA). Modeling and prediction methods — Build dynamic models for a univariate or multivariate (vector) time series and perform predictions based on the. For MICE, MF, and PCA methods, we treat a multi-variate time series \(X\in {{\mathbb{R}}}^{T\times D}$$ as T data samples and impute them independently, so that these methods can be applied to. the multivariate time series which are typical of process data. Smyth [29] clustered sequential data using polynomial re- Huang et al. [33] used PCA models to cluster multivariate time-series data by splitting large clusters into smaller clus-ters based on the amount of variance explained by a numbe In classical multivariate statistical analysis, there is a hierarchy of methods, starting with linear regression at the base, followed by principal component analysis (PCA) and finally canonical correlation analysis (CCA). A multivariate time series method, the singular spectrum analysis (SSA), has been a fruitful extension of the PCA technique overview of many multivariate process-monitoring techniques, such as the multivariate EWMA and multivariate CUSUM, but provide minimal coverage of techniques for high-dimensional processes. Barcel´o et al. (2010) compare the classical multivariate time-series Box-Jenkins methodology with a partial least squares (PLS) method

Analysis (PCA) is the standard tool for dimension reduction. For autocorrelated processes, however, PCA fails to take into account the autocorrelation information. Thus, it is doubtful that PCA is the best choice. A two-step dimension reduction procedure is devised for multivariate time series. Comparisons based on both simulated examples an PCA revisited Eigenvectors (spatial patterns) can be thought of as empirically derived normal modes. PC time series are the time-varying amplitudes of each mode: like a drum head. Truncated PCA is a good way to reduce the data set to subspace -least variability lost. Recent work developing nonlinear PCA techniques (e.g., Monahan & Fyfe multivariate time series are considered in [17, 11, 1]. In [10] multivariate control charts for nonlinear autocorrelated processes are introduced using the support vector regression approach. The monitoring of the covariance matrix of multivariate time series is dis-cussed only in a few papers. In [15, 16] several types of exponentially weighte the analysis of multivariate time series data. The PCA projection algorithm is applied to arrange multivariate time-series on the (2D) display screen (the Time Series Path Map). We connect temporally adjacent data ele-ments and receive a sequentially ordered set of points

extraction methods such as principal components analysis (PCA) and linear discriminant analysis (LDA) cannot work well on multivariate time series because of the failure of cap-turing the implicit nonlinearity. Popular feature extraction for multivariate time series ca Abstract: We report on the results of two new approaches to considering how many principal components to retain from an analysis of a multivariate time series. The first is by using a heat map based approach. A heat map in this context refers to a series of principal component coefficients created by applying a sliding window to a multivariate time series Abstract. Multivariate time series (MTS) data sets are common in various multimedia, medical and financial application domains. These applications perform several data-analysis operations on large number of MTS data sets such as similarity searches, feature-subset-selection, clustering and classification

### python - PCA with several time series as features of one

1. Multivariate, Sequential, Time-Series . Classification, Clustering, Causal-Discovery . Real . 27170754 . 115 . 201
2. I have multivariate time series data that contains coffee prices and tea prices with weekly frequency and I have added lagged versions of each variable. After applied the steps as you explain for feature selection of lag variables, I have found most relevant lagged features for coffe as coffee_t_1, coffee_t_2, coffee_t_3 and, coffee_t_4.
3. A method for decomposing multivariate time series into a causal hierarchy within specific frequency bands J Comput Neurosci. 2018 Oct;45(2):59-82. doi: 10.1007/s10827-018-0691-y. Epub 2018 Jul 30. Authors Jonathan D Drover 1 , Nicholas D Schiff 2 Affiliations 1 Weill.
4. Time series are everywhere! In user behavior on a website, or stock prices of a Fortune 500 company, or any other time-related example. whereas the multivariate time series is composed of three variables in Fig. 3b, and has both univariate (O3) and multivariate (O1 and O2) point outliers. (PCA), for detecting outliers. Why do we need.

