Centrality measures in network analysis

There are four measures of centrality that are widely used in network analysis: degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality. Google's PageRank is a variant of the eigenvector centrality measure.

Dirichlet prior for smoothing

Using Dirichlet distribution as the prior for smoothing in statistical language modeling leads to additive smoothing (a.k.a. Lidstone smoothing) that includes Laplace smoothing (i.e., add one) and Jeffreys-Perks smoothing (i.e., add half) (a.k.a. Expected Likelihood Estimation) as special cases. This family of smoothing methods can be regarded as a document dependent extension of linear interpolated smoothing.

It has been shown that Laplace smoothing, though most popular (in textbooks), is often inferior to Lidstone smoothing (using a value less than one) in modeling natural language data, e.g., for text classification tasks (see Athena: Mining-based interactive management of text databases).

PyMat

PyMat exposes the MATLAB engine interface allowing Python programs to start, close, and communicate with a MATLAB engine session. In addition, the package allows transferring matrices to and from an MATLAB workspace. These matrices can be specified as NumPy arrays, allowing a blend between the mathematical capabilities of NumPy and those of MATLAB.

Global Ranking

Global Ranking looks a promising direction in the research area of Learning to Rank for Information Retrieval.

[1] Global Ranking Using Continuous Conditional Random Fields
[2] Global Ranking by Exploiting User Clicks

PyLucene

PyLucene is a Python extension that allows the usage of Lucene's text indexing and searching capabilities from Python.