More on Microarrays

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More on Microarrays

• Chitta Baral
• Arizona State University

2
Some case studies

• Yeast cell cycle
• Goal Find groups of yeast genes whose expression
  profiles are similar over a 24-hour period.
• Approach Obtain gene expression measurements
  using Affymetrix S98 genome microarrays for a
  synchronized sample of yeast cells over a 24-hr
  period by sampling the total RNA populations at
  30-minute intervals.
• 48 separate time points were sampled twice (for
  duplicate measurements) at each time point. (T1
  T48 and replicates T1T48)
• Drug intervention study
• Goal Characterize effect(s) of drug X three
  hours after it is introduced into normal adult
  mice by the expression level of liver cell genes.
• Approach Gene expression profiles of normal
  adult mice liver cells that are not treated with
  drug X are used as the control state.
• Call the preintervention or control state A, and
  the post intervention state B
• For replicate measurements, liver samples were
  obtained without drug X application from MA adult
  mice and another MB adult mice liver samples were
  obtained after drug X was applied.

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Some potential questions when trying to cluster

• What uncategorized genes have an expression
  pattern similar to these genes that are
  well-characterized?
• How different is the pattern of expression of
  gene X from other genes?
• What genes closely share a pattern of expression
  with gene X?
• What category of function might gene X belong to?
• What are all the pairs of genes that closely
  share patterns of expression?
• Are there subtypes of disease X discernible by
  tissue gene expression?
• What tissue is this sample tissue closest to?

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Questions cont.

• Which are the different patterns of gene
  expression?
• Which genes have a pattern that may have been a
  result of the influence of gene X?
• What are all the gene-gene interactions present
  among these tissue samples?
• Which genes best differentiate these two group of
  tissues?
• Which gene-gene interactions best differentiate
  these two groups of tissue samples.
• DIFFERENT ALGORITHMS ARE MORE PARTICULARLY SUITED
  TO ANSWER SOME OF THESE QUESTIONS, COMPARED WITH
  THE OTHERS.

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Bioinformatics algorithms and some known uses --
Unsupervised

• Feature determination Determining genes with
  interesting properties, without looking for a
  particular pattern determined a priori.
• Principal component analysis determine genes
  explaining the majority of the variance in the
  data set.
• Cluster determination Determine groups of genes
  or samples with similar patterns of gene
  expression.
• Nearest neighbour clustering clusters are
  decided first , the clusters are calculated and
  each gene is assigned to a single cluster.
• Self-organizing maps
• Tamayao et al. used it to functionally cluster
  genes into various patterned time courses in
  HL-60 cell macrophage differentiation.
• Toronen used hierarchical SOM to cluster yeast
  genes responsible fore diauxic shift.
• K-means clustering
• Soukas et al. used it to cluster genes involved
  in leptin signalling.
• Tavazoie et al. used it to cluster genes with
  common regulatory sequences.

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k-means clustering basic idea

• Input n objects (or points) and a number k
• A set of k-clusters that mimimizes the
  squared-error criterion (sum of squared errors
  Si1k S p in Ci p-mi2, where mi is the mean of
  cluster ci.)
• Algorithm complexity is O(nkt), where t
  iterations
• Arbitrarily choose k objects as the initial
  cluster centers
• Repeat
• (Re)assign each object to the cluster to which
  the object is the most similar based on the mean
  value of the objects in the cluster.
• Update the cluster means, (i.e., calculate the
  mean value of the objects for each cluster)
• Until no change.

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Pluses and minuses of k-means

• Pluses Low complexity
• Minuses
• Mean of a cluster may not be easy to define (data
  with categorical attributes)
• Necessity of specifying k
• Not suitable for discovering clusters of
  non-convex shape or of very different sizes
• Sensitive to noise and outlier data points (a
  small number of such data can substantially
  influence the mean value)
• Some of the above objections (especially the last
  one) can be overcomed by the k-medoid algorithm.
• Instead of the mean value of the objects in a
  cluster as a reference point, the medoid can be
  used, which is the most centrally located object
  in a cluster.

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K-Medoid clustering

• Input Set of objects (often points in a
  multi-dimensional space)
• Output These objects clustered into k clusters
• Algorithm Complexity O(n2) when k ltltn for each
  iteration
• Select arbitrarily k representative objects.
• Mark these objects as selected and mark the
  remaining as non-selected
• Repeat
• For all selected objects Oi do
  (complexity O(k(n-k)n))
• For all non-selected objects Oh compute Cih,
  where
• Cih, denotes the total cost of swapping i
  with h, i.e., Cih Sj Cjih, where Cjih dhj d
  ij, and dij denotes d(Oi, Oj) the distance
  between Oi and Oj.
• Select imin, hmin such that Cimin,hmin Mini,h
  Cih (complexity O(k(n-k)))
• If Cimin,hmin lt 0 then mark Oi as non-selected
  and Oh as selected.
• Until no change
• The selected objects now define the clusters.
• A non-selected object Oj belongs to the cluster
  represented by an object Oi if d(Oi, Oj) Min Oe
  d(Oj, Oe), where min is taken over all selected
  objects Oe.

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Self organizing maps

• A neural network algorithm that has been used for
  a wide variety of applications, mostly for
  engineering problems but also for data analysis.
• SOM can be used at the same time both to reduce
  the amount of data by clustering, and for
  projecting the data nonlinearly onto a
  lower-dimensional display.
• SOM vs k-means
• In the SOM the distance of each input from all of
  the reference vectors instead of just the closest
  one is taken into account, weighted by the
  neighborhood kernel h. Thus, the SOM functions as
  a conventional clustering algorithm if the width
  of the neighborhood kernel is zero.
• Whereas in the K-means clustering algorithm the
  number K of clusters should be chosen according
  to the number of clusters there are in the data,
  in the SOM the number of reference vectors can be
  chosen to be much larger, irrespective of the
  number of clusters. The cluster structures will
  become visible on the special displays

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Bioinformatics algorithms and some known uses
Unsupervised cont.

• Cluster determination (cont.)
• Aggolmerative clustering bottom up method, where
  clusters start as empty, then genes are
  successively added to the existing clusters
• Dendograms Groups are defined as sub-trees in a
  phylogenetic-type tree created by a comprehensive
  pair-wise dissimilarity measure.
• 2-D Dendograms
• Divisive or partitional clustering top-down
  method, where large clusters are successively
  broken down into smaller ones, until each
  sub-cluster contains only one object (gene)
• Dendograms and 2-D Dendograms.