SlideShare a Scribd company logo

RDataMining slides-time-series-analysis

Yanchang Zhao, profile picture
Yanchang Zhao

The document describes time series analysis techniques in R including decomposition, forecasting, clustering, and classification. It provides examples of decomposing the AirPassengers dataset, building an ARIMA forecasting model, hierarchical clustering with Euclidean and DTW distances, and classifying the synthetic control chart time series data using decision trees with and without discrete wavelet transform feature extraction. Accuracy improved from 81.8% to 88.8% when using DWT features with decision trees.

Technology
Related topics:
Data Mining Insights
1 of 41
Downloaded 17 times
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
Time Series Analysis with R Yanchang Zhao http://www.RDataMining.com R and Data Mining Course Beijing University of Posts and Telecommunications, Beijing, China July 2019 1 / 40
Contents Introduction Time Series Decomposition Time Series Forecasting Time Series Clustering Time Series Classification Online Resources 2 / 40
Time Series Analysis with R ∗ time series data in R time series decomposition, forecasting, clustering and classification autoregressive integrated moving average (ARIMA) model Dynamic Time Warping (DTW) Discrete Wavelet Transform (DWT) k-NN classification ∗ Chapter 8: Time Series Analysis and Mining, in book R and Data Mining: Examples and Case Studies. http://www.rdatamining.com/docs/RDataMining-book.pdf 3 / 40
Time Series Data in R class ts represents data which has been sampled at equispaced points in time frequency=7: a weekly series frequency=12: a monthly series frequency=4: a quarterly series 4 / 40
Time Series Data in R ## an example of time series data a <- ts(1:20, frequency = 12, start = c(2011, 3)) print(a) ## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec ## 2011 1 2 3 4 5 6 7 8 9 10 ## 2012 11 12 13 14 15 16 17 18 19 20 str(a) ## Time-Series [1:20] from 2011 to 2013: 1 2 3 4 5 6 7 8 9 10... attributes(a) ## $tsp ## [1] 2011.167 2012.750 12.000 ## ## $class ## [1] "ts" 5 / 40
Contents Introduction Time Series Decomposition Time Series Forecasting Time Series Clustering Time Series Classification Online Resources 6 / 40
What is Time Series Decomposition To decompose a time series into components [Brockwell and Davis, 2016]: Trend component: long term trend Seasonal component: seasonal variation Cyclical component: repeated but non-periodic fluctuations Irregular component: the residuals 7 / 40
Data AirPassengers Data AirPassengers: monthly totals of Box Jenkins international airline passengers, 1949 to 1960. It has 144(=12×12) values. ## load time series data plot(AirPassengers) AirPassengers 1950 1952 1954 1956 1958 1960 100200300400500600 8 / 40
Decomposition ## time series decomposation apts <- ts(AirPassengers, frequency = 12) f <- decompose(apts) plot(f$figure, type = "b") # seasonal figures 2 4 6 8 10 12 −40−200204060 f$figure 9 / 40
Decomposition plot(f) 100300500 observed 150250350450 trend −400204060 seasonal −400204060 2 4 6 8 10 12 random Time Decomposition of additive time series 10 / 40
Contents Introduction Time Series Decomposition Time Series Forecasting Time Series Clustering Time Series Classification Online Resources 11 / 40
Time Series Forecasting To forecast future events based on known past data For example, to predict the price of a stock based on its past performance Popular models Autoregressive moving average (ARMA) Autoregressive integrated moving average (ARIMA) 12 / 40
Forecasting ## build an ARIMA model fit <- arima(AirPassengers, order=c(1,0,0), list(order=c(2,1,0), period=12)) ## make forecast fore <- predict(fit, n.ahead=24) ## error bounds at 95% confidence level upper.bound <- fore$pred + 2*fore$se lower.bound <- fore$pred - 2*fore$se ## plot forecast results ts.plot(AirPassengers, fore$pred, upper.bound, lower.bound, col = c(1, 2, 4, 4), lty = c(1, 1, 2, 2)) legend("topleft", col = c(1, 2, 4), lty = c(1, 1, 2), c("Actual", "Forecast", "Error Bounds (95% Confidence)")) 13 / 40
Forecasting Time 1950 1952 1954 1956 1958 1960 1962 100200300400500600700 Actual Forecast Error Bounds (95% Confidence) 14 / 40
Contents Introduction Time Series Decomposition Time Series Forecasting Time Series Clustering Time Series Classification Online Resources 15 / 40
