Just minutes before writing this post, I was lazily browsing on Amazon.com. My attention was called to a module titled “New For You,” where it was suggested that I buy “Fundamentals of Matrix Computations” by David S. Watkins. Boring, sure. Certainly a bit drab for my then current mood. But there was some sense to their suggestion. Sure, in the past, I have surfed for my share of obscure linear algebra books, even purchased a couple. So although the underlying black-box of algorithms that generated the recommendation is hidden, I know the wisdom of the crowds powers its results. Particularly, a technology called Collaborative Filtering (CF).
(Google Images)
Now when I first began researching CF (back when I was young and beautiful), it made immediate sense that consumers with similar histories and like ratings on things could somehow be collected into neighborhoods of similarity and that those neighborhoods could be used as proxies for consumer recommendations. That we can exploit the browsing or purchasing behavior of the collective to help individuals discover new things they will like, is somehow intuitive.
It was around that time that I stumbled upon a paper called Influence in Ratings-Based Recommender Systems, that uncovered a fundamental insight: If we were to define a measure as to the effect that one consumer has on another’s recommendation, based on the CF algorithm, we could determine the implied influence that one user has on another (of course, granted that our predictions are correct). Now if we were to do this for the whole network of consumers, we would effectively be generating an influence network (or influence graph), in which the nodes are consumers and the edges represent the direction and the strength of the influence (for more on social graphs, see my previous post). This is incredibly interesting! But we are left with a question: Why does this work?
There are some interesting properties about real-world networks worth noting:
- Small-world – networks have small characteristic path lengths, ensuring that any two nodes are reachable in few hops (6-degrees of separation).
- Clustered – a high degree of “cliqueness”. My friends tend to be friends with each other (we refer to this as redundancy).
- Scale-free – number of connections for nodes follows a (heavy-tailed) or power-law distribution.
Without going too deep into these ideas, the properties above ensure that when it comes to real-world networks, we are able to:
- Predict and Compress – prediction and compression are the same in this regard. If we understand the probabilistic distribution and redundancy of node linkages, we are able to tightly compress the network (see information theory). Low entropy implies a high predictability, so the two features are tightly related.
- **Pattern Storage – in this regard networks act like associative memories, they are able to store patterns (or memories) through the topology of interconnections between nodes (like a neural network). Thanks to Manny Aparicio at Saffron Technology for this insight!
When we look at the Sociocast Hypergraph, its multi-relational nature allows us to store the myriad of ways in which people influence each other. We extrapolate and infer these connections between people, based on their behaviors (their movements through ideas, topics, and concepts) and explicitly through their social relationships online. Our model allows us to build a network that mimics the real network, to the extent that it stores the same memories. Memories, for us, are the opinions people have for (ranking) and the associations (relationships) they have between things.
The underlying structure of real-world networks, and their natural redundancy, give us an incredible predictor of individual behaviors.
We will expound on this, with empirical evidence, in our forthcoming whitepaper.
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