### multivariate-timeseries · GitHub Topics · GitHu

dimensionality of multivariate dependent variable to a conﬁdence score, indicating whether the batch production is on-spec or off-spec. 2. Instead of using classical Multivariate classiﬁcation techniques like PCA/PLS or Nearest neighbour methods explore the usage and application of novel concept of Time Series shapelet Time-delayed embedding of scalar time series + PCA Multivariate Singular Spectrum AnalysisAndreas Groth, LMD, ENS, Paris 7/27. Univariate SSA Multivariate SSA Monte-Carlo (M)SSAConclusions Combination with Principal Component Analysis (PCA) IdeaApply PCA to x(t) in order to extract the entire attracto We propose a two-stage approach Spec PC-CP to identify change points in multivariate time series. In the first stage, we obtain a low-dimensional summary of the high-dimensional time series by Spectral Principal Component Analysis (Spec-PCA). In the second stage, we apply cumulative sum-type test on the Spectral PCA component using a binary segmentation algorithm We are not the first to develop a kernel capable of representing sequential real-valued data [cuturi2011fast, cuturi2007kernel, gartner2004kernels, haussler1999convolution, kiraly2019, lodhi2002text] but the series kernel that we propose is the first to represent time series in all their generality. Our method for building series kernels represents multivariate real-valued observations, their.

Thank you for the A2A. ML models will give you better result than traditional Statistical models. LSTM is the best for multivariate time series, in my opinion, if you are not worried about execution time. However, GRU gives you good enough result. We study sparse principal component analy- sis (sparse PCA) for high dimensional multi- variate vector autoregressive (VAR) time se- ries. By treating the transition matrix as a nuisance parameter, we show that sparse PCA can be directly applied on analyzing multivariate time series as if the data are i.i.d. generated The purpose of this course is to teach you some matrix-based data analysis methods in neural time series data, with a focus on multivariate dimensionality reduction and source-separation methods. This includes covariance matrices, principal components analysis (PCA), generalized eigendecomposition (even better than PCA!), and independent. An accessible guide to the multivariate time series tools used in numerous real-world applications. Multivariate Time Series Analysis: With R and Financial Applications is the much anticipated sequel coming from one of the most influential and prominent experts on the topic of time series. Through a fundamental balance of theory and methodology, the book supplies readers with a comprehensible. This function computes the empirical cross-covariance of two stationary multivariate time series. If only one time series is provided it determines the empirical autocovariance function. Usage cov.structure(X, Y = X, lags = 0) Arguments X vector or matrix. If matrix, then each row corresponds to a timepoint of a vector time series. Y vector or.

Multivariate time-series modeling with generative neural networks. 02/25/2020 ∙ by Marius Hofert, et al. ∙ University of Waterloo ∙ 9 ∙ share . Generative moment matching networks (GMMNs) are introduced as dependence models for the joint innovation distribution of multivariate time series (MTS) PCA & multivariate signal processing, applied to neural data. 8 hours of instruction on theory, practice, and implementation of covariance-based dimension-reduction and source-separation methods for multivariate data. Sample EEG data are provided, and the methods are applicable to any multichannel time series data The algorithm favors contiguous clusters in time and able to detect changes in the hidden structure of multivariate time-series. A fuzzy decision making algorithm based on a compatibility criteria of the clusters have been worked out to determine the required number of segments, while the required number of principal components are determined. Outlier time series: when an entire time series is behaving unusually (only for multivariate time series) Source. Variable 4 is an outlier time series in a multivariate time series. 1.3. Nature of the method. Univariate detection method: can only consider a single time-dependent variable (can be applied to univariate or multivariate time series

