Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A unified framework for harmonic analysis of functions on directed
  graphs and changing data   We present a general framework for studying harmonic analysis of functions in
the settings of various emerging problems in the theory of diffusion geometry.
The starting point of the now classical diffusion geometry approach is the
construction of a kernel whose discretization leads to an undirected graph
structure on an unstructured data set. We study the question of constructing
such kernels for directed graph structures, and argue that our construction is
essentially the only way to do so using discretizations of kernels. We then use
our previous theory to develop harmonic analysis based on the singular value
decomposition of the resulting non-self-adjoint operators associated with the
directed graph. Next, we consider the question of how functions defined on one
space evolves to another space in the paradigm of changing data sets recently
introduced by Coifman and Hirn. While the approach of Coifman and Hirn require
that the points on one space should be in a known one-to-one correspondence
with the points on the other, our approach allows the identification of only a
subset of landmark points. We introduce a new definition of distance between
points on two spaces, construct localized kernels based on the two spaces and
certain interaction parameters, and study the evolution of smