image. This cluster mainly affects the recognition result for “5” and “6.” Cluster $8$ uses the input information of the area with the shape of a $9$, however, its main recognition target is “2.” Cluster $9$ correlates positively with the area extending from the upper right to the lower left of an image, and it correlates negatively with the digits “4” and “9.”

- Cluster $8$ consists of two smaller clusters, $17$ and $18$. Cluster $17$ is mainly affected by the upper part and lower right part of an image, and the absolute value of its correlations with output dimensions are all less than $0.2$, while the role of Cluster $18$ is almost the same as that of Cluster $8$.

![Representative input-output mappings of extracted clusters. []{data-label="fig:mnist_roles"}](mnist_input_data_samples.png){width="70mm"}

\[fig:mnist\_samples\] ![Representative input-output mappings of extracted clusters. []{data-label="fig:mnist_roles"}](mnist_align_lnn.png "fig:"){width="110mm"}

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Experiment Using the Consumer Price Index Data Set {#sec:food}
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We also applied the proposed method to an LNN trained with a data set of a consumer price index[@estat] to predict the consumer price indices of taro, radish and carrot for a month from $36$ months’ input data. With this data set, we plotted the results for $c=3,6,12$, where 