

![0_image_0.png](0_image_0.png)

Figure 5: The weighting learned by Algorithm 4 using all five kernels and diagonal Wp. Each bar plot contains the diagonal of the corresponding kernel's learned metric. The horizontal axis corresponds the index of the training set, and the vertical axis corresponds to the learned weight in each kernel space.

## 5.2.4 Graph Processing Results

To evaluate the effects of processing the constraint set for consistency and redundancy, we repeat the experiment of the previous section with different levels of processing applied to C. Here, we focus on the Biography kernel, since it exhibits the largest gap in performance between the native and learned spaces.

As a baseline, we first consider the full set of similarity measurements as provided by human judgements, including all inconsistencies. In the 80-20 split, there are 7915 total training measurements. To first deal with what appear to be the most eggregious inconsistencies, we prune all directly inconsistent training measurements; *i.e.*, whenever (**i, j, i, k**) and (**i, k, i, j**) both appear, both are removed.3 This variation results in 6583 training measurements, and while they are not wholly consistent, the worst violators have been pruned. Finally, we consider the fully processed case by finding a maximal consistent subset (partial order) of C and removing all redundancies, resulting in a partial order with 4401 measurements.

Using each of these variants of the training set, we test the embedding algorithm with both diagonal and full-matrix formulations. The results are presented in Table 5. Each level of graph processing results in a small improvement in the accuracy of the learned space, and provides substantial reductions in computational overhead at each step of the optimization procedure for Algorithm 3.