# Re: [R] Compact Indicator Matrices

From: Douglas Bates <bates_at_stat.wisc.edu>
Date: Mon, 12 May 2008 08:30:49 -0500

On Sun, May 11, 2008 at 9:49 AM, amarkos <amarkos_at_gmail.com> wrote:
> On May 11, 4:47 pm, "Douglas Bates" <ba...@stat.wisc.edu> wrote:
>
>> Do you mean that you want to collapse similar rows into a single row
>> and perhaps a count of the number of times that this row occurs?
>
> Let me rephrase the problem by providing an example.
>
> Input:
>
> A =
> [,1] [,2]
> [1,] 1 1
> [2,] 1 3
> [3,] 2 1
> [4,] 1 2
> [5,] 2 1
> [6,] 1 2
> [7,] 1 1
> [8,] 1 2
> [9,] 1 3
> [10,] 2 1

An important question here is do you start with two or more variables like the columns of your matrix A? If so, there is a more direct method of getting the answers that you want. The natural way to store such variables in R is as factors. I prefer to use letters instead of numbers to represent the levels of a factor (that way I don't confuse a factor with a numeric variable when I look at rows) so I would create a data frame with two factors instead of a matrix.

> V1 <- factor(c(1,1,2,1,2,1,1,1,1,2), labels = LETTERS[1:2])
> V2 <- factor(c(1,3,1,2,1,2,1,2,3,1), labels = letters[1:3])
> df <- data.frame(f1 = V1, f2 = V2)
> df

f1 f2
1 A a
2 A c
3 B a
4 A b
5 B a
6 A b
7 A a
8 A b
9 A c
10 B a

You could produce the indicator matrix and check for unique rows, etc. - I will show that below - but all you need is the interaction of the two factors

> df\$f12 <- with(df, f1:f2)[drop = TRUE]
> df

f1 f2 f12

```1   A  a A:a
2   A  c A:c
3   B  a B:a
4   A  b A:b
5   B  a B:a
6   A  b A:b
7   A  a A:a
8   A  b A:b
9   A  c A:c
10  B  a B:a

> str(df)
'data.frame':	10 obs. of  3 variables:
\$ f1 : Factor w/ 2 levels "A","B": 1 1 2 1 2 1 1 1 1 2
```
\$ f2 : Factor w/ 3 levels "a","b","c": 1 3 1 2 1 2 1 2 3 1  \$ f12: Factor w/ 4 levels "A:a","A:b","A:c",..: 1 3 4 2 4 2 1 2 3 4
> table(df\$f12)

A:a A:b A:c B:a
2 3 2 3
> as.numeric(df\$f12)

[1] 1 3 4 2 4 2 1 2 3 4

Notice that this shows you that there are four distinct combinations that occur 2, 3, 2 and 3 times respectively; the first combination occurs in rows 1 and 7, it consists of the first level of f1 and the first level of f2, etc.

If you really do want the indicator matrix you could generate it as

> (ind <- cbind(model.matrix(~ 0 + f1, df), model.matrix(~ 0 + f2, df)))

f1A f1B f2a f2b f2c
1 1 0 1 0 0
2 1 0 0 0 1
3 0 1 1 0 0
4 1 0 0 1 0
5 0 1 1 0 0
6 1 0 0 1 0
7 1 0 1 0 0
8 1 0 0 1 0
9 1 0 0 0 1
10 0 1 1 0 0
> unique(ind)

f1A f1B f2a f2b f2c
1 1 0 1 0 0
2 1 0 0 0 1
3 0 1 1 0 0
4 1 0 0 1 0

but working with the factors is generally much simpler than working with the indicators.

> # Indicator matrix
> A <- data.frame(lapply(data.frame(obj), as.factor))
>
> nocases <- dim(obj)[1]
> novars <- dim(obj)[2]
>
> # variable levels
> levels.n <- sapply(obj, nlevels)
> n <- cumsum(levels.n)
>
> # Indicator matrix calculations
> Z <- matrix(0, nrow = nocases, ncol = n[length(n)])
> newdat <- lapply(obj, as.numeric)
> offset <- (c(0, n[-length(n)]))
> for (i in 1:novars)
> Z[1:nocases + (nocases * (offset[i] + newdat[[i]] - 1))] <- 1
>
> #######
>
> Output:
>
> Z =
>
> [,1] [,2] [,3] [,4] [,5]
> [1,] 1 0 1 0 0
> [2,] 1 0 0 0 1
> [3,] 0 1 1 0 0
> [4,] 1 0 0 1 0
> [5,] 0 1 1 0 0
> [6,] 1 0 0 1 0
> [7,] 1 0 1 0 0
> [8,] 1 0 0 1 0
> [9,] 1 0 0 0 1
> [10,] 0 1 1 0 0
>
>
> Z is an indicator matrix in the Multiple Correspondence Analysis
> framework.
> My problem is to collapse identical rows (e.g. 2 and 9) into a single
> row and
> store the row ids.
>
> ______________________________________________
> R-help_at_r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help