These web pages only give a general view to Icasso. The detailed documentation of the functions is found in the help texts in MATLAB, e.g.,

>> help icassoStruct

- Parameters for the estimation algorithm(s) are selected: e.g.,
for FastICA the estimation approach (symmetrical or deflatory),
contrast function, etc. The estimation is run
`N`times using the selected training parameters. Each time the data is bootstrapped and/or the initial conditions of the estimation algorithm are changed. - Mutual similarities between all the estimates are computed. As the measure of similarity, we use the absolute value of the linear correlation coefficient between the independent components. The estimates are clustered according to their mutual (dis)similarities. In principle, the clustering method can be freely selected. We apply agglomerative clustering with average-linkage criterion.
- The clustering is visualized as a dendrogram and a 2D plot. The user investigates how dense the clusters are. The clustering of the estimates is expected to yield information on the reliability (robustness) of estimation. A compact cluster emerges when a similar estimate repeatedly comes up despite of the randomization.
- The user can retrieve the estimates belonging to certain cluster(s) for further analysis and visualization.

- the (reduced) data dimension (
`d`) that may be less than the original input data dimension (PCA dimension reduction is often applied in FastICA) and - the number of ICA estimates (
`m`) extracted on each resampling cycle.

For Icasso you have to select also

- the resampling mode,
- the number of resampling cycles (
`N`), and - the number of estimate-clusters (
`L`).

- both a different random initial condition and resampling of the data (by bootstrapping) in each resampling cycle,
- different random initial condition for FastICA on each resampling cycle but keep the training data set fixed, or
- fixed initial condition in each cycle but bootstraps every time the data.

In FastICA, you can extract less independent components than there are
dimesnsions in FastICA (`m` < `d`). In Icasso, you
can also freely select the number of estimate-clusters. For example,
you can run FastICA in the deflatory mode and extract, e.g., only one
component at each run but extract *several* "robust" estimates
after Icasso. You can also group the estimates to bigger or smaller
number of estimate-clusters. Interpreting the results is up to you.

However, the computational results that Icasso give *do usually not
represent a strictly orthogonal base* in the whitened data space
since they are directly the natural centroids (centrotypes) of the
estimate-clusters. You have to orthogonalize the result in an
appropriate manner if necessary.

The mixing matrix `A` is a pseudoinverse of `W` and the
sources are returned by computing `S`=`WX` by using the
original data that is stored in Icasso data structure.

Local minima of this index are "good" solutions in terms of having mutually isolated "natural" clusters.

As any relative clustering
validity index *The index is heuristic and should be used only as a
guideline.* If the structure of the estimate space is complex,
this index is dubious.

`megdemo`

for example.
First step (`icassoEst`

) is to compute randomized ICA
estimates `N` times from data `X` using function
`icassoEst`

. Output of this function (we will use variable
name `sR`

is called *Icasso result data structure*. It
logs all the methods and parameters used in the process, and the
results from the Icasso procedure. You can extract information from
this data structure either directly or by using functions
`icassoResult`

and `icassoGet`

.

The batch of Icasso functions that perform similarity computation, clustering
and the 2D projection are collected in `icassoExp`

Finally, you can explore the clustering and get the results by
launching `icassoShow`

. You can examine rel ationships between
estimates and clusters in detail.

Functions that start with string `icasso`

are main
functions: they use the Icasso result structure as input and/or
output.

`icassoEst`

- FastICA parameters and resampling
- [
`icassoStruct`

] -
This is a subfunction automatically called by
`icassoEst`

. However, its help text describes in detail the Icasso data structure with reference to the Icasso process. This might be of interest to you if you are going extract information directly from the data structure. `icassoExp`

- Performs clustering and projections for visualization
`icassoShow`

- Visualizes and returns results
`icassoResult`

- Returns results

`icasso`

implements
the basic procedure from resampling to visualization in one batch.
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Page maintained by webmaster@cis.hut.fi, last updated Thursday, 17-Mar-2005 15:17:37 EET