Time Series Clustering To partition time series data into groups based on similarity or distance, so that time series in the same cluster are similar Measure of distance/dissimilarity Euclidean distance Manhattan distance Maximum norm Hamming distance The angle between two vectors (inner product) Dynamic Time Warping (DTW) distance ... 16 / 40
Dynamic Time Warping (DTW) DTW finds optimal alignment between two time series [Keogh and Pazzani, 2001]. ## Dynamic Time Warping (DTW) library(dtw) idx <- seq(0, 2 * pi, len = 100) a <- sin(idx) + runif(100)/10 b <- cos(idx) align <- dtw(a, b, step = asymmetricP1, keep = T) dtwPlotTwoWay(align) Queryvalue 0 20 40 60 80 100 −1.0−0.50.00.51.0 17 / 40
Synthetic Control Chart Time Series The dataset contains 600 examples of control charts synthetically generated by the process in Alcock and Manolopoulos (1999). Each control chart is a time series with 60 values. Six classes: 1-100 Normal 101-200 Cyclic 201-300 Increasing trend 301-400 Decreasing trend 401-500 Upward shift 501-600 Downward shift http://kdd.ics.uci.edu/databases/synthetic_control/synthetic_ control.html 18 / 40
Synthetic Control Chart Time Series # read data into R # sep="": the separator is white space, i.e., one # or more spaces, tabs, newlines or carriage returns sc <- read.table("../data/synthetic_control.data", header=F, sep="") # show one sample from each class idx <- c(1, 101, 201, 301, 401, 501) sample1 <- t(sc[idx,]) plot.ts(sample1, main="") 19 / 40
Six Classes 24262830323436 1 15202530354045 101 2530354045 0 10 20 30 40 50 60 201 Time 0102030 301 2530354045 401 101520253035 0 10 20 30 40 50 60 501 Time 20 / 40
Hierarchical Clustering with Euclidean distance # sample n cases from every class n <- 10 s <- sample(1:100, n) idx <- c(s, 100 + s, 200 + s, 300 + s, 400 + s, 500 + s) sample2 <- sc[idx, ] observedLabels <- rep(1:6, each = n) ## hierarchical clustering with Euclidean distance hc <- hclust(dist(sample2), method = "ave") plot(hc, labels = observedLabels, main = "") 21 / 40
Hierarchical Clustering with Euclidean distance 6 4 6 6 6 6 6 6 6 6 6 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 5 5 5 5 5 5 3 3 3 3 5 5 5 5 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 20406080100120140 hclust (*, "average") dist(sample2) Height 22 / 40
Hierarchical Clustering with Euclidean distance # cut tree to get 8 clusters memb <- cutree(hc, k = 8) table(observedLabels, memb) ## memb ## observedLabels 1 2 3 4 5 6 7 8 ## 1 10 0 0 0 0 0 0 0 ## 2 0 3 1 1 3 2 0 0 ## 3 0 0 0 0 0 0 10 0 ## 4 0 0 0 0 0 0 0 10 ## 5 0 0 0 0 0 0 10 0 ## 6 0 0 0 0 0 0 0 10 23 / 40
Hierarchical Clustering with DTW Distance # hierarchical clustering with DTW distance myDist <- dist(sample2, method = "DTW") hc <- hclust(myDist, method = "average") plot(hc, labels = observedLabels, main = "") # cut tree to get 8 clusters memb <- cutree(hc, k = 8) table(observedLabels, memb) ## memb ## observedLabels 1 2 3 4 5 6 7 8 ## 1 10 0 0 0 0 0 0 0 ## 2 0 4 3 2 1 0 0 0 ## 3 0 0 0 0 0 6 4 0 ## 4 0 0 0 0 0 0 0 10 ## 5 0 0 0 0 0 0 10 0 ## 6 0 0 0 0 0 0 0 10 24 / 40
Hierarchical Clustering with DTW Distance 3 3 3 3 3 3 5 5 3 3 3 3 5 5 5 5 5 5 5 5 6 6 6 4 6 4 4 4 4 4 4 4 4 4 6 6 6 6 6 6 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 02004006008001000 hclust (*, "average") myDist Height 25 / 40
Contents Introduction Time Series Decomposition Time Series Forecasting Time Series Clustering Time Series Classification Online Resources 26 / 40
Time Series Classification Time Series Classification To build a classification model based on labelled time series and then use the model to predict the lable of unlabelled time series Feature Extraction Singular Value Decomposition (SVD) Discrete Fourier Transform (DFT) Discrete Wavelet Transform (DWT) Piecewise Aggregate Approximation (PAA) Perpetually Important Points (PIP) Piecewise Linear Representation Symbolic Representation 27 / 40
Decision Tree (ctree) ctree from package party ## build a decision tree classId <- rep(as.character(1:6), each = 100) newSc <- data.frame(cbind(classId, sc)) library(party) ct <- ctree(classId ~ ., data = newSc, controls = ctree_control(minsplit = 20, minbucket = 5, maxdepth = 5)) 28 / 40
Decision Tree pClassId <- predict(ct) table(classId, pClassId) ## pClassId ## classId 1 2 3 4 5 6 ## 1 100 0 0 0 0 0 ## 2 1 97 2 0 0 0 ## 3 0 0 99 0 1 0 ## 4 0 0 0 100 0 0 ## 5 4 0 8 0 88 0 ## 6 0 3 0 90 0 7 # accuracy (sum(classId == pClassId))/nrow(sc) ## [1] 0.8183333 29 / 40
DWT (Discrete Wavelet Transform) Wavelet transform provides a multi-resolution representation using wavelets [Burrus et al., 1998]. Haar Wavelet Transform – the simplest DWT http://dmr.ath.cx/gfx/haar/ DFT (Discrete Fourier Transform): another popular feature extraction technique 30 / 40
