$c$ is the number of clusters. Figures \[fig:food\_align\_lnn\] and \[fig:food\_roles\], respectively, show the hierarchical cluster structure extracted from the trained LNN and the roles or representative input-output mappings of the extracted clusters. From these figures, we can gain knowledge about the LNN structure as follows.

- Clusters $1$, $2$ and $3$ represent the main input-output function of the hidden layer units. Interestingly, all of these clusters have similar correlations with the output dimensions ($0<$ radish $<$ taro $<$ carrot). However, these three clusters use different input information: Cluster $1$ strongly reflects seasonal information, and its correlation is especially high with the consumer price indices of the three vegetables one month before and one, two and three years earlier. Cluster $3$ also reflects seasonal information, however, the absolute values of the correlations are less than $0.3$ and it correlates strongly with the input information of eight, $20$ and $32$ months before. On the other hand, Cluster $2$ does not use such a seasonal effect very much, and it is affected almost equally by the information of all months, except the recent information of radish from nine months before.

- Cluster $1$ is composed of smaller clusters of $16$ and $17$. Cluster 