Today recommender systems are the work horse behind every eCommerce portal - Amazon, Netflix, iTunes, Flipkart, Jabong. Each of these sell hundreds of thousands of items; they cannot expect the users to sift through all the items to find what they like. These portals need to automatically suggest relevant items to users if they want to keep an edge in the cyber world. The algorithms that are used for such recommender systems are termed as Collaborative Filtering.

There are two approaches to this. The first one is simple and intuitive. The algorithm finds out similar users and items, and recommends objects based on similarity to the user. The second approach is mathematically more complex - it is based on the latent factor model. Here it is assumed that the user's preference on an item is determined by his / her affinity towards certain characteristics of the item's possession of those characteristics. Although abstract, latent factor models are powerful and yields significant improvement over the simpler similarity based approach.

Traditionally, the latent factor model was solved using a matrix factorization approach - which although computationally efficient, is a non-convex problem. Recently the latent factor model was further abstracted into a low-rank matrix completion problem. This leads to a convex formulation but computationally challenging.

Collaborative filtering requires solving for a partially sampled choices matrix. On one direction are the users and the other constitutes the items. Some of the choices are known (ratings, buying patter, browsing history etc.); if this matrix is completely known, our problem is solved. Only highly preferred items will be suggested for each user.

Basically this is an interpolation problem, where the task is to complete this matrix. This matrix is low-rank - following from the latent factor model.

At this Lab, we work on various matrix completion algorithms. How to make these algorithms efficient and computationally less demanding?

We are also looking at new models for collaborative filtering where we can incorporate prior knowledge about the users and items from the available metadata. For example, how to improve the prediction by using age, occupation, demography or gender information? How to increase variations in user's choices while predicting new items?

We are looking for industrial partners in this area. Please contact us if interested.