DWT (Discrete Wavelet Transform) # extract DWT (with Haar filter) coefficients library(wavelets) wtData <- NULL for (i in 1:nrow(sc)) { a <- t(sc[i, ]) wt <- dwt(a, filter = "haar", boundary = "periodic") wtData <- rbind(wtData, unlist(c(wt@W, wt@V[[wt@level]]))) } wtData <- as.data.frame(wtData) wtSc <- data.frame(cbind(classId, wtData)) 31 / 40
Decision Tree with DWT ## build a decision tree ct <- ctree(classId ~ ., data = wtSc, controls = ctree_control(minsplit=20, minbucket=5, maxdepth=5)) pClassId <- predict(ct) table(classId, pClassId) ## pClassId ## classId 1 2 3 4 5 6 ## 1 98 2 0 0 0 0 ## 2 1 99 0 0 0 0 ## 3 0 0 81 0 19 0 ## 4 0 0 0 74 0 26 ## 5 0 0 16 0 84 0 ## 6 0 0 0 3 0 97 (sum(classId==pClassId)) / nrow(wtSc) ## [1] 0.8883333 32 / 40
plot(ct, ip_args = list(pval = F), ep_args = list(digits = 0)) V57 1 ≤ 117 > 117 W43 2 ≤ −4 > −4 W5 3 ≤ −8 > −8 Node 4 (n = 68) 123456 0 0.2 0.4 0.6 0.8 1 Node 5 (n = 6) 123456 0 0.2 0.4 0.6 0.8 1 W31 6 ≤ −6 > −6 Node 7 (n = 9) 123456 0 0.2 0.4 0.6 0.8 1 Node 8 (n = 86) 123456 0 0.2 0.4 0.6 0.8 1 V57 9 ≤ 140 > 140 Node 10 (n = 31) 123456 0 0.2 0.4 0.6 0.8 1 V57 11 ≤ 178 > 178 W22 12 ≤ −6 > −6 Node 13 (n = 80) 123456 0 0.2 0.4 0.6 0.8 1 W31 14 ≤ −13 > −13 Node 15 (n = 9) 123456 0 0.2 0.4 0.6 0.8 1 Node 16 (n = 99) 123456 0 0.2 0.4 0.6 0.8 1 W31 17 ≤ −15 > −15 Node 18 (n = 12) 123456 0 0.2 0.4 0.6 0.8 1 W43 19 ≤ 3 > 3 Node 20 (n = 103) 123456 0 0.2 0.4 0.6 0.8 1 Node 21 (n = 97) 123456 0 0.2 0.4 0.6 0.8 1 33 / 40
k-NN Classification find the k nearest neighbours of a new instance label it by majority voting needs an efficient indexing structure for large datasets ## k-NN classification k <- 20 newTS <- sc[501, ] + runif(100) * 15 distances <- dist(newTS, sc, method = "DTW") s <- sort(as.vector(distances), index.return = TRUE) # class IDs of k nearest neighbours table(classId[s$ix[1:k]]) ## ## 4 6 ## 3 17 34 / 40
k-NN Classification find the k nearest neighbours of a new instance label it by majority voting needs an efficient indexing structure for large datasets ## k-NN classification k <- 20 newTS <- sc[501, ] + runif(100) * 15 distances <- dist(newTS, sc, method = "DTW") s <- sort(as.vector(distances), index.return = TRUE) # class IDs of k nearest neighbours table(classId[s$ix[1:k]]) ## ## 4 6 ## 3 17 Results of majority voting: class 6 34 / 40
The TSclust Package TSclust: a package for time seriesclustering † measures of dissimilarity between time series to perform time series clustering. metrics based on raw data, on generating models and on the forecast behavior time series clustering algorithms and cluster evaluation metrics † http://cran.r-project.org/web/packages/TSclust/ 35 / 40
Contents Introduction Time Series Decomposition Time Series Forecasting Time Series Clustering Time Series Classification Online Resources 36 / 40
Online Resources Book titled R and Data Mining: Examples and Case Studies [Zhao, 2012] http://www.rdatamining.com/docs/RDataMining-book.pdf R Reference Card for Data Mining http://www.rdatamining.com/docs/RDataMining-reference-card.pdf Free online courses and documents http://www.rdatamining.com/resources/ RDataMining Group on LinkedIn (27,000+ members) http://group.rdatamining.com Twitter (3,300+ followers) @RDataMining 37 / 40
The End Thanks! Email: yanchang(at)RDataMining.com Twitter: @RDataMining 38 / 40
How to Cite This Work Citation Yanchang Zhao. R and Data Mining: Examples and Case Studies. ISBN 978-0-12-396963-7, December 2012. Academic Press, Elsevier. 256 pages. URL: http://www.rdatamining.com/docs/RDataMining-book.pdf. BibTex @BOOK{Zhao2012R, title = {R and Data Mining: Examples and Case Studies}, publisher = {Academic Press, Elsevier}, year = {2012}, author = {Yanchang Zhao}, pages = {256}, month = {December}, isbn = {978-0-123-96963-7}, keywords = {R, data mining}, url = {http://www.rdatamining.com/docs/RDataMining-book.pdf} } 39 / 40
References I Brockwell, P. J. and Davis, R. A. (2016). Introduction to Time Series and Forecasting, ISBN 9783319298528. Springer. Burrus, C. S., Gopinath, R. A., and Guo, H. (1998). Introduction to Wavelets and Wavelet Transforms: A Primer. Prentice-Hall, Inc. Keogh, E. J. and Pazzani, M. J. (2001). Derivative dynamic time warping. In the 1st SIAM Int. Conf. on Data Mining (SDM-2001), Chicago, IL, USA. Zhao, Y. (2012). R and Data Mining: Examples and Case Studies, ISBN 978-0-12-396963-7. Academic Press, Elsevier. 40 / 40

