Icasso

Main functions

Functions that start with string icasso are main functions: they use the Icasso result structure as input and/or output:

To get started

Script megdemo is a demo script of the Icasso procdure.

Function icasso
Complete Icasso procedure: computes randomized ICA estimates N times for data X, does visualization and/or returns results. If you wish to use functions icassoResult and icassoShow. Re-using function icasso will do the resampling again!

Function icasso always uses both random initial conditions and bootstrappin the data.

Icasso data structure

icassoStruct
initiates an Icasso result data structure which is meant for storing and keeping organized all data, parameters and results when performing the Icasso procedure.

The help text of function icassoStruct contains a description of the Icasso process.

Icasso procedure

Resampling

icassoEst
computes randomized ICA estimates N times from data X. Output of this function (sR) is called an 'Icasso result structure' (see icassoStruct). sR keeps the on all the methods, parameters, and results in the Icasso procedure.

Clustering

icassoExp
prepares Icasso result structure for exploratory analysis, i.e., to compute (dis)similarity matrix, clustering, and projection.

Function icassoExp is a simple script consisting of the following functions that may also be used independently if a customized process is needed: If the results are not visualized by using icassoGraph, function icassoProjection is not needed.

icassoCluster: computes (dis)similarities between the estimates, clusters the estimates according to the dissimilarities, and computes a relative clustering validity index.
icassoProjection: makes a 2D repesentation of the estimates space. Functio icassoProjection projects points on plane so that Euclidean distances between the projected points correspond to the similarity matrix between IC estimates in the Icasso result structure.

Results and visualization

icassoResult
returns computational results of the Icasso procedure.

icassoShow
generates explorative visualizations for Icasso and returns computational results.

Function icassoShow uses the following functions that may also be used independently if necessary:

icassoDendrogram: visualizes the clustering and similarities between estimates as a dendrogram and a corrgram.
icassoGraph: visualizes the estimate space as a 2D projection and the similarities between the estimates as a graph. Estimates are presented as black points that are located so that the distances between the points approximate the similarities between the estimates. Estimates belonging to the same cluster are bounded by a red convex hull whose background color expresses its average density.
icassoRindex: returns and/or plots a relative clustering validity index.
icassoStability: computes and/or plots the stability (quality) indices of the ICA estimate-clusters.

The following functions can be used to return results from the Icasso result data structure:

icassoIdx2Centrotype
To compute the centrotype of estimate-clusters. Centrotype is an estimate close to the centroid of the estimate-cluster. (see help in function centrotype for an exact definition). This estimate represents better the "true" estimate than an arbitrary estimate from a single run.

icassoGet
Auxiliary function for obtaining various information from the Icasso result data structure. Using icassoGet, you can return information related to original data, e.g.: data matrix, (de)whitening matrix, total number of estimates, number of estimates on each round. You can also return specified estimated independent components (sources), and rows of demixing matrices from. (However, it is easier to use function icassoResult to return the final estimation results from the complete Icasso procedure.)

Other functions

The rest of functions operate on matrices/vectors/strings. They may be interesting for the user as well:

cca (from SOM Toolbox): Curvilinear component analysis
centrotype: To compute the centrotype of objects whose relations are defined by similarity matrix S. Centrotype means the object that is most similar to all the others, i.e., it should be close to the centroid of the data set.
clusterhull: To draw a 2D cluster visualization where the objects (represented by points) belonging to the same cluster are presented by "cluster hulls", polygons where the edge of the polygon is the convex hull of the points that belong to the same cluster.
clusterquality: To compute a simple quality (compactness) index for the given clusters. The more dense and isolated a cluster is the bigger value the index gets; however, if there is only one item in a cluster the index is not computed (a NaN is returned for that cluster)
clusterstat: To compute various intra- and extra-cluster statistics.
corrw: To compute mutual linear correlation coefficients between M independent component estimates using the demixing matrix W and the dewhitening matrix D of the original data.
hcluster: To perform a hierarchical agglomerative clustering on a distance matrix. Returns partition vectors for each level of the clustering hierarchy and information for visualizing the clustering hierarchy as a dendrogram.
mmds: To compute principal coordinates (linear Metric Multi-Dimensional Scaling)
redscale: Makes a colormap of shades of red from white to red.
rindex: To compute a clustering validity index called R-index to assist in selecting a proper number of clusters. Input argument 'partition' defines different clustering results, partitions, of the same data. Clustering result that has minimum value for R-index among the compared ones is the "best" one.
signalplot: To plot several signals, e.g., estimated sources into the same graphic axis; a simplified alternative to MATLAB's native subplot command.
sammon (from SOM Toolbox): Sammon's projection
sqrtsim2dis
sim2dis: To transform elements of a similarity matrix S into dissimilarities D by D=1-S.; To transform elements of a similarity matrix S into dissimilarities D by S=sqrt(1-S);
similaritygraph: Draws a2D visualization of a weighted graph where the black points are vertices and the red shaded lines between them are edges. The level is determined by dividing values of S (the weights) into the given bins Note that the function always adds to a plot (turns 'hold on' temporarily).

Auxiliary functions

som_linkage, som_grid, som_set: SOM Toolbox routines needed by hcluster and similaritygraph)
reducesim: reduces the number of lines that are drawn when the similarity matrix is visualized. That is, to set similarities below certain threshold to zero, and optionally, also within-cluster similarities above certain threshold to zero, processvarargin
processvarargin: checks that the format of identifier-value pairs is correct. Adds default identifier-value pairs.