Download ArrayCluster: an analytic tool for clustering, data visualization and

ArrayCluster:
an analytic tool for clustering, data visualization
and module finder on gene expression profiles
組員：李祥豪
謝紹陽
江建霖
Outline
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Introduction
Mixed Factors Model
Analytic Tools
Summary
Demo
Introduction
 This task can be addressed by
grouping gene expression patterns of
a large number of genes
 Typical microarray data have a fairly
small sample size, less than 100,
whereas the number of genes
involved is more than several
thousands
Introduction
 One major difficulty in this problem is
that the number of samples to be
clustered is much smaller than the
dimension of data
 Most clustering technologies, e.g. kmeans, Gaussian mixture clustering,
hierarchical clustering and so on,
would be limited by over-learning
Introduction
 In statistics, overfitting is fitting a
statistical model that has too many
parameters.
 When the degrees of freedom in
parameter selection exceed the data,
this leads to arbitrariness in the final
(fitted) model parameters which
reduces or destroys the ability of the
model to generalize beyond the fitting
data.
Introduction
 In machine learning, usually a
learning algorithm is trained using
some set of training examples,
especially in learning was performed
too long or training are rare, the
learner may adjust to very specific
random features of the training data,
that have no causal relation to the
target function.
Introduction
 In both statistics and machine
learning, in order to avoid overfitting,
it is necessary to use additional
techniques (e.g. cross-validation,
early stopping, Bayesian Priors on
parameters or model comparison),
that can indicate when further
training is not resulting in better
generalization.
Mixed Factors Model
 The mixed factors model presents a
parsimonious parameterization of Gaussian
mixture model
 Our primal intention is parsimoniously to
describe the group structure of data based
on the factor variables. To this end, we
devise the mixed factors that follow a Gcomponents Gaussian mixture as
G
p( f j )   g ( f j ; g ,  g )
g 1
Mixed Factors Model
 The mixed factors model, we possibly
avoid the over-fitting of the Gaussian
mixture by choosing an appropriate
factor dimension regardless to the
high dimensionality of data.
 Once the model has been fitted to a
given dataset, clustering can be
addressed by the Bayes rule.
Mixed Factors Model
 To avoid it, we impose the orthogonality on
the q columns of the factor loading matrix
 This imposition leads to a canonical
representation of the mixed factors model
as
AT X j  f j  AT  j
 From this equation, one achieves the fact
that the q canonical variates in ATxj€Rq are
distributed according
to
G
p( AT X j )   g ( AT X j ; g ,  g  I )
g 1
Mixed Factors Model
 The canonical variates can be
considered as the q modules of genes
which are relevant to the existing
molecular subtypes.
 This process yields a feature selection
that constructs good discriminators
for existing groups as linear
combination d genes.
Analytic Tools
 File format of data
file
Analytic Tools
 model selection based on BIC curve
Analytic Tools
 In this plot, the horizontal and
vertical axes correspond to the factor
dimension and the BIC scores,
respectively. The each line represents
curve of BIC scores against to varying
factor dimensions (q) for a fixed
number of clusters (G)
Analytic Tools
 File format of mixed_factors
Analytic Tools
 Box plot of the computed factor scores
Analytic Tools
 Each cluster is separated with the
blank lines. All samples in one cluster
are ordered according to the degree
of the belongings that are measured
by the Maharanobis distance between
each sample point and the
corresponding group centeroid. The
calculated distances are indicated
next to the sample identifiers
Analytic Tools
 File format of relevant_set
Analytic Tools
 relevant module profiling
 After selecting rows (genes) of
interest, the enlarged expression
image will be displayed on the right
window
Analytic Tools
 The ArrayCluster provides users an usable
environment to perform the following tasks:
 Parameter estimation of the mixed factors model:
The ArrayCluster computes the maximum
likelihood estimators by using the EM algorithm
 Determination of the number of clusters and the
factor dimension (the number of grouprelatedmodules):These are selected based on
the Bayesian information criterion (BIC)
 Clustering based on the Bayes rule
Analytic Tools
 Dimension reduction of data: This task is
addressed by the same way of the classical
factor analysis, the mixed factors analysis
explicitly reflects the existing group structure of
original data, while the classical factor analysis
ignores it during the dimension reduction
 Identification of the group-related genes: In the
ArrayCluster, the relevant genes in each module
are selected to be top L (user can specify) of the
highest positive (negative) correlation with each
element of the factor vector
Analytic Tools
 Identification of the modules: By
separating positive and negative
correlated genes with the factor vector in
a module, totally we identify 2q modules
 Missing data imputation
 Data preprocessing: The methods
include normalization and gene filtering
Summary
 The ArrayCluster visualizes the
computed factor scores using the box
plot matrix
 Enhancing the graphical
understanding of the group structure.
 A casual link from the calibrated
clusters to biological knowledge can
be elucidated through the inspection
of the group-related modules.
Summary
 The ArrayCluster displays the
expression patterns of these modules.
 Genes at these modules and their
visualization give us a scope to
question where the calibrated clusters
come from.
Thanks for your attention
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