More Related Content

PDF
RDataMining slides-regression-classification
Yanchang Zhao
 
PDF
RDataMining slides-clustering-with-r
Yanchang Zhao
 
PDF
Time Series Analysis and Mining with R
Yanchang Zhao
 
PDF
Data Exploration and Visualization with R
Yanchang Zhao
 
PDF
Regression and Classification with R
Yanchang Zhao
 
PDF
An Introduction to Data Mining with R
Yanchang Zhao
 
PPTX
R programming language
Alberto Minetti
 
PDF
R Workshop for Beginners
Metamarkets
 
RDataMining slides-regression-classification
Yanchang Zhao
 
RDataMining slides-clustering-with-r
Yanchang Zhao
 
Time Series Analysis and Mining with R
Yanchang Zhao
 
Data Exploration and Visualization with R
Yanchang Zhao
 
Regression and Classification with R
Yanchang Zhao
 
An Introduction to Data Mining with R
Yanchang Zhao
 
R programming language
Alberto Minetti
 
R Workshop for Beginners
Metamarkets
 

What's hot (20)

PDF
RDataMining slides-network-analysis-with-r
Yanchang Zhao
 
PPTX
R Language Introduction
Khaled Al-Shamaa
 
PDF
R learning by examples
Michelle Darling
 
PDF
R programming intro with examples
Dennis
 
PDF
Data Clustering with R
Yanchang Zhao
 
PPTX
Language R
Girish Khanzode
 
KEY
Presentation R basic teaching module
Sander Timmer
 
PDF
Introduction to R Programming
izahn
 
PPTX
Datamining with R
Shitalkumar Sukhdeve
 
PDF
Next Generation Programming in R
Florian Uhlitz
 
PPTX
R language
LearningTech
 
PDF
[系列活動] Data exploration with modern R
台灣資料科學年會
 
PDF
RDataMining slides-data-exploration-visualisation
Yanchang Zhao
 
PDF
Data Analysis with R (combined slides)
Guy Lebanon
 
PPTX
Programming in R
Smruti Sarangi
 
PDF
Python for R developers and data scientists
Lambda Tree
 
PPTX
An Interactive Introduction To R (Programming Language For Statistics)
Dataspora
 
PPTX
R language introduction
Shashwat Shriparv
 
PDF
Grouping & Summarizing Data in R
Jeffrey Breen
 
PDF
4 R Tutorial DPLYR Apply Function
Sakthi Dasans
 
RDataMining slides-network-analysis-with-r
Yanchang Zhao
 
R Language Introduction
Khaled Al-Shamaa
 
R learning by examples
Michelle Darling
 
R programming intro with examples
Dennis
 
Data Clustering with R
Yanchang Zhao
 
Language R
Girish Khanzode
 
Presentation R basic teaching module
Sander Timmer
 
Introduction to R Programming
izahn
 
Datamining with R
Shitalkumar Sukhdeve
 
Next Generation Programming in R
Florian Uhlitz
 
R language
LearningTech
 
[系列活動] Data exploration with modern R
台灣資料科學年會
 
RDataMining slides-data-exploration-visualisation
Yanchang Zhao
 
Data Analysis with R (combined slides)
Guy Lebanon
 
Programming in R
Smruti Sarangi
 
Python for R developers and data scientists
Lambda Tree
 
An Interactive Introduction To R (Programming Language For Statistics)
Dataspora
 
R language introduction
Shashwat Shriparv
 
Grouping & Summarizing Data in R
Jeffrey Breen
 
4 R Tutorial DPLYR Apply Function
Sakthi Dasans
 
Ad

Similar to RDataMining slides-time-series-analysis (20)

PDF
R data mining-Time Series Analysis with R
Dr. Volkan OBAN
 
PDF
Anomaly Detection in Sequences of Short Text Using Iterative Language Models
Cynthia Freeman
 
PPTX
wasim 1
wasim94
 
PDF
Forecasting time series powerful and simple
Ivo Andreev
 
PPTX
Time Series Analysis - 2 | Time Series in R | ARIMA Model Forecasting | Data ...
Simplilearn
 
PPTX
Long Memory presentation to SURF
Richard Hunt
 
PDF
Lecture9_Time_Series_2024_and_data_analysis (1).pdf
adiworks30
 
PDF
TIME SERIES ANALYSIS USING ARIMA MODEL FOR FORECASTING IN R (PRACTICAL)
Laud Randy Amofah
 
PPTX
Seasonal Decomposition of Time Series Data
Programming Homework Help
 
PDF
IRJET-Forecasting of Time Series Data using Hybrid ARIMA Model with the Wavel...
IRJET Journal
 
PDF
MFx_Module_3_Properties_of_Time_Series.pdf
tilfani
 
PPTX
time_series and the forecastring age of RNNS.pptx
shahzebTariq11
 
PDF
Module 5.pptx (Data science in engineering)
JhaJee5
 
PPTX
Forecasting_CO2_Emissions.pptx
MOINDALVS
 
PDF
Accurate time series classification using shapelets
IJDKP
 
PDF
lecture3.pdf
Elio Laureano
 
PDF
Forecasting%20Economic%20Series%20using%20ARMA
Nagendra Belvadi
 
PDF
Combination of Similarity Measures for Time Series Classification using Genet...
Deepti Dohare
 
PPTX
Presentation On Time Series Analysis in Mechine Learning
mahfuzur32785
 
PPTX
Time series analysis
Utkarsh Sharma
 
R data mining-Time Series Analysis with R
Dr. Volkan OBAN
 
Anomaly Detection in Sequences of Short Text Using Iterative Language Models
Cynthia Freeman
 
wasim 1
wasim94
 
Forecasting time series powerful and simple
Ivo Andreev
 
Time Series Analysis - 2 | Time Series in R | ARIMA Model Forecasting | Data ...
Simplilearn
 
