PrologMethods/Transformation/radical.md

+# RADICAL
+
+An implementation of RADICAL, a method for independent component analysis (ICA). Given a dataset, this can decompose the dataset into an unmixing matrix and an independent component matrix. This can be useful for preprocessing.
+
+# Available Predicates
+
+* [initModel/5](/PrologMethods/Transformation/radical#initmodel5)
+* [doRadical/9](/PrologMethods/Transformation/radical#doradical9)
+* [doRadical2D/4](/PrologMethods/Transformation/radical#doradical2d4)
+
+---
+
+[links/resources](/PrologMethods/Transformation/radical#connected-linksresources)
+
+## **_initModel/5_**
+
+Initilizes the radical model.
+
+```prolog
+%% part of the predicate definition
+initModel(+float32, +integer, +integer, +integer, +integer).
+```
+
+### Parameters
+| Name | Type | Description | Default |
+|------|------|-------------|---------|
+| noiseStdDev | +float | Standard deviation of the Gaussian noise added to the replicates of the data points during Radical2D. | 0.175 |
+| replicates | +integer | Number of Gaussian-perturbed replicates to use (per point) in Radical2D. | 30 |
+| angles | +integer | Number of angles to consider in brute-force search during Radical2D. | 150 |
+| sweeps | +integer | Number of sweeps. Each sweep calls Radical2D once for each pair of dimensions. | 0 |
+| m | +integer | The variable m from Vasicek's m-spacing estimator of entropy. | 0 |
+
+---
+
+## **_doRadical/9_**
+
+Run RADICAL.
+
+```prolog
+%% part of the predicate definition
+doRadical(  +pointer(float_array), +integer, +integer, 
+            -pointer(float_array), -integer, -integer, 
+            -pointer(float_array), -integer, -integer).
+```
+
+### Parameters
+| Name | Type | Description | Default |
+|------|------|-------------|---------|
+| X | +matrix | Input data into the algorithm - a matrix where each column is a point and each row is a dimension. | - |
+| Y | -matrix | Estimated independent components - a matrix where each column is a point and each row is an estimated independent component. | - |
+| W | -matrix | Estimated unmixing matrix, where Y = W \* X. | - |
+
+---
+
+## **_doRadical2D/4_**
+
+Two-dimensional version of RADICAL.
+
+```prolog
+%% part of the predicate definition
+doRadical2D(  +pointer(float_array), +integer, +integer, 
+              [-float32]).
+```
+
+### Parameters
+| Name | Type | Description | Default |
+|------|------|-------------|---------|
+| X | +matrix | Input data into the algorithm - a matrix where each column is a point and each row is a dimension. | - |
+| result | -float | - | - |
+
+---
+
+# Connected Links/Resources
+
+If you want a more detailed explanation, then go to the python documentation. There is most of the time a good explanation on how the methods work and what the parameters do.
+
+* [**MLpack::radical_C++\_documentation**](https://www.mlpack.org/doc/stable/doxygen/classmlpack_1_1radical_1_1Radical.html)
+* [**MLpack::radical_Python_documentation**](https://www.mlpack.org/doc/stable/python_documentation.html#radical)
+
+added some of the links from the python documentation
+
+* [**Independent component analysis on Wikipedia**](https://en.wikipedia.org/wiki/Independent_component_analysis)
+* [**ICA using spacings estimates of entropy (pdf)**](http://www.jmlr.org/papers/volume4/learned-miller03a/learned-miller03a.pdf)
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