# Time Series Similarity : Differing Lengths with R

I am experimenting with creating a distance matrix between time series for clustering and similarity searching. The main reference I am using is for the Similarity procedure in SAS (Paper). I would like to conduct the analysis in R using the dtw package.

What I am confused about it the application of DTW to series of different lengths.

1) Is this possible? 2) Any hints on how to do it with the R package?

Regarding question #2, trying to calculate a distance matrix on a matrix of series that differ in length immediately fails:

dist_mat<-dist(appliances_t,method="DTW")

Error in dtw(distance.only = TRUE, ...) :
No warping paths exists that is allowed by costraints


dput(appliances_t)

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128L, 86L, 207L, 118L, 1011L, 541L, 86L, 75L, 223L, 244L, NA,
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221L, 113L, 3112L, 140L, 91L, 152L, 145L, 1268L, 436L, 91L, 76L,
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286L, 92L, 77L, 278L, 321L, NA, 138L, 92L, 125L, 357L, 357L,
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199L, 833L, 198L, 103L, 3038L, 160L, 82L, 145L, 179L, 814L, 210L,
81L, 80L, 243L, 199L, NA, 125L, 82L, 115L, 294L, 294L, 294L,
220L, 199L, 294L, 209L, 580L, 207L, 109L, 2303L, 179L, 87L, 156L,
182L, 952L, 280L, 87L, 81L, 244L, 209L, NA, 131L, 88L, 120L,
321L, 321L, 321L, 240L, 209L, 321L, 1063L, 654L, 212L, 118L,
2959L, 148L, 95L, 162L, 202L, 920L, 332L, 95L, 82L, 202L, 214L,
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950L, 225L, 113L, 2509L, 306L, 91L, 297L, 167L, 907L, 393L, 91L,
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227L, 343L, 1705L, 1252L, 227L, 135L, 2718L, 397L, 109L, 332L,
166L, 804L, 320L, 108L, 84L, 121L, 228L, NA, 162L, 109L, 150L,
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1813L, 481L, 76L, 451L, 174L, 869L, 308L, 75L, 85L, 91L, 256L,
NA, 113L, 76L, 104L, 366L, 366L, 366L, 275L, 256L, 366L, 1176L,
1127L, 210L, 140L, 2103L, 441L, 111L, 425L, 188L, 872L, 447L,
111L, 86L, 160L, 212L, NA, 167L, 111L, 154L, 408L, 408L, 408L,
306L, 212L, 408L, 943L, 1168L, 206L, 176L, 2156L, 600L, 141L,
346L, 179L, 980L, 478L, 141L, 87L, 169L, 209L, NA, 213L, 141L,
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129L, 2212L, 414L, 104L, 373L, 214L, 1195L, 764L, 104L, 88L,
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332L, 951L, 690L, 234L, 164L, 1995L, 358L, 130L, 522L, 150L,
849L, 441L, 129L, 89L, 145L, 236L, NA, 196L, 130L, 182L, 348L,
348L, 348L, 261L, 236L, 348L, 779L, NA, 227L, 147L, 1995L, 648L,
118L, 398L, 222L, NA, NA, 118L, 90L, NA, 228L, NA, 178L, 118L,
165L, 378L, 378L, 378L, 283L, 228L, 378L, 853L, NA, 266L, 167L,
2252L, 352L, 133L, 437L, 282L, NA, NA, 135L, 91L, NA, 270L, NA,
202L, 136L, 188L, 364L, 364L, 364L, 274L, 270L, 364L, 593L, NA,
186L, 213L, 2142L, 415L, 160L, 346L, 208L, NA, NA, 170L, 92L,
NA, 188L, NA, 257L, 170L, 236L, 430L, 430L, 430L, 324L, 188L,
430L, 844L, NA, 276L, 129L, 1933L, 584L, 135L, 423L, 261L, NA,
NA, 104L, 93L, NA, 280L, NA, 157L, 104L, 143L, 301L, 301L, 301L,
227L, 280L, 301L, 1055L, NA, 352L, 150L, 1973L, 606L, 177L, 507L,
236L, NA, NA, 119L, 94L, NA, 354L, NA, 180L, 119L, 167L, 447L,
447L, 447L, 334L, 354L, 447L, 773L, NA, 258L, 159L, 1656L, 1012L,
281L, 399L, 269L, NA, NA, 126L, 95L, NA, 261L, NA, 191L, 127L,
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1883L, 617L, 267L, 430L, 340L, NA, NA, 134L, 96L, NA, 326L, NA,
202L, 134L, 187L, 417L, 417L, 417L, 311L, 326L, 417L, 687L, NA,
