arXiv subjects

Srinivas Nambirajan

Publications and source records attributed to Srinivas Nambirajan.

3 recordsLinked to original sources

arXiv2026

Tracking and Predicting Evolution of Social Communities

We develop an algorithmic framework for studying the evolution of communities in social networks. We begin with the theoretical foundation, from which we conclude that an evolution is at most as strong as its weakest link. This allows us to formulate an efficient algorithm to identify all evolutionary sequences in a dynamic social network. We use this algorithm to empirically study community evolution in several large social networks, to identify those features of the early stages of a community that indicate whether a community is going to be shortlived or not. Our results show that it is possible to correlate the lifespan of a community to structural parameters of its early evolution; these conclusions are robust across all the social networks we have investigated.

cs.SI↗

arXiv2026

Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds

Markovian Whittle-Matérn fields have been convergently approximated by discrete Gauss Markov Random Fields (GMRFs) with sparse precision matrices using a Finite Element approximation of the two-parameter family, \[ (κ^2 - Δ)^{α/2} u = \mathcal{W}, \;\; κ\in \mathbb{R}, \; α\in \mathbb{N}. \] of SPDEs. Using recent developements in the analysis of Discrete Exterior Calculus (DEC), we present a different, yet closely related, convergent GMRF approximation to these Matérn fields over complete, boundaryless Riemannian manifolds discretized as well-centered simplicial complexes. This convergent method (i) is agnostic to $α, κ$ and thus allows a universal approximation scheme for the precision and covariance matrices of the entire $(α, κ)$-family of GMRFs, so they may be inferred rather than guessed. (ii) inherently models pointwise and piecewise-smoothed measurements of a random field and approximates both equally well (iii) is computationally independent of the interpolants used - it suffers no overhead if one convergent interpolant were replaced with another suitable interpolant over the same mesh. Furthermore, we show that, on discretizations that are well-connected in a precise sense, and volume-concentrated, the precision matrices are spectral functions of a graph-laplacian. We provide a low rank approximator to the family of such Matérn GMRFs and mention a use case: reducing the number of measurements needed to model the GMRF by compressed-sensing.

math.NA↗

arXiv2013

Identifying Influential Entries in a Matrix

For any matrix A in R^(m x n) of rank ρ, we present a probability distribution over the entries of A (the element-wise leverage scores of equation (2)) that reveals the most influential entries in the matrix. From a theoretical perspective, we prove that sampling at most s = O ((m + n) ρ^2 ln (m + n)) entries of the matrix (see eqn. (3) for the precise value of s) with respect to these scores and solving the nuclear norm minimization problem on the sampled entries, reconstructs A exactly. To the best of our knowledge, these are the strongest theoretical guarantees on matrix completion without any incoherence assumptions on the matrix A. From an experimental perspective, we show that entries corresponding to high element-wise leverage scores reveal structural properties of the data matrix that are of interest to domain scientists.

math.NA↗