We start with $k_0$ individual hidden layer units, and sequentially combine clusters with the minimum *error sum of squares (ESS)*, which is given by $$\begin{aligned}
ESS \equiv \sum_m \Bigl( \sum_{k: u_k\in C_m} \|v_k\|^2 -\frac{1}{|C_m|}\Bigl\|\sum_{k: u_k\in C_m} v_k\Bigr\|^2 \Bigr), 
\label{eq:ESS}\end{aligned}$$ where $u_k$ and $v_k$, respectively, are the $k$-th hidden layer unit ($k=1, \cdots , k_0$) and its corresponding feature vector, $C_m$ is the unit set assigned to the $m$-th cluster, and $|\cdot |$ represents the cluster size. From Equation (\[eq:ESS\]), the ESS is the value given by first computing the cluster size ($|C_m|$) times the variance of the feature vectors in each cluster, and then by taking the sum of all these values for all the clusters. When combining a pair of clusters $(C_{m_1}, C_{m_2})$ into one cluster, the ESS increases by $$\begin{aligned}
\Delta ESS &=&
\frac{|C_{m_1}||C_{m_2}|}{|C_{m_1}|+|C_{m_2}|}\Bigl\|\frac{1}{|C_{m_1}|}\sum_{k: u_k\in C_{m_1}} v_k-\frac{1}{|C_{m_2}|}\sum_{k: u_k\in C_{m_2}} v_k\Bigr\|^2. 
\label{eq:deltaESS}\end{aligned}$$ Therefore, in each iteration, we do not have to compute the error sum of squares for all the clusters, instead we simply have to compute the error increase $\Delta ESS$ given by Equation (\[eq:deltaESS\]) for all the pairs of current clusters $(C_{m_1}, C_{m_2})$, find the optimal pair of clusters that achieves the minimum error increase, and combine 