"modeling" entries

Graphs in the world: Modeling systems as networks

See, extract, and create value with networks.


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Networks of all kinds drive the modern world. You can build a network from nearly any kind of data set, which is probably why network structures characterize some aspects of most phenomenon. And yet, many people can’t see the networks underlying different systems. In this post, we’re going to survey a series of networks that model different systems in order to understand different ways networks help us understand the world around us.

We’ll explore how to see, extract, and create value with networks. We’ll look at four examples where I used networks to model different phenomenon, starting with startup ecosystems and ending in network-driven marketing.

Networks and markets

Commerce is one person or company selling to another, which is inherently a network phenomenon. Analyzing networks in markets can help us understand how market economies operate.

Strength of weak ties

Mark Granoveter famously researched job hunting and discovered the Strength of Weak Ties. Read more…

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The tensor renaissance in data science

The O'Reilly Data Show Podcast: Anima Anandkumar on tensor decomposition techniques for machine learning.


After sitting in on UC Irvine Professor Anima Anandkumar’s Strata + Hadoop World 2015 in San Jose presentationI wrote a post urging the data community to build tensor decomposition libraries for data science. The feedback I’ve gotten from readers has been extremely positive. During the latest episode of the O’Reilly Data Show Podcast, I sat down with Anandkumar to talk about tensor decomposition, machine learning, and the data science program at UC Irvine.

Modeling higher-order relationships

The natural question is: why use tensors when (large) matrices can already be challenging to work with? Proponents are quick to point out that tensors can model more complex relationships. Anandkumar explains:

Tensors are higher order generalizations of matrices. While matrices are two-dimensional arrays consisting of rows and columns, tensors are now multi-dimensional arrays. … For instance, you can picture tensors as a three-dimensional cube. In fact, I have here on my desk a Rubik’s Cube, and sometimes I use it to get a better understanding when I think about tensors.  … One of the biggest use of tensors is for representing higher order relationships. … If you want to only represent pair-wise relationships, say co-occurrence of every pair of words in a set of documents, then a matrix suffices. On the other hand, if you want to learn the probability of a range of triplets of words, then we need a tensor to record such relationships. These kinds of higher order relationships are not only important for text, but also, say, for social network analysis. You want to learn not only about who is immediate friends with whom, but, say, who is friends of friends of friends of someone, and so on. Tensors, as a whole, can represent much richer data structures than matrices.

Read more…