MATLAB has the concept of Not-a-Number, also known as NaN for quite some time. Following the IEEE 754 Standard for Binary Floating-Point Arithmetic, some floating point calculations result in NaN, for example, 0/0. You can also use them as placeholders in numeric arrays, for example to denote missing data. If you do so, how to you operate on these arrays and get answers that account for them as missing? I'll show an example here.
Contents
Sample Data Set
Let's create a dataset that has some missing values.
m = 10; n = 3; data = randn(m,n); missing = abs(data) > 1.2; data(missing) = NaN
data =
-0.3999 NaN -1.0106
0.6900 0.2573 0.6145
0.8156 -1.0565 0.5077
0.7119 NaN NaN
NaN -0.8051 0.5913
0.6686 0.5287 -0.6436
1.1908 0.2193 0.3803
NaN -0.9219 -1.0091
-0.0198 NaN -0.0195
-0.1567 -0.0592 -0.0482
Calculating the Column Means
Now let's calculate the mean of the data, columnwise.
meanc = sum(data)/m
meanc = NaN NaN NaN
Assuming NaN indicates missing values, the mean that we've just calculated isn't very useful since the NaN values propagate into the mean.
Calculating the Column Means Accounting for NaN Values
Now let's try calculating the mean, while disregarding the missing values. To do so, first we need to find those values. Actually we will do this using logical indexing, a useful concept in MATLAB. We'll generate a matrix with logical values, i.e., true and false, true indicating locations where NaN values do not exist in our data.
notNaN = ~isnan(data)
notNaN =
1 0 1
1 1 1
1 1 1
1 0 0
0 1 1
1 1 1
1 1 1
0 1 1
1 0 1
1 1 1
Next we find out how many in each column are legitimate data values.
howMany = sum(notNaN)
howMany =
8 7 9
We replace the missing data values with 0.
data(~notNaN) = 0
data =
-0.3999 0 -1.0106
0.6900 0.2573 0.6145
0.8156 -1.0565 0.5077
0.7119 0 0
0 -0.8051 0.5913
0.6686 0.5287 -0.6436
1.1908 0.2193 0.3803
0 -0.9219 -1.0091
-0.0198 0 -0.0195
-0.1567 -0.0592 -0.0482
Next we sum those values.
columnTot = sum(data)
columnTot =
3.5006 -1.8373 -0.6373
And finally we compute the column means.
colMean = columnTot ./ howMany
colMean =
0.4376 -0.2625 -0.0708
Generalizing to Other Dimensions
Statistics Toolbox contains functionality similar to what we've just stepped through with the function nanmean, and allows you to choose which dimension to calculate the mean along. In addition, the toolbox includes a suite of related functions for dealing with missing data.
Missing Any Data Yourself?
Do you work with data sets that have gaps or missing data? How do you handle them? Post your thoughts here.
Get
the MATLAB code
Published with MATLAB® 7.5
I am constantly working with missing data and using Matlab functions nanmean, nansum and nanstd.
Some additional functions like nancorrcoef are also available in the newsgroup.
why bother about substitution of zeros ?
Michel-
I substitute zeros so I can do the sums without indexing. The reason is that not every column is guaranteed to have the same number of NaNs.
–Loren
I do not see why it matters.
If you want the sum over the columns do nansum over the columns; if you want the rows, nansum over the rows
Y = nansum(X,dim)
The only problem is that these functions are available only in the Statistics Toolbox
Michel-
My point wasn’t to say to not use nansum but to show HOW to do this sort of operation in MATLAB.
–Loren
Another approach is to use accumarray
notNaN = ~isnan(data) ;
[r,c] = find(notNaN) ;
r(:) = 1 ;
colSum = accumarray([r c],data(notNaN))
colProd = accumarray([r c],data(notNaN),[1,size(data,2),@prod)
colMean = accumarray([r c],data(notNaN),[1,size(data,2),@mean)
etc …
Jos
For those looking for a partial solution without the stats toolbox, there is #10235 on the file exchange. It demonstrates what Loren illustrates here for all common stat measures.
I covered the uses of NaN in graphics in a movie on my blog earlier this week:
http://blogs.mathworks.com/pick/2007/10/08/matlab-basics-video-using-nan-as-placeholder-data-in-graphics/
Doug
I run into this exact problem all the time. A few months ago I posted a function in the File Exchange named “ignorenan”. It also uses the accumarray function but handles n-d data and has an input to specify which dimension to operate on. Hopefully someone else may find it useful…
Replacing NaN’s with zeros prior to heavy-duty computation is a good thing (assuming that it still gives you the right answer of course). NaN’s, Inf’s and the like cause the floating-point hardware to slow *way* down. Try this:
A=rand(2000);
B=rand(2000);
C=nan(2000);
tic; E = A+B ; toc
tic; D = A+C ; toc
The first computation takes 1.3 seconds on my Pentium 4 desktop in MATLAB 7.5. The 2nd takes 0.1 seconds. So NaN’s are great when used carefully, but keep an eye on performance if MATLAB seems sluggish when you abuse them.
Is a sum over logicals, as in howMany=sum(isnan(DataMatrix)), optimized for speed? It seems inefficient to convert logicals to doubles and then add, especially since it already had to iterate through the entire matrix to do the isnan check.
Chris-
MATLAB is smart enough to not convert the logicals to doubles in their entirety before doing the summation. You can convince yourself on windows by watching the task manager as you perform the operation on a large enough array.
–Loren
hi…Loren thanx for the article,it was quite helpful for me.I was handling some data where i needed a NAN replacement..so nansum type function was not helpful.
Loren-
I have a different sort of problem with NaNs and 0s. My data has zeros where data is missing, but also has zeros that are real values. Having the missing values as zeros skews my correlations. I want to replace the zeros with NaNs, but only in columns where zeros can’t be real values.
Eleanor-
You either need an algorithm to determine which 0s should be replaced by NaN values or you will need to pre-edit the data yourself.
–Loren
hi,
thnx a lot….. its amazing code.
it has saved mine hell lot of time… :)
rly thnx…..