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I try to understand the step 2.5 of the DCCA clustering algorithm pasted below. The original reference is here and the PowerPoint presentation is here. I have the following questions:

  • Do we perform step 2.5 for each variable (gene) in the dataset?
  • What exactly is $AVGC_{pk}$ and what exactly $AVGC_{qk}$

The algorithm goes as follows.

  1. Initially, consider all the genes in one cluster. Set number of cluster $K = 1$.
  2. For each iteration, do:

    2.1 For each cluster $C_p$ calculate Pearson correlation coefficient between all pairs of genes in $C_p$.

    2.2 If no repulsion (if correlation between two variables is negative then there is repulsion between variables) exists between a pair of genes inside any cluster then STOP, otherwise perform Step 2.3.

    2.3 Identify a cluster $C$ for which a pair of genes $x_i, x_j$ have the most negative repulsion value among all the clusters.

    2.4 Replace cluster $C$ with two clusters $C_p$ and $C_q$, and increase number of clusters $K$ by one. Place gene $x_i$ to $C_p$ and $x_j$ to $C_q$. For all the other genes $x_k$ in $C$, compare $Cor(x_i, x_k)$ and $Cor(x_j, x_k)$. If $Cor(x_i, x_k) > Cor(x_j, x_k)$ then place $x_k$ to $C_p$, otherwise place $x_k$ to $C_q$.

    2.5 For each $x_k$ in $X$, do:

    a) For each cluster $C_p$, $1 \leq p \leq K$, calculate average correlation value $AVGC_{pk}$.

    b) If $AVGC_{pk} > AVGC_{qk}$, for each $q$, $1 \leq q \leq K$, and $p \neq q$ then place a copy of $x_k$ to new $p$ cluster $CNEW_p$.

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