Semi-supervised random decision forests for machine learning using mahalanobis distance to identify geodesic paths

A machine learning process comprising:

• accessing, using a processor, a plurality of labeled observations each labeled observation having a label indicating one of a plurality of classes that the labeled observation is a member of, at least one of the plurality of labeled observations and the at least one label corresponding to the at least one of the plurality of labeled observations being machine generated;
• accessing a plurality of unlabeled observations which are unlabeled in that, for each unlabeled observation, it is not known to which one of the plurality of classes the unlabeled observation belongs;
• training a plurality of random decision trees to form a semi-supervised random decision forest using both the labeled observations and the unlabeled observations and according to a training objective which optimizes an information gain comprising an unsupervised term and a supervised term, training the plurality of random decision trees comprising:
• assigning labels and certainties of those labels to the unlabeled observations by giving unlabeled observations the labels of close labeled observations where close labeled observations are selected on the basis of clusters of labeled and unlabeled observations generated by the plurality of random decision trees;
• and
• identifying geodesic paths between the unlabeled observations and the close labeled observations, the paths being determined using at least one Mahalanobis distance.

A machine learning system comprising:

• an input, the input comprising at least one processor, arranged to receive a plurality of labeled observations each labeled observation having a label indicating one of a plurality of classes that the labeled observation is a member of;
• the input also arranged to access a plurality of unlabeled observations which are unlabeled in that, for each unlabeled observation, it is not known to which one of the plurality of classes the unlabeled observation belongs;
• a training engine arranged to train a plurality of random decision trees to form a semi-supervised random decision forest using both the labeled observations and the unlabeled observations such that each random decision tree partitions the labeled and the unlabeled observations into clusters according to similarity of the observations and according to the labels;
• a transducer arranged to assign labels and certainties of those labels to the unlabeled observations by giving unlabeled observations the labels of close labeled observations where close labeled observations are selected on the basis of the clusters;
• the transducer being further arranged to discourage geodesic paths between labeled points and unlabeled points from cutting across regions of low data density using at least one Mahalanobis distance;
• and
• an active learning module arranged to use the assigned labels and certainties to identify regions in a data space from which the observations are drawn and to train the semi-supervised random decision forest using new observations drawn from the identified regions.