.TH "matrices" 3 "Tue Sep 9 2014" "Version 1.0.10" "MLPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
matrices \- Matrices in MLPACK 

.SH "Introduction"
.PP
MLPACK uses Armadillo matrices for matrix support\&. Armadillo is a fast C++ matrix library which makes use of advanced template techniques to provide the fastest possible matrix operations\&.
.PP
Documentation on Armadillo can be found on their website:
.PP
http://arma.sourceforge.net/docs.html
.PP
Nonetheless, there are a few further caveats for MLPACK Armadillo usage\&.
.SH "Column-wise Matrices"
.PP
Armadillo matrices are stored in a column-major format; this means that on disk, each column is located in contiguous memory\&.
.PP
This means that, for the vast majority of machine learning methods, it is faster to store observations as columns and dimensions as rows\&. This is counter to most standard machine learning texts!
.PP
Major implications of this are for linear algebra\&. For instance, the covariance of a matrix is typically
.PP
$ C = X^T X $.PP
but for a column-wise matrix, it is
.PP
$ C = X X^T $.PP
and this is very important to keep in mind! If your MLPACK code is not working, this may be a factor in why\&.
.SH "Loading Matrices"
.PP
MLPACK provides a \fBdata::Load()\fP and \fBdata::Save()\fP function, which should be used instead of Armadillo's loading and saving functions\&.
.PP
Most machine learning data is stored in row-major format; a CSV, for example, will generally have one observation per line and each column will correspond to a dimension\&.
.PP
The \fBdata::Load()\fP and \fBdata::Save()\fP functions transpose the matrix upon loading, meaning that the following CSV:
.PP
.PP
.nf
$ cat data\&.csv
3,3,3,3,0
3,4,4,3,0
3,4,4,3,0
3,3,4,3,0
3,6,4,3,0
2,4,4,3,0
2,4,4,1,0
3,3,3,2,0
3,4,4,2,0
3,4,4,2,0
3,3,4,2,0
3,6,4,2,0
2,4,4,2,0
.fi
.PP
.PP
is actually loaded with 5 rows and 13 columns, not 13 rows and 5 columns like the CSV is written\&.
.PP
This is important to remember!