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
. Reusing 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
estimateclusters.
The following functions can be used to return results from the Icasso result data structure:
icassoIdx2Centrotype
To compute the centrotype of estimateclusters. Centrotype is an
estimate close to the centroid of the estimatecluster. (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 extracluster 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 MultiDimensional Scaling)
redscale

Makes a colormap of shades of red from white to red.
rindex
 To compute a clustering validity index called Rindex 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
Rindex 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=1S
.
 To transform elements of a similarity matrix
S
into
dissimilarities D
by S=sqrt(1S);
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 withincluster
similarities above certain threshold to zero, processvarargin
processvarargin
 checks that the format of identifiervalue pairs is correct. Adds default identifiervalue pairs.
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last updated Tuesday, 21Dec2010 15:55:05 EET