293L, 169L, 1788L, 530L, 275L, 444L, 206L, NA, NA, 136L, 97L,
NA, 295L, NA, 205L, 136L, 189L, 521L, 521L, 521L, 392L, 295L,
521L, 711L, NA, 334L, 186L, 1763L, 597L, 234L, 460L, 240L, NA,
NA, 147L, 98L, NA, 338L, NA, 222L, 147L, 205L, 473L, 473L, 473L,
354L, 338L, 473L, 889L, NA, 422L, 198L, 1337L, 446L, 303L, 584L,
253L, NA, NA, 166L, 99L, NA, 427L, NA, 237L, 158L, 220L, 540L,
540L, 540L, 405L, 427L, 540L, 635L, NA, 258L, 310L, 1749L, 558L,
396L, 600L, 269L, NA, NA, 239L, 100L, NA, 261L, NA, 373L, 247L,
345L, 683L, 683L, 683L, 512L, 261L, 683L, 669L, NA, 298L, 359L,
1960L, 590L, 608L, 588L, 271L, NA, NA, 372L, 101L, NA, 303L,
NA, 431L, 288L, 398L, 416L, 416L, 416L, 311L, 303L, 416L, 712L,
NA, 315L, 214L, 1383L, 576L, 355L, 893L, 295L, NA, NA, 256L,
102L, NA, 319L, NA, 257L, 170L, 236L, 482L, 482L, 482L, 361L,
319L, 482L, 727L, NA, 334L, NA, 1631L, 730L, NA, 864L, 316L,
NA, NA, NA, 103L, NA, 336L, NA, NA, NA, NA, 509L, 509L, 509L,
382L, 336L, 509L, 887L, NA, 339L, NA, 1513L, 736L, NA, 580L,
496L, NA, NA, NA, 104L, NA, 340L, NA, NA, NA, NA, 539L, 539L,
539L, 403L, 340L, 539L, 794L, NA, 369L, NA, 1687L, 647L, NA,
632L, 572L, NA, NA, NA, 105L, NA, 264L, NA, NA, NA, NA, 546L,
546L, 546L, 408L, 325L, 546L, 838L, NA, 392L, NA, 2145L, NA,
NA, 712L, 340L, NA, NA, NA, 106L, NA, 357L, NA, NA, NA, NA, 594L,
594L, 382L, 443L, 462L, 594L, 880L, NA, 616L, NA, 1522L, NA,
NA, 700L, NA, NA, NA, NA, 107L, NA, 456L, NA, NA, NA, NA, 634L,
634L, 424L, 476L, 447L, 634L, 1030L, NA, 712L, NA, 1578L, NA,
NA, 703L, NA, NA, NA, NA, 108L, NA, 873L, NA, NA, NA, NA, 996L,
996L, 497L, 746L, 518L, 996L, 842L, NA, 256L, NA, 1546L, NA,
NA, 753L, NA, NA, NA, NA, 109L, NA, 337L, NA, NA, NA, NA, 1151L,
1151L, 515L, 862L, 465L, 1151L, NA, NA, NA, NA, 1685L, NA, NA,
699L, NA, NA, NA, NA, 110L, NA, NA, NA, NA, NA, NA, 685L, 685L,
310L, 512L, NA, 685L, NA, NA, NA, NA, 1726L, NA, NA, 857L, NA,
NA, NA, NA, 111L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, 1561L, NA, NA, 1099L, NA, NA, NA, NA, 112L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
1411L, NA, NA, 1156L, NA, NA, NA, NA, 113L, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1714L, NA, NA, 3876L,
NA, NA, NA, NA, 114L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, 2258L, NA, NA, 1507L, NA, NA, NA, NA,
115L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, 1442L, NA, NA, 1524L, NA, NA, NA, NA, 116L, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
2073L, NA, NA, NA, NA, 117L, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2725L, NA, NA, NA,
NA, 118L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, 2255L, NA, NA, NA, NA, 119L, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, 1634L, NA, NA, NA, NA, 120L, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1360L, NA, NA,
NA, NA, 121L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, 1270L, NA, NA, NA, NA, 122L, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, 1328L, NA, NA, NA, NA, 123L, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1470L, NA,
NA, NA, NA, 124L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, 1040L, NA, NA, NA, NA, 125L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, 1095L, NA, NA, NA, NA, 126L, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1823L,
NA, NA, NA, NA, 127L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, 3221L, NA, NA, NA, NA, 128L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, 3986L, NA, NA, NA, NA, 129L, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 3632L,
