Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing methods work only for data with structures that are not self-intersected, which is quite restrictive for real applications. A few methods can overcome the above...

Belief Propagation (BP) is a message-passing algorithm that computes the exact marginal distributions at every vertex of a graphical model without cycles. While BP is designed to work correctly on trees, it is routinely applied to general graphical models that may contain cycles, in which case neither convergence, nor correctness in the case of convergence is guaranteed. Nonetheless, BP gained ...

This paper is concerned with power-weighted weight functionals associated with a minimal graph spanning a random sample of n points from a general multivariate Lebesgue density f over [0, 1]. It is known that under broad conditions, when the functional applies power exponent γ ∈ (1, d) to the graph edge lengths, the log of the functional normalized by n(d−γ)/d is a strongly consistent estimator...

The development and refinement of natural-language communication systems among networked individuals is not well understood and difficult to study. This paper uses a task providing a controlled environment for the goal-oriented, collaborative exchange of short, natural-language messages between experimental participants (20 per group) in order to demonstrate lexical convergence. A technique for...

Search-based optimization methods have been used for software engineering activities such as software testing. In the field of software testing, search-based test data generation refers to application of meta-heuristic optimization methods to generate test data that cover the code space of a program. Automatic test data generation that can cover all the paths of software is known as a major cha...

We propose an accelerated path-following iterative shrinkage thresholding algorithm (APISTA) for solving high dimensional sparse nonconvex learning problems. The main difference between APISTA and the path-following iterative shrinkage thresholding algorithm (PISTA) is that APISTA exploits an additional coordinate descent subroutine to boost the computational performance. Such a modification, t...

For subdivision surfaces, it is important to characterize local shape near flat spots and points where the surface is not twice continuously differentiable. Applying general principles derived in [PR0x], this paper characterizes shape near such points for the subdivision schemes devised by Catmull and Clark and by Loop. For generic input data, both schemes fail to converge to the hyperbolic or ...

We study the phenomenon that regularly spaced subsequences of the control points in subdivision may converge to scalar multiples of the same limit function, even though subdivision itself is divergent. We present different sets of easily checkable sufficient conditions for this phenomenon (which we term subsequence convergence) to occur, study the basic properties of subsequence convergence, sh...

We study the problem of finding the maximum of a function defined on the nodes of a connected graph. The goal is to identify a node where the function obtains its maximum. We focus on local iterative algorithms, which traverse the nodes of the graph along a path, and the next iterate is chosen from the neighbors of the current iterate with probability distribution determined by the function val...

How can we approximate sparse graphs and sequences of sparse graphs (with average degree unbounded and o(n))? We consider convergence in the first k moments of the graph spectrum (equivalent to the numbers of closed k-walks) appropriately normalized. We introduce a simple, easy to sample, random graph model that captures the limiting spectra of many sequences of interest, including the sequence...