Long Memory presentation to SURF
Richard Hunt
 
Lecture9_Time_Series_2024_and_data_analysis (1).pdf
adiworks30
 
TIME SERIES ANALYSIS USING ARIMA MODEL FOR FORECASTING IN R (PRACTICAL)
Laud Randy Amofah
 
Seasonal Decomposition of Time Series Data
Programming Homework Help
 
IRJET-Forecasting of Time Series Data using Hybrid ARIMA Model with the Wavel...
IRJET Journal
 
MFx_Module_3_Properties_of_Time_Series.pdf
tilfani
 
time_series and the forecastring age of RNNS.pptx
shahzebTariq11
 
Module 5.pptx (Data science in engineering)
JhaJee5
 
Forecasting_CO2_Emissions.pptx
MOINDALVS
 
Accurate time series classification using shapelets
IJDKP
 
lecture3.pdf
Elio Laureano
 
Forecasting%20Economic%20Series%20using%20ARMA
Nagendra Belvadi
 
Combination of Similarity Measures for Time Series Classification using Genet...
Deepti Dohare
 
Presentation On Time Series Analysis in Mechine Learning
mahfuzur32785
 
Time series analysis
Utkarsh Sharma
 
Ad

More from Yanchang Zhao (9)

PDF
RDataMining slides-text-mining-with-r
Yanchang Zhao
 
PDF
RDataMining slides-r-programming
Yanchang Zhao
 
PDF
RDataMining slides-association-rule-mining-with-r
Yanchang Zhao
 
PDF
RDataMining-reference-card
Yanchang Zhao
 
PDF
Text Mining with R -- an Analysis of Twitter Data
Yanchang Zhao
 
PDF
Association Rule Mining with R
Yanchang Zhao
 
PDF
Introduction to Data Mining with R and Data Import/Export in R
Yanchang Zhao
 
PDF
Time series-mining-slides
Yanchang Zhao
 
PDF
R Reference Card for Data Mining
Yanchang Zhao
 
RDataMining slides-text-mining-with-r
Yanchang Zhao
 
RDataMining slides-r-programming
Yanchang Zhao
 
RDataMining slides-association-rule-mining-with-r
Yanchang Zhao
 
RDataMining-reference-card
Yanchang Zhao
 
Text Mining with R -- an Analysis of Twitter Data
Yanchang Zhao
 
Association Rule Mining with R
Yanchang Zhao
 
Introduction to Data Mining with R and Data Import/Export in R
Yanchang Zhao
 
Time series-mining-slides
Yanchang Zhao
 
R Reference Card for Data Mining
Yanchang Zhao
 

Recently uploaded (20)

PDF
Heart disease approach using modified random forest and particle swarm optimi...
IAESIJAI
 
PDF
A novel scalable deep ensemble learning framework for big data classification...
IAESIJAI
 
PDF
MIND Revenue Release Quarter 2 2025 Press Release
MIND CTI
 
PDF
Unlocking AI with Model Context Protocol (MCP)
Brian McKeiver
 
PDF
Encapsulation theory and applications.pdf
gurumoop
 
PDF
gpt5_lecture_notes_comprehensive_20250812015547.pdf
Chinchu40
 
PDF
Mushroom cultivation and it's methods.pdf
mailmeonrishi
 
PDF
NewMind AI Weekly Chronicles - August'25-Week II
NewMind AI
 
PDF
Accuracy of neural networks in brain wave diagnosis of schizophrenia
IAESIJAI
 
PPTX
A Presentation on Touch Screen Technology
memembruh336
 
PDF
Approach and Philosophy of On baking technology
30anthuong17
 
PDF
DP Operators-handbook-extract for the Mautical Institute
LeonelMejiaLarios
 
PDF
WOOl fibre morphology and structure.pdf for textiles
Rajendrakumar868651
 
PPTX
Tartificialntelligence_presentation.pptx
ry7r52mzb4
 
PPTX
TLE Review Electricity (Electricity).pptx
JayPolicarpio2
 
PDF
Building Integrated photovoltaic BIPV_UPV.pdf
SandeepSingh286037
 
PDF
Video forgery: An extensive analysis of inter-and intra-frame manipulation al...
IAESIJAI
 
PDF
Encapsulation_ Review paper, used for researhc scholars
gurumoop
 
PDF
Enhancing emotion recognition model for a student engagement use case through...
IAESIJAI
 
PDF
Assigned Numbers - 2025 - Bluetooth® Document
Bloombase
 
Heart disease approach using modified random forest and particle swarm optimi...
IAESIJAI
 
A novel scalable deep ensemble learning framework for big data classification...
IAESIJAI
 
MIND Revenue Release Quarter 2 2025 Press Release
MIND CTI
 
Unlocking AI with Model Context Protocol (MCP)
Brian McKeiver
 
Encapsulation theory and applications.pdf
gurumoop
 
gpt5_lecture_notes_comprehensive_20250812015547.pdf
Chinchu40
 
Mushroom cultivation and it's methods.pdf
mailmeonrishi
 
NewMind AI Weekly Chronicles - August'25-Week II
NewMind AI
 
Accuracy of neural networks in brain wave diagnosis of schizophrenia
IAESIJAI
 
A Presentation on Touch Screen Technology
memembruh336
 
Approach and Philosophy of On baking technology
30anthuong17
 
DP Operators-handbook-extract for the Mautical Institute
LeonelMejiaLarios
 
WOOl fibre morphology and structure.pdf for textiles
Rajendrakumar868651
 
Tartificialntelligence_presentation.pptx
ry7r52mzb4
 
TLE Review Electricity (Electricity).pptx
JayPolicarpio2
 
Building Integrated photovoltaic BIPV_UPV.pdf
SandeepSingh286037
 
Video forgery: An extensive analysis of inter-and intra-frame manipulation al...
IAESIJAI
 
