Using participant-votes data, it is possible to predict future votes as follows:
- Use a tensor to store participant-votes data, one slice per positive/negative/pass votes.
- Use modified tensor decomposition such as CP to derive latent matrices, as follows:
- When updating the elements of the latent matrices, evaluate their fitness using a weight matrix. The weight elements should be
- 1 when the observation is present in the same place in participant-votes data
- 0 when the observation is missing (i.e. link to be predicted)
- At the end of the update, the latent matrices would be optimized with respect to the missing observations.
- When updating the elements of the latent matrices, evaluate their fitness using a weight matrix. The weight elements should be
- Recover the tensor from the latent matrices.
- The values in the missing observations contain the predicted links, if any.
Code:
- Julia lang:
- Python, with TensorLy:
Bibliography:
- Gao, Sheng, Ludovic Denoyer, and Patrick Gallinari. "Link pattern prediction with tensor decomposition in multirelational networks." In 2011 IEEE Symposium on Computational Intelligence and Data Mining (CIDM), pp. 333-340. IEEE, 2011.
While the above method works, it updates the full latent matrices every time. This is computentionally expensive, when only some elements/row/columns of some slice are updated.
For example, this is the case when a participant submits one new vote on some statement. This vote changes one element in one of the slices (positive/negative/pass), but might change future link predictions for that participant. We would like to have a way to make partial updates to the latent matrices, without recalculating them from scratch.
This is possible by implementing the SCED algorithm of Zhou et al, together with the generic method above.
Bibliography:
- Zhou, Shuo, Sarah M. Erfani, and James Bailey. “Sced: A general framework for sparse tensor decomposition with constraints and elementwise dynamic learning.” In 2017 IEEE International Conference on Data Mining (ICDM), pp. 675-684. IEEE, 2017.
- Zhou, Shuo. “On dynamic tensor decompositions.” PhD diss., 2019.