### Unsupervised learning for time series data: Singular

1. X: time series data; Outputs: tr_time: time (in seconds) used to generate the representations; Additionally, the representations of the input data X are stored in the attribute RC_model.input_repr. Time series datasets. A collection of univariate and multivariate time series dataset is available for download here. The dataset are provided both.
2. Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable.Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other
3. This text is a good reference for a broad range of topics in the analysis of multivariate time series. It covers not only proven mainstream methods (VARMA, cointegration, PCA) but also delves into some cutting-edge techniques such as those used in volatility modelling
4. For a cleaner and clearer view, Figure 2 illustrates the multivariate time series only for sensors that detected the malfunction zone of the dynamic machine. Therefore, of total of 28 sensors, 18 were chosen to illustrate the multivariate time series. The machinery malfunction was detected in all sensor groups, except for the M1
5. ShapeNet: A Shapelet-Neural Network Approach for Multivariate Time Series Classiﬁcation Guozhong Li1, Byron Choi1, Jianliang Xu1, Sourav S Bhowmick2, Kwok-Pan Chun3, Grace L.H Wong4 1Department of Computer Science, Hong Kong Baptist University, Hong Kong 2School of Computing Engineering, Nanyang Technological University, Singapore 3Department of Geography, Hong Kong Baptist University, Hong Kon
6. Multivariate Time Series Analysis and Applications / Edition 1 available in Hardcover, NOOK Book. Read an excerpt of this book! Add to Wishlist. ISBN-10: 1119502853 ISBN-13: 9781119502852 Pub. Date: 03/26/2019 Publisher: Wiley. Multivariate Time Series Analysis and Applications / Edition 1

### A PCA-based similarity measure for multivariate time serie

Huang et al. (2000) used principal component analysis (PCA) models to cluster multivariate time-series data by splitting large clusters into smaller clusters on the basis of the amount of vari- ance in the data that is explained by a specified number of principal components The main purpose of principal components analysis (PCA) is to enable you to isolate and remove extraneous or redundant variables in a multivariate time series. Extraneous and redundant variables increase the dimensionality of a time series and prevent you from finding important underlying patterns in the data Some researchers have applied PCA for change point detection in multidimen-sional time series. Kuncheva and Faithfull [5] developed an approach based on PCA feature extraction for change detection in unlabelled, multidimensional streaming data and showed that many datasets bene t signi cantly from using PCA

### Multivariate time series analysis based on principal

Simulated data in the form of sine waves with noise were analyzed as time series using principal component analysis (PCA). Multiple replicates of each underlying signal were used so that the number of features exceeded the number extracted principal components (PCs). Both the covariance matrix and correlation matrix were used during eigendecomposition, and the standardized (scaled) and non. Kiyoung Yang and Cyrus Shahabi. 2004. A PCA-based similarity measure for multivariate time series. In Proceedings of the 2nd ACM international workshop on Multimedia databases. 65--74. Google Scholar Digital Library; Matthew Yglesias. 2013. The U.S. Virgin Islands Are in a Catastrophic Recession. website (PCA). Our measure consists of three components that separately take into account di erences in the means, correlations, and variances of the data sets (time series) being compared. As such, our mea-sure takes into account much of the information in the data set. It is also possible to weight the com-ponents di erently, so one can incorporate. Generative moment matching networks (GMMNs) are introduced as dependence models for the joint innovation distribution of multivariate time series (MTS). Following the popular copula-GARCH approach for modeling dependent MTS data, a framework based on a GMMN-GARCH approach is presented. First, ARMA-GARCH models are utilized to capture the serial dependence within each univariate marginal time. In view of the importance of various components and asynchronous shapes of multivariate time series, a clustering method based on dynamic time warping and affinity propagation is proposed. From the two perspectives of the global and local properties information of multivariate time series, the relationship between the data objects is described

### classification - Classify multivariate time series - Data

Dynamic principal component analysis (DPCA) decomposes multivariate time series into uncorrelated components. Compared to classical principal components, DPCA decomposition outputs components which are uncorrelated in time, allowing simpler modeling of the processes and maximizing long run variance of the projection It can make or break your forecasting. So let us go through some of the crucial preprocessing steps for time series —. First of all, cast your Date column in date datatype and set it as your. PCA on the time series • By deﬁnition there is a correlation between successive samples • Resulting covariance matrix will be symmetric Toeplitz with a diagonal tapering towards 0 Cov(X)≈ 11−e 0 1−e11−e 1−e11−e 0 1−e1 ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

