Comparison of clustering techniques for breast cancer data

1
Comparison of clustering techniquesfor breast
cancer data

• Daniele Soria
• http//www.cs.nott.ac.uk/dqs
• 22nd European Conference on Operational Research
• Prague, 11-07-2007

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Outline

• Introduction
• Case study
• Methods
• Results
• Future work

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Background

• Identification of biologically distinct groups
  with clinical and prognostic relevance.
• TMA technology allows concomitant analyses of
  many proteins on tumour samples.
• Started from Abd El-Rehim et al. (2005) 1
• IHC applied to TMA preparations of cases of
  invasive breast cancer
• To study the combined protein expression profiles
  of a large panel of biomarkers.

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Abd El-Rehim et al. (2005)

• IHC results analyzed with hierarchical clustering
• ANN to categorize cases into groups
• Six groups obtained
• Each group driven by different markers
• Arbitrary choice of clusters number

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Aims of our work

• Apply different clustering techniques
• Integrate previous results and compare them with
  ours
• Verify stability of results across different
  methods
• Refine the phenotypic characterisation of breast
  cancer

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Case study

• Patients entered into the Nottingham Tenovus
  Primary Breast Carcinoma Series between 1986 and
  1998
• 1076 cases informative for all 25 biological
  markers
• Clinical information (grade, size, age, survival,
  follow-up, etc.)

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Methods

• Three different algorithms (2?20)
• Fuzzy c-means (FCM)
• K-means (KM)
• Partitioning Around Medoids (PAM)
• Validity indices computed
• Software R used (www.r-project.org)

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FCM method

• Minimization of the objective function
• X x1,x2,...,xn n data points
• V v1,v2,,vc c cluster centres
• U(µij)nc fuzzy partition matrix
• µij membership degree of xi to vj
• m fuzziness index (often m2)

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KM method

• Minimization of the objective function
• xi-vj Euclidean distance between xi and vj
  
• cj data points in cluster j
• vj can be calculated as

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PAM method

• Based on the search for k representative objects
  (medoids) among the observations
• Minimum sum of dissimilarities among the
  observations to their closest medoid
• k clusters are constructed by assigning each
  observation to the nearest medoid

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Fuzzy C-means results

• Hierarchical starting point
• If c gt 3, no data assigned to all clusters
• Not clear classification (poor membership)
• No help from validity indices

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K-means results
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3
3
3
6
4
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PAM results
4
4
4
4
4
4
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Principal Components
K-Means
PAM
km1, km2, km3, km4, km5, km6
pam1, pam2, pam3, pam4
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Principal Components
Hierarchical
ART
h1, h2, h3, h4, h5, h6
art1, art2, art3, art4, art5, art6
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From Clusters to Classes
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Classes
class1 class2 class3 class4 class5 cla
ss6 62 of data 3-D Visualisation
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Previous papers
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Our results
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Actual and future work

• New data available from NCH
• How to assign them to classes?
• k Nearest Neighbour classification

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Main references

• D.M. Abd El-Rehim, G. Ball, S.E. Pinder, E.
  Rakha, C. Paish, J.F. Robertson, D. Macmillan,
  R.W. Blamey, I.O. Ellis, High-throughput protein
  expression analysis using tissue microarray
  technology of a large well-characterised series
  identifies biologically distinct classes of
  breast cancer confirming recent cDNA expression
  analyses, Int. Journal of Cancer, 116, 340-350,
  2005.
• L. Kaufman, P.J. Rousseeuw, Finding groups in
  data, Wiley series in probability and
  mathematical statistics, 1990.
• A. Weingessel, E. Dimitriadou and S. Dolnicar, An
  Examination Of Indexes For Determining The Number
  Of Clusters In Binary Data Sets, Working Paper
  No.29, 1999.

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Thank You!

• This work was supported by Marie
• Curie Action MEST-CT-2004-7597
• under the Sixth Framework Programme
• of the European Community
• Contact daniele.soria_at_cs.nott.ac.uk