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Incidence of Missing Values in Hierarchical
Clustering of Microarrays Data Alexandre G. de
Brevern1, Serge Hazout1 and Alain Malpertuy2 1
Equipe de Bioinformatique Génomique et
Moléculaire (EBGM), INSERM E0346, Université
PARIS VII, 2 place Jussieu, case 7113, 75251
Paris France - debrevern,hazout_at_urbb.jussieu.fr
2 Atragene Bioinformatics, 4 Rue Pierre Fontaine,
91000 Evry France - alain.malpertuy_at_atragene.com

• 1 - Introduction
• Microarray technologies enable to determine
  expressed genes in various cell types, time and
  experimental conditions. These experiments are
  performed on a large scale and produced large
  amount of data. Clustering methods such as
  Hierarchical Clustering (HC) 1 or Self
  Organizing Map (SOM) 2 are frequently used to
  analyse microarray data and led to the
  identification of co-expressed genes. However,
  microarray datasets often contain missing values
  (MV) which occurred during the multistep
  experimental process (spotting, hybridization,
  image scanning). These missing data represent a
  major drawback for the use of HC, K-means 3 and
  SOM and do not allowed to perform Principal
  Component Analysis 4.
•  
• Since the presence of MV may significantly modify
  the clustering results, the users usually remove
  the genes with MV or replace the MV by a constant
  (zero or the average expression level of the
  entire experiment). Recently, Troyanskaya et al.
  showed that the values of MV could be estimated
  by using the weighted K - Nearest Neighbours
  method (KNN). The KNN approach computes the
  estimated value from the k closest expression
  profils among the dataset. The authors considered
  that KNN, with k 15, is the most accurate
  method to estimate MV in microarray data 5.
•  
• In order to evaluate the influence of MV in
  clustering results, we analysed the missing
  values distribution in different public sets of
  Saccharomyces cerevisiae and we studied the
  effects of MV on HC. We finally compared the KNN
  replacement method with the most frequently used
  zero approach.
• 2 - Materials and Methods
• We used the following microarray datasets from
  Saccharomyces cerevisiae Ogawa et al. 6,
  Spellman et al. 7, Ferrea et al. 8 and Gasch
  et al. 9. To study the incidence of the
  presence of MV in microarray experiments, the
  genes containing MV were removed from the
  original datasets and different subsets were
  selected from the resulting set. For example, the
  treatment of Ogawa published data gave a set of
  5783 genes, which led to six subsets of 827, 968,
  1159, 1448, 1929 and 2892 genes. For each subset,
  we introduced randomly MV with a rate e (1.0 to
  50.0). Hierarchical Clustering was then
  performed with seven metrics (average, centroid,
  complete, mcquitty, median, single and ward using
  hclust from R software) and compared with the HC
  results obtained with the corresponding original
  subsets containing no MV.
•  
• For the 5783 genes set and subsets containing no
  MV we defined C clusters from the HC trees
  (figure 1). We then compared the consistency of
  these C clusters with the corresponding trees
  computed with MV (100 distinct simulations have
  been done for each e value). The number of
  clusters C is function of the metric used. C must
  be defined to give at least ten clusters
  representing 80 of the whole genes.
•  
• In a second step, we used the KNN and zero
  methods to replace the MV and performed HC on the
  resulting sets.

• Evaluation of the KNN replacement method
• Table 2 Presentation of the optimal k values
  obtained
• from Ogawa sets.
•  
• We observed that the optimal k values were lower
  in small subsets
• than in sets with higher number of genes. The
  error rate decreased
• with high number of genes.
• Figure 3 Comparison of real and KNN predicted
• values distribution
•