NA, NA, NA, NA, 130L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, 3760L, NA, NA, NA, NA, 131L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, 3225L, NA, NA, NA, NA, 132L, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 3473L,
NA, NA, NA, NA, 133L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, 3359L, NA, NA, NA, NA, 134L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, 2032L, NA, NA, NA, NA, 135L, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 3337L,
NA, NA, NA, NA, 136L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, 2474L, NA, NA, NA, NA, 137L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, 1748L, NA, NA, NA, NA, 138L, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1581L,
NA, NA, NA, NA, 139L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, 2590L, NA, NA, NA, NA, 140L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, 2769L, NA, NA, NA, NA, 141L, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2134L,
NA, NA, NA, NA, 142L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, 2312L, NA, NA, NA, NA, 143L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, 1822L, NA, NA, NA, NA, 144L, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1890L,
NA, NA, NA, NA, 145L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, 1770L, NA, NA, NA, NA, 146L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, 1664L, NA, NA, NA, NA, 147L, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1533L,
NA, NA, NA, NA, 148L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, 1628L, NA, NA, NA, NA, 149L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, 1682L, NA, NA, NA, NA, 150L, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1416L,
NA, NA, NA, NA, 151L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, 1721L, NA, NA, NA, NA, 152L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, 1732L, NA, NA, NA, NA, 153L, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1748L,
NA, NA, NA, NA, 154L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA, NA, NA, 1312L, NA, NA, NA, NA, 155L,
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,
NA, NA, NA, 1659L, NA, NA, NA, NA, 156L, NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA, NA), .Dim = c(25L, 156L), .Dimnames = list(
c("units_1", "units_2", "units_3", "units_4", "units_5",
"units_6", "units_7", "units_8", "units_9", "units_10", "units_11",
"units_12", "units_13", "units_14", "units_15", "units_16",
"units_17", "units_18", "units_19", "units_20", "units_21",
"units_22", "units_23", "units_24", "units_25"), NULL))

• Please post only the necessary amount of numerical information. There is no value in the endless string of numbers you included. – Has QUIT--Anony-Mousse May 12 '13 at 13:30

This feels like a hack, but I can get the dtw function to work as follows.

#this shows how to register a distance function with proxy

install.packages("proxy")
require("proxy")

DWT.DIST<-function (x,y)
{

a<-na.omit(x)
b<-na.omit(y)

return(dtw(a,b)$normalizedDistance) } ## create a new entry in the registry with two aliases pr_DB$set_entry(FUN = DWT.DIST, names = c("DWT.DIST"))

d<-dist(appliances_t, method = "DWT.DIST")
hc<-hclust(d,"ave")
plot(hc)

pr_DB\$delete_entry("DWT.DIST")

• I received confirmation from the package author that this is indeed the properly method to use to deal with series of differing lengths (to obtain a distance matrix). – B_Miner May 13 '13 at 12:55

It looks like you should be using the open.end=TRUE flag to enable variable-length matching, but unfortunately I still get errors.