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Attractor metagene algorithm for feature engineering using mutual information-based learning

`M = metafeatures(X)`

```
[M,W] =
metafeatures(X)
```

```
[M,W,GSorted]
= metafeatures(X,G)
```

```
[M,W,GSorted,GSortedInd]
= metafeatures(___)
```

`[___] = metafeatures(___,Name,Value)`

`[___] = metafeatures(T)`

`[___] = metafeatures(T,Name,Value)`

returns
the weighted sums of features `M`

= metafeatures(`X`

)`M`

in `X`

using
the attractor metagene algorithm described in [1].

M is a *r*-by-*n* matrix. *r* is
the number of metafeatures identified during each repetition of the
algorithm. The default number of repetitions is 1. By default, only
unique metafeatures are returned in M. If multiple repetitions result
in the same metafeature, then just one copy is returned in `M`

. *n* is
the number of samples (patients or time points).

`X`

is a *p*-by-*n* numeric
matrix. *p* is the number of variables, features,
or genes. In other words, rows of `X`

correspond
to variables, such as measurements of gene expression for different
genes. Columns correspond to different samples, such as patients or
time points.

`[`

uses
a `M`

,`W`

,`GSorted`

]
= metafeatures(`X`

,`G`

)*p*-by-1 cell array of character vectors `G`

containing
the variable names and returns a *p*-by-*r* cell
array of variable names `GSorted`

sorted by the
decreasing weight.

The *i*th column of `GSorted`

lists
the feature (variable) names in order of their contributions to the *i*th
metafeature.

`[`

returns the indices `M`

,`W`

,`GSorted`

,`GSortedInd`

]
= metafeatures(___)`GSortedInd`

such
that `GSorted`

= `G`

(`GSortedInd`

).

`[___] = metafeatures(___,`

uses additional options specified by one or more `Name,Value`

)`Name,Value`

pair
arguments.

`[___] = metafeatures(`

uses
a `T`

)*p*-by-*n* table `T`

.
Gene names are the row names of the table. `M = W'*T{:,:}`

.

`[___] = metafeatures(`

uses additional options specified by one or more `T`

,`Name,Value`

)`Name,Value`

pair
arguments.

It is possible that the number of metafeatures (*r*)
returned in `M`

can be fewer than the number of
replicates (repetitions). Even though you may have set the number
of replicates to a positive integer greater than 1, if each repetition
returns the same metafeature, then *r* is 1, and `M`

is
1-by-*n*. This is because, by default, the function
returns only unique metafeatures. If you prefer to get all metafeatures,
set `'ReturnUnique'`

to `false`

.
A metafeature is considered unique if the Pearson correlation between
it and all previously found metafeatures is less than the `'UniqueTolerance'`

value
(the default value is `0.98`

).

[1] Cheng, W-Y., Ou Yang, T-H., and Anastassiou, D. (2013). Biomolecular events in cancer revealed by attractor metagenes. PLoS Computational Biology 9(2): e1002920.

[2] Daub, C., Steuer, R., Selbig, J., and Kloska, S. (2004). Estimating mutual information using B-spline functions – an improved similarity measure for analysing gene expression data. BMC Bioinformatics 5, 118.

[3] Hefti, M.M., Hu, R., Knoblauch, N.W., Collins, L.C., Haibe-Kains, B., Tamimi, R.M., and Beck, A.H. (2013). Estrogen receptor negative/progesterone receptor positive breast cancer is not a reproducible subtype. Breast Cancer Research. 15:R68.

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