The authors presented a PCA based multivariate time-series segmentation method which addressed the first problem. The nonlinear processes were split into locally linear segments by using T2 and Q statistics as cost functions. Based on this solution, we demonstrate how the homogeneous operation ranges and changes in process dynamics can also be. Multivariate time series is usually used in multimedia, finance, medical, gesture and speech recognition. MTS dataset consists of (PCA). The idea is to select features based on the time of observation that have most influences on other observation. Only observation times relation to learning or data mining algorithms, in contrast with th 6.5.12. Hotelling's T² — Process Improvement using Data. 6.5.12. Hotelling's T². The final quantity from a PCA model that we need to consider is called Hotelling's T 2 value. Some PCA models will have many components, A, so an initial screening of these components using score scatterplots will require reviewing A ( A − 1) / 2. The course PCA & multivariate signal processing, applied to neural data is an online class provided by Udemy. It may be possible to receive a verified certification or use the course to prepare for a degree. Learn and apply cutting-edge data analysis techniques for the age of big data in neuroscience (theory and MATLAB code) Course.

### machine learning - Multivariate Time-Series Clustering

This is the first step to transform the time series. The second step is grouping the transformed time series, see permutationMax, permutationFDR. Author(s) Jinyuan Chang, Bin Guo and Qiwei Yao References. Chang, J., Guo, B. and Yao, Q. (2014). Segmenting Multiple Time Series by Contemporaneous Linear Transformation: PCA for Time Series Selection of the proper similarity measure is the cornerstone of all time series data mining task. In the recent years, many similarity measures have been introduced to fulfill the needs of chemical process engineering. These measures have been guided by data reduction methods due to the large amount of data. This data reduction can be done explicitly (by segmentation) as well as implicitly. Implementation of dynamic principal component analysis (DPCA), simulation of VAR and VMA processes and frequency domain tools. These frequency domain methods for dimensionality reduction of multivariate time series were introduced by David Brillinger in his book Time Series (1974). We follow implementation guidelines as described in Hormann, Kidzinski and Hallin (2016), Dynamic Functional.

novel approach to multivariate time series analysis— hierarchical decomposition ~HD!—that exploits the causal ~i.e., forward in time! dynamic content of multi-variate temporal data. In contrast to HD, standard decomposition techniques including principal components analysis ~PCA!, alone or modiﬁed by varimax rotations ~VR!,4 independent com Visualization of multivariate time series assists our understanding of the process. In the last part of this dissertation a simple three-dimensional graph is proposed to assist visualizing the results of PCA. It is intended to complement existing graphical methods for multivariate time series data Multivariate Time Series 11.1 Introduction The vector autoregression (VAR) model is one of the most successful, ﬂexi-ble, and easy to use models for the analysis of multivariate time series. It is a natural extension of the univariate autoregressive model to dynamic mul-tivariate time series. The VAR model has proven to be especially useful fo

MultivariateOLS¶. _MultivariateOLS is a model class with limited features. Currently it supports multivariate hypothesis tests and is used as backend for MANOVA. _MultivariateOLS (endog, exog [, missing, ]) MultivariateTestResults (mv_test_df, ) Multivariate test results class Returned by mv_test method of _MultivariateOLSResults class multivariate time series; TS-PCA; dimension reduction; Access to Document. Alshammri-Pan-ERHS2017-Dimension-reduction-for-stationary-multivariate-time-series-data Final published version, 1 MB. Prizes Best Talk Prize. Alshammri, Fayed Awdah M (Recipient), 2017. Prize:. Abstract: Due to high dimensionality and multiple variables, unsupervised classification of multivariate time series (MTS) involves more challenging problems than those of univariate ones. Unlike the vectorization of a feature matrix in traditional clustering algorithms, an unsupervised pattern recognition scheme based on matrix data is proposed for MTS samples in this paper A PCA-based Kernel for Kernel PCA on Multivariate Time Series . By . Download PDF (120 KB) Abstract. Multivariate time series (MTS) data sets are common in various multimedia, medical and financial application domains. These applications perform several data-analysis operations on large number of MTS data sets such as similarity searches. Time series component analysis : ForeCA implements forecastable component analysis by searching for the best linear transformations that make a multivariate time series as forecastable as possible. PCA4TS finds a linear transformation of a multivariate time series giving lower-dimensional subseries that are uncorrelated with each other Recurrent neural networks are a type of neural network that add the explicit handling of order in input observations. This capability suggests that the promise of recurrent neural networks is to learn the temporal context of input sequences in order to make better predictions. That is, that the suite of lagged observations required to make a prediction no longer must b