Number sequence recognition

Question

developing on from another question:

Identifying sequences of repeated numbers in R

I have used the answers from that question to identify sequences within my data, not a problem, however I am stuck when it comes to identifying sequences of differing numbers, for example: the sequence maybe: 126,126,25 rather than repetitive numbers,

The code I am currently using is the same as in the above question (rle)

sample data:

   d<-read.table(text='Date.Time Aerial
794  "2012-10-01 08:18:00"      1
795  "2012-10-01 08:34:00"      1
796  "2012-10-01 08:39:00"      1
797  "2012-10-01 08:42:00"      1
798  "2012-10-01 08:48:00"      1
799  "2012-10-01 08:54:00"      1
800  "2012-10-01 08:58:00"      1
801  "2012-10-01 09:04:00"      1
802  "2012-10-01 09:05:00"      1
803  "2012-10-01 09:11:00"      1
1576 "2012-10-01 09:17:00"      2
1577 "2012-10-01 09:18:00"      2
804  "2012-10-01 09:19:00"      1
805  "2012-10-01 09:20:00"      1
1580 "2012-10-01 09:21:00"      2
1581 "2012-10-01 09:23:00"      2
806  "2012-10-01 09:25:00"      1
807  "2012-10-01 09:32:00"      1
808  "2012-10-01 09:37:00"      1
809  "2012-10-01 09:43:00"      1', header=TRUE, stringsAsFactors=FALSE, row.names=1)

code that will recognise repeated sequence of numbers (same number repeated 4 times):

tmp <- rle(d$Aerial)
d$newCol <- rep(tmp$lengths>=4, times = tmp$lengths)

However I do not know how to identify a sequence which contains different numbers, for example the sequence may be: 1,2,2,1 (as in d$Aerial) at "2012-10-01 09:11:00"

There are various patterns. The data is detections of a signal at a given time on a given Aerial, but to keep the question open I have simplified it as above. so the pattern is 1,2,2,1 i.e. detection at Aerial 1, then 2, then, 2, then 1 (in the Aerial column). In my data when this pattern occurs it indicates a behavioural movement of an animal. If I am able to identify it, I can then perform more calculations on it.

The code above indicates when a number is repeated 4 times, however it is unable to identify repetition of 4 numbers which are different from each other: 1,2,2,1

This sequence (1,2,2,1) may come up multiple times in the data and I would like to identify it each time.

Answer 1

Brute-force solution:

pat <- c(1,2,2,1)
x <- sapply(1:(nrow(d)-length(pat)), function(x) all(d$Aerial[x:(x+length(pat)-1)] == pat))

d[which(x),]  # "which" prevents recycling of the shorter vector "x"
##               Date.Time Aerial
## 803 2012-10-01 09:11:00      1
## 805 2012-10-01 09:20:00      1

zoo has rollapply which can be used for this:

require(zoo)
x <- rollapply(d$Aerial, length(pat), FUN=function(x) all(x == pat))

d[which(x),]
##               Date.Time Aerial
## 803 2012-10-01 09:11:00      1
## 805 2012-10-01 09:20:00      1

For the (now deleted) comment, to find the rows which match the final character of the pattern:

d[which(x)+length(pat)-1,]
##               Date.Time Aerial
## 804 2012-10-01 09:19:00      1
## 806 2012-10-01 09:25:00      1

Answer 2

If you don't know what the patterns are going to be in advance (which is what I initially took from your question), then here's a brute force solution that will find repeated patterns of a given length:

pattern_length = 4
patterns = list()
for (i in 1:(nrow(d) - pattern_length)) {
  patterns[[i]] = d$Aerial[i:(i + pattern_length - 1)]
}
unique(patterns[duplicated(patterns)])

[[1]]
[1] 1 1 1 1

[[2]]
[1] 1 1 2 2

[[3]]
[1] 1 2 2 1

[[4]]
[1] 2 2 1 1

You could then feed these into Matthew Lundberg's answer.