Graph-Based Semisupervised Learning Action Set

The labelSpread action implements the graph-based semisupervised learning algorithm that relies on label propagation (Zhou et al. 2003). The semisupervised learning algorithm has numerous applications, including web page classification, image recognition, medical imaging, natural language processing, and action recognition.

The labelSpread action uses the well-known radial basis function (RBF) kernel metric to compute distances. Because the value of the RBF kernel decreases with distance and ranges between zero and one, it has good interpretation as a similarity measure between the pairs of unlabeled and labeled data observations. The labelSpread action stores the predicted output for the target variables for both the unlabeled data and the labeled data in the output data table that is specified by the output parameter. For each row in the output data table, the WARN column indicates whether the row of data is coming from labeled data or unlabeled data. The WARN value is 1 for labeled data and 0 for unlabeled data.

Following Chang et al. (2010), the distance metric in the labelSpread action is defined as

where D is the RBF kernel distance metric, K is the total number of variables in the data, k is the feature index for the input observation, is the inverse of the variance for the Gaussian kernels, and p and q represent the index of the data in the combined input from both the unlabeled data and the labeled data.

Because in most cases the labeled data are relatively small, the labelSpread action distributes the unlabeled data and repeats the labeled data in different threads in order to maximize the prediction performance. For each thread, the distance matrix computes the pairwise distance in the combined list of unlabeled data and labeled data. If there are M observations for the unlabeled data and N observations for the labeled data in one thread, the distance matrix is of the size M+N in that thread.