Encapsulation_ Review paper, used for researhc scholars
gurumoop
 
Enhancing emotion recognition model for a student engagement use case through...
IAESIJAI
 
Assigned Numbers - 2025 - Bluetooth® Document
Bloombase
 

RDataMining slides-time-series-analysis

  • 1. Time Series Analysis with R Yanchang Zhao http://www.RDataMining.com R and Data Mining Course Beijing University of Posts and Telecommunications, Beijing, China July 2019 1 / 40
  • 2. Contents Introduction Time Series Decomposition Time Series Forecasting Time Series Clustering Time Series Classification Online Resources 2 / 40
  • 3. Time Series Analysis with R ∗ time series data in R time series decomposition, forecasting, clustering and classification autoregressive integrated moving average (ARIMA) model Dynamic Time Warping (DTW) Discrete Wavelet Transform (DWT) k-NN classification ∗ Chapter 8: Time Series Analysis and Mining, in book R and Data Mining: Examples and Case Studies. http://www.rdatamining.com/docs/RDataMining-book.pdf 3 / 40
  • 4. Time Series Data in R class ts represents data which has been sampled at equispaced points in time frequency=7: a weekly series frequency=12: a monthly series frequency=4: a quarterly series 4 / 40
  • 5. Time Series Data in R ## an example of time series data a <- ts(1:20, frequency = 12, start = c(2011, 3)) print(a) ## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec ## 2011 1 2 3 4 5 6 7 8 9 10 ## 2012 11 12 13 14 15 16 17 18 19 20 str(a) ## Time-Series [1:20] from 2011 to 2013: 1 2 3 4 5 6 7 8 9 10... attributes(a) ## $tsp ## [1] 2011.167 2012.750 12.000 ## ## $class ## [1] "ts" 5 / 40
  • 6. Contents Introduction Time Series Decomposition Time Series Forecasting Time Series Clustering Time Series Classification Online Resources 6 / 40
  • 7. What is Time Series Decomposition To decompose a time series into components [Brockwell and Davis, 2016]: Trend component: long term trend Seasonal component: seasonal variation Cyclical component: repeated but non-periodic fluctuations Irregular component: the residuals 7 / 40
  • 8. Data AirPassengers Data AirPassengers: monthly totals of Box Jenkins international airline passengers, 1949 to 1960. It has 144(=12×12) values. ## load time series data plot(AirPassengers) AirPassengers 1950 1952 1954 1956 1958 1960 100200300400500600 8 / 40
  • 9. Decomposition ## time series decomposation apts <- ts(AirPassengers, frequency = 12) f <- decompose(apts) plot(f$figure, type = "b") # seasonal figures 2 4 6 8 10 12 −40−200204060 f$figure 9 / 40
  • 10. Decomposition plot(f) 100300500 observed 150250350450 trend −400204060 seasonal −400204060 2 4 6 8 10 12 random Time Decomposition of additive time series 10 / 40
  • 11. Contents Introduction Time Series Decomposition Time Series Forecasting Time Series Clustering Time Series Classification Online Resources 11 / 40
  • 12. Time Series Forecasting To forecast future events based on known past data For example, to predict the price of a stock based on its past performance Popular models Autoregressive moving average (ARMA) Autoregressive integrated moving average (ARIMA) 12 / 40
  • 13. Forecasting ## build an ARIMA model fit <- arima(AirPassengers, order=c(1,0,0), list(order=c(2,1,0), period=12)) ## make forecast fore <- predict(fit, n.ahead=24) ## error bounds at 95% confidence level upper.bound <- fore$pred + 2*fore$se lower.bound <- fore$pred - 2*fore$se ## plot forecast results ts.plot(AirPassengers, fore$pred, upper.bound, lower.bound, col = c(1, 2, 4, 4), lty = c(1, 1, 2, 2)) legend("topleft", col = c(1, 2, 4), lty = c(1, 1, 2), c("Actual", "Forecast", "Error Bounds (95% Confidence)")) 13 / 40
  • 14. Forecasting Time 1950 1952 1954 1956 1958 1960 1962 100200300400500600700 Actual Forecast Error Bounds (95% Confidence) 14 / 40
  • 15. Contents Introduction Time Series Decomposition Time Series Forecasting Time Series Clustering Time Series Classification Online Resources 15 / 40
  • 16. Time Series Clustering To partition time series data into groups based on similarity or distance, so that time series in the same cluster are similar Measure of distance/dissimilarity Euclidean distance Manhattan distance Maximum norm Hamming distance The angle between two vectors (inner product) Dynamic Time Warping (DTW) distance ... 16 / 40
  • 17. Dynamic Time Warping (DTW) DTW finds optimal alignment between two time series [Keogh and Pazzani, 2001]. ## Dynamic Time Warping (DTW) library(dtw) idx <- seq(0, 2 * pi, len = 100) a <- sin(idx) + runif(100)/10 b <- cos(idx) align <- dtw(a, b, step = asymmetricP1, keep = T) dtwPlotTwoWay(align) Queryvalue 0 20 40 60 80 100 −1.0−0.50.00.51.0 17 / 40
  • 18. Synthetic Control Chart Time Series The dataset contains 600 examples of control charts synthetically generated by the process in Alcock and Manolopoulos (1999). Each control chart is a time series with 60 values. Six classes: 1-100 Normal 101-200 Cyclic 201-300 Increasing trend 301-400 Decreasing trend 401-500 Upward shift 501-600 Downward shift http://kdd.ics.uci.edu/databases/synthetic_control/synthetic_ control.html 18 / 40
  • 19. Synthetic Control Chart Time Series # read data into R # sep="": the separator is white space, i.e., one # or more spaces, tabs, newlines or carriage returns sc <- read.table("../data/synthetic_control.data", header=F, sep="") # show one sample from each class idx <- c(1, 101, 201, 301, 401, 501) sample1 <- t(sc[idx,]) plot.ts(sample1, main="") 19 / 40
  • 20. Six Classes 24262830323436 1 15202530354045 101 2530354045 0 10 20 30 40 50 60 201 Time 0102030 301 2530354045 401 101520253035 0 10 20 30 40 50 60 501 Time 20 / 40
  • 21. Hierarchical Clustering with Euclidean distance # sample n cases from every class n <- 10 s <- sample(1:100, n) idx <- c(s, 100 + s, 200 + s, 300 + s, 400 + s, 500 + s) sample2 <- sc[idx, ] observedLabels <- rep(1:6, each = n) ## hierarchical clustering with Euclidean distance hc <- hclust(dist(sample2), method = "ave") plot(hc, labels = observedLabels, main = "") 21 / 40
  • 22. Hierarchical Clustering with Euclidean distance 6 4 6 6 6 6 6 6 6 6 6 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 5 5 5 5 5 5 3 3 3 3 5 5 5 5 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 20406080100120140 hclust (*, "average") dist(sample2) Height 22 / 40
  • 23. Hierarchical Clustering with Euclidean distance # cut tree to get 8 clusters memb <- cutree(hc, k = 8) table(observedLabels, memb) ## memb ## observedLabels 1 2 3 4 5 6 7 8 ## 1 10 0 0 0 0 0 0 0 ## 2 0 3 1 1 3 2 0 0 ## 3 0 0 0 0 0 0 10 0 ## 4 0 0 0 0 0 0 0 10 ## 5 0 0 0 0 0 0 10 0 ## 6 0 0 0 0 0 0 0 10 23 / 40
  • 24. Hierarchical Clustering with DTW Distance # hierarchical clustering with DTW distance myDist <- dist(sample2, method = "DTW") hc <- hclust(myDist, method = "average") plot(hc, labels = observedLabels, main = "") # cut tree to get 8 clusters memb <- cutree(hc, k = 8) table(observedLabels, memb) ## memb ## observedLabels 1 2 3 4 5 6 7 8 ## 1 10 0 0 0 0 0 0 0 ## 2 0 4 3 2 1 0 0 0 ## 3 0 0 0 0 0 6 4 0 ## 4 0 0 0 0 0 0 0 10 ## 5 0 0 0 0 0 0 10 0 ## 6 0 0 0 0 0 0 0 10 24 / 40
  • 25. Hierarchical Clustering with DTW Distance 3 3 3 3 3 3 5 5 3 3 3 3 5 5 5 5 5 5 5 5 6 6 6 4 6 4 4 4 4 4 4 4 4 4 6 6 6 6 6 6 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 02004006008001000 hclust (*, "average") myDist Height 25 / 40
  • 26. Contents Introduction Time Series Decomposition Time Series Forecasting Time Series Clustering Time Series Classification Online Resources 26 / 40
  • 27. Time Series Classification Time Series Classification To build a classification model based on labelled time series and then use the model to predict the lable of unlabelled time series Feature Extraction Singular Value Decomposition (SVD) Discrete Fourier Transform (DFT) Discrete Wavelet Transform (DWT) Piecewise Aggregate Approximation (PAA) Perpetually Important Points (PIP) Piecewise Linear Representation Symbolic Representation 27 / 40
  • 28. Decision Tree (ctree) ctree from package party ## build a decision tree classId <- rep(as.character(1:6), each = 100) newSc <- data.frame(cbind(classId, sc)) library(party) ct <- ctree(classId ~ ., data = newSc, controls = ctree_control(minsplit = 20, minbucket = 5, maxdepth = 5)) 28 / 40
  • 29. Decision Tree pClassId <- predict(ct) table(classId, pClassId) ## pClassId ## classId 1 2 3 4 5 6 ## 1 100 0 0 0 0 0 ## 2 1 97 2 0 0 0 ## 3 0 0 99 0 1 0 ## 4 0 0 0 100 0 0 ## 5 4 0 8 0 88 0 ## 6 0 3 0 90 0 7 # accuracy (sum(classId == pClassId))/nrow(sc) ## [1] 0.8183333 29 / 40
  • 30. DWT (Discrete Wavelet Transform) Wavelet transform provides a multi-resolution representation using wavelets [Burrus et al., 1998]. Haar Wavelet Transform – the simplest DWT http://dmr.ath.cx/gfx/haar/ DFT (Discrete Fourier Transform): another popular feature extraction technique 30 / 40
