The scoring function is trained on a small set of manually aligned graphs using the averaged perceptron algorithm.

In order to learn the parameter vector w, we use the averaged version of the perceptron algorithm (Freund and Schapire, 1999; Collins, 2002).

The pseudocode for the learning algorithm is shown in Table l. After training the perceptron , these 32 student answers are removed from the dataset, not used as training further along in the pipeline, and are not included in the final results.

In addition, the student answers used to train the perceptron are removed from the pipeline after the perceptron training stage.

Following the same line of work in the textual entailment world are (Raina et al., 2005), (MacCartney et al., 2006), (de Marneffe et al., 2007), and (Chambers et al., 2007), which experiment variously with using diverse knowledge sources, using a perceptron to learn alignment decisions, and exploiting natural logic.

We independently test two components of our overall grading system: the node alignment detection scores found by training the perceptron , and the overall grades produced in the final stage.

5.1 Perceptron Alignment

However, as the perceptron is designed to minimize error rate, this may not reflect an optimal objective when seeking to detect matches.