Having obtained the initial cluster centroids, passing them to the k-means algorithm allows us to obtain the centroids corresponding to each production route. When new yield data, Y, needs to be assigned a cluster (production route), we simply identify the nearest centroid for each member in Y, thus assigning that member to the corresponding cluster.

The process is as follows:

Prediction data Y:

Where each row of Y represents the yields of the various outputs for a given day’s production data. These rows can be viewed as points in a high-dimensional space. To classify each point, we calculate its distance to all centroids; the point is then assigned to the cluster associated with the nearest centroid.

Training data cluster centroid, C:

Cluster assignments for data points in Y, Yc:

yc_i=t,t=pmin(dis(Y_i,C_t))

Where yc_i represents the cluster label assigned to the i-th data point Y_i in Y, and C_t is the centroid of the t-th cluster.

SPL routine:

Calculation result example:

Predicted data Y:

Centroid C:

Cluster assignments for members in Y, Yc: