An Improved Pearson’s Correlation Proximity-Based Hierarchical Clustering for Mining Biological Association between Genes

Algorithm 1

Hierarchical clustering algorithm to measure the similar gene expression pattern.

Begin

Input gene expression dataset, threshold 𝛿

Let the gene expression data be represented as vectors

𝑉_𝑖={𝑣_𝑖,𝑗 ∣ where 𝑗 lies between 1 and f}

Let the Expression Matrix be EM = (𝑅, 𝐶) and 𝑤_𝑖,𝑗 be the log ratio factor

Let 𝑣_𝑖 and 𝑣_𝑗 be two gene values and vector, 𝑣^′_𝑖 and 𝑣^′_𝑗

Let 𝜇_𝑣𝑖 and 𝜇_𝑣𝑗 be average values for two vectors 𝑣^′_𝑖 and 𝑣^′_𝑗,

Measure the proximity level using

Σ=1 (𝑣_𝑖dim−𝜇_𝑣𝑖) (𝑣_𝑗dim−𝜇_𝑣𝑗)/√ 𝑣_𝑖dim−𝜇_𝑣𝑖√ 𝑣_𝑗dim−𝜇_𝑣𝑗

For 𝑅={𝑟₁,…,𝑟_𝑛}

 Form the expression patterns for rows

For 𝐶={𝑐₁,…,𝑐_𝑛}

  Form the expression profiles of samples

  Obtain log ratio factor 𝑤_𝑖,𝑗

End for

End for

If (𝑊_𝑖,𝑗<𝛿) Similarity gene expression patterns are obtained

Else If (𝑊_𝑖,𝑗>𝛿) Similarity gene expression patterns are not obtained

End