  • 31. DWT (Discrete Wavelet Transform) # extract DWT (with Haar filter) coefficients library(wavelets) wtData <- NULL for (i in 1:nrow(sc)) { a <- t(sc[i, ]) wt <- dwt(a, filter = "haar", boundary = "periodic") wtData <- rbind(wtData, unlist(c(wt@W, wt@V[[wt@level]]))) } wtData <- as.data.frame(wtData) wtSc <- data.frame(cbind(classId, wtData)) 31 / 40
  • 32. Decision Tree with DWT ## build a decision tree ct <- ctree(classId ~ ., data = wtSc, controls = ctree_control(minsplit=20, minbucket=5, maxdepth=5)) pClassId <- predict(ct) table(classId, pClassId) ## pClassId ## classId 1 2 3 4 5 6 ## 1 98 2 0 0 0 0 ## 2 1 99 0 0 0 0 ## 3 0 0 81 0 19 0 ## 4 0 0 0 74 0 26 ## 5 0 0 16 0 84 0 ## 6 0 0 0 3 0 97 (sum(classId==pClassId)) / nrow(wtSc) ## [1] 0.8883333 32 / 40
  • 33. plot(ct, ip_args = list(pval = F), ep_args = list(digits = 0)) V57 1 ≤ 117 > 117 W43 2 ≤ −4 > −4 W5 3 ≤ −8 > −8 Node 4 (n = 68) 123456 0 0.2 0.4 0.6 0.8 1 Node 5 (n = 6) 123456 0 0.2 0.4 0.6 0.8 1 W31 6 ≤ −6 > −6 Node 7 (n = 9) 123456 0 0.2 0.4 0.6 0.8 1 Node 8 (n = 86) 123456 0 0.2 0.4 0.6 0.8 1 V57 9 ≤ 140 > 140 Node 10 (n = 31) 123456 0 0.2 0.4 0.6 0.8 1 V57 11 ≤ 178 > 178 W22 12 ≤ −6 > −6 Node 13 (n = 80) 123456 0 0.2 0.4 0.6 0.8 1 W31 14 ≤ −13 > −13 Node 15 (n = 9) 123456 0 0.2 0.4 0.6 0.8 1 Node 16 (n = 99) 123456 0 0.2 0.4 0.6 0.8 1 W31 17 ≤ −15 > −15 Node 18 (n = 12) 123456 0 0.2 0.4 0.6 0.8 1 W43 19 ≤ 3 > 3 Node 20 (n = 103) 123456 0 0.2 0.4 0.6 0.8 1 Node 21 (n = 97) 123456 0 0.2 0.4 0.6 0.8 1 33 / 40
  • 34. k-NN Classification find the k nearest neighbours of a new instance label it by majority voting needs an efficient indexing structure for large datasets ## k-NN classification k <- 20 newTS <- sc[501, ] + runif(100) * 15 distances <- dist(newTS, sc, method = "DTW") s <- sort(as.vector(distances), index.return = TRUE) # class IDs of k nearest neighbours table(classId[s$ix[1:k]]) ## ## 4 6 ## 3 17 34 / 40
  • 35. k-NN Classification find the k nearest neighbours of a new instance label it by majority voting needs an efficient indexing structure for large datasets ## k-NN classification k <- 20 newTS <- sc[501, ] + runif(100) * 15 distances <- dist(newTS, sc, method = "DTW") s <- sort(as.vector(distances), index.return = TRUE) # class IDs of k nearest neighbours table(classId[s$ix[1:k]]) ## ## 4 6 ## 3 17 Results of majority voting: class 6 34 / 40
  • 36. The TSclust Package TSclust: a package for time seriesclustering † measures of dissimilarity between time series to perform time series clustering. metrics based on raw data, on generating models and on the forecast behavior time series clustering algorithms and cluster evaluation metrics † http://cran.r-project.org/web/packages/TSclust/ 35 / 40
  • 37. Contents Introduction Time Series Decomposition Time Series Forecasting Time Series Clustering Time Series Classification Online Resources 36 / 40
  • 38. Online Resources Book titled R and Data Mining: Examples and Case Studies [Zhao, 2012] http://www.rdatamining.com/docs/RDataMining-book.pdf R Reference Card for Data Mining http://www.rdatamining.com/docs/RDataMining-reference-card.pdf Free online courses and documents http://www.rdatamining.com/resources/ RDataMining Group on LinkedIn (27,000+ members) http://group.rdatamining.com Twitter (3,300+ followers) @RDataMining 37 / 40
  • 40. How to Cite This Work Citation Yanchang Zhao. R and Data Mining: Examples and Case Studies. ISBN 978-0-12-396963-7, December 2012. Academic Press, Elsevier. 256 pages. URL: http://www.rdatamining.com/docs/RDataMining-book.pdf. BibTex @BOOK{Zhao2012R, title = {R and Data Mining: Examples and Case Studies}, publisher = {Academic Press, Elsevier}, year = {2012}, author = {Yanchang Zhao}, pages = {256}, month = {December}, isbn = {978-0-123-96963-7}, keywords = {R, data mining}, url = {http://www.rdatamining.com/docs/RDataMining-book.pdf} } 39 / 40
  • 41. References I Brockwell, P. J. and Davis, R. A. (2016). Introduction to Time Series and Forecasting, ISBN 9783319298528. Springer. Burrus, C. S., Gopinath, R. A., and Guo, H. (1998). Introduction to Wavelets and Wavelet Transforms: A Primer. Prentice-Hall, Inc. Keogh, E. J. and Pazzani, M. J. (2001). Derivative dynamic time warping. In the 1st SIAM Int. Conf. on Data Mining (SDM-2001), Chicago, IL, USA. Zhao, Y. (2012). R and Data Mining: Examples and Case Studies, ISBN 978-0-12-396963-7. Academic Press, Elsevier. 40 / 40