Oct 4

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Presentation volunteer needed

• Oct 4
• A genome-wide study of gene activity reveals
  developmental signaling pathways in the
  preimplantation mouse embryo. Wang et al, Dev
  Cell 2004.
• Gene expression in the preimplantation embryo
  in-vitro developmental changes. Reproductive
  BioMedicine 2005

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Dimension Reduction Methods
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Motivation

• High dimensional data points are difficult to
  visualize to detect or confirm the relationship
  among them
• In microarray data, one sample point has
  thousands of genes, and one gene points has tens
  of samples

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If applying dimension reduction

• Better visualize the unsupervised clustering
  results
• Color hierarchical or K-means clusters in reduced
  dimension (2 or 3D) to assess cluster tightness
  and outliers
• Discover clusters visually in lower dimensions

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Better visualize unsupervised clustering results
-- HC Sample clustering use the 167 filtered
genes -- Three major samples clusters identified
and colored by HC -- Use the cluster information
to project samples from 167 dimension to 2D using
Linear Discriminant Analysis (LDA)
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Discover clusters visually in lower dimensions
-- HC Sample clustering use the 167 filtered
genes -- Three major samples clusters identified
and colored by HC -- Do NOT use the cluster
information to project samples from 167 dimension
to 2D using Principle Component Analysis (PCA)
The visual clustering after PCA may not agree
with the HC results well
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Viewing clustering result through dimension
reduction, more example
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Viewing clustering result through dimension
reduction, more example
Clustering of gene expression data. a,
Hierarchical clustering dendrogram with the
cluster of 19 melanomas at the centre. b, MDS
three-dimensional plot of all 31 cutaneous
melanoma samples showing major cluster of 19
samples (blue, within cylinder), and remaining 12
samples (gold). Bitter et al. Nature. VOL 406
p536, 2000
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Dimension Reduction Methods

• Principle Component Analysis (PCA)
• Linear Discriminant Analysis (LDA)
• Multi-Dimensional Scaling (MDS)

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Principle Component Analysis (PCA)

• Given N data vectors from k-dimensions, find c lt
  k orthogonal vectors that can be best used to
  represent data
• The original data set is reduced to one
  consisting of N data vectors on c principal
  components (reduced dimensions)
• Each data vector is a linear combination of the c
  principal component vectors
• Project on the subspace which preserve the most
  of the data variability

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Principle Component Analysis (PCA)
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E.g. a sample point X (gene 1, gene 2, gene 3
gene n) a gene point X (sample 1, sample2,
sample p)
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by
First three PC directions
First two PC directions
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Homework (Due Sept 25)

• Read more on Principle Component Analysis
• http//csnet.otago.ac.nz/cosc453/student_tutorial
  s/principal_components.pdfsearch22Principle20c
  omponent22
• (Team) Download a gene expression
  datasethttp//bioinfor.bioen.uiuc.edu/bioe598/da
  ta/colon-cancer.xlsRead it into R. Find the top
  200 genes with the largest standard deviation.
  Use these 200 genes to cluster the samples (the
  pam function is k-means clustering). Are you
  satisfied with your clustering result? Are there
  alternative ways to do this? Hand in your report.
• Inspect the course project datasets on the course
  webpage. What can you do with them?

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Self-organizing maps (SOM)
Interpreting patterns of gene expression with
self-organizing maps Methods and application to
hematopoietic differentiation, Tamayo et al. PNAS
Vol. 96, pp. 2907, 1999
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• Method
• choose a geometry of nodes (e.g. a 6 by 5
  grid)
• The nodes are mapped into k-dimensional gene
  expression space (kno. of conditions),
  initially at random, and then iteratively
  adjusted
• Each iteration involves randomly selecting a data
  point P and moving the nodes in the direction of
  P. The closest node N_P is moved the most,
  whereas other nodes are moved by smaller amounts
  depending on their distance from N_P in the
  initial geometry.

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The position of node N at iteration i is denoted
fi(N). The initial mapping f0 is random. On
subsequent iterations, a data point P is selected
and the node NP that maps nearest to P is
identified. The mapping of nodes is then adjusted
by moving points toward P
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Yeast cell cycle data Cho et al. 1998, Mol. Cell
2, 65-73
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SOM clustering of periodic genes