

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

## 4.3 Learning The Neighborhood

Our final experiments test the ability of L1 regularization of the random field to learn the neighborhood. We firstly considered the motion capture data and used the DRILL with a large neighborhood size of 20 and L1 regularization on the parameters. As we varied the regularization coefficient we found a maximum under the GP-LVM score
(figure 8(a)). The visualization associated with this maximum is shown in figure 8(b) this may be compared with figure 4(c) which used 6 neighbors. Finally we investigated whether L1 regularization alone could recover a reasonable representation of the data. We again considered the motion capture data but initialized all points as neighbors. We then applied L1 regularization to learn a neighborhood structure. Again a maximum under the GP-LVM score was found (figure 9(a)) and the visualization associated with this maximum is shown figure 9(b).

The structural learning prior was able to improve the model fitted with 20 neighbors considerably until its performance was similar to that of the the six neighbor model shown in figure 4(c). However, L1 regularization alone was not able to obtain such a good performance, and was unable to tease out the starting position from the rest of the run in the final visualization. It appears that structural learning using L1-priors for sparsity is not on its own enough to find an appropriate neighborhood structure for this data set.

## 5 Discussion And Conclusions

We have introduced a new perspective on dimensionality reduction algorithms based around maximum entropy.

Our starting point was the maximum variance unfolding and our end point was a novel approach to dimensionality