Figure 10

An illustration of the DistBoost algorithm. At each boosting round t the weak learner is trained using weighted input points and some equivalence constraints. In the example above, points 1, 2 and 5, 6 are negatively constrained (belong to different classes) and points 3, 4 and 4, 7 are positively constrained (belong to the same class). All other pairs of points (e.g. 8, 9 and 1, 4) are unconstrained. The constrained EM algorithm is used to learn a GMM (step (1)). This GMM is then used to generate a "weak" distance function (step (2)) that assigns a value in [0, 1] to each pair of points. The distance function is assigned a hypothesis weight (steps (3–4)) which corresponds to its success in satisfying the current weighted constraints. The weights of the equivalence constraints are updated (steps (5–6)) – increasing the weights of constraints that were unsatisfied by the current weak learner. Finally, the weights on pairs are translated to weights on data points (step (7)). In the example above, the distance between the negatively constrained points 1, 2 is small (0.1) and therefore the weight of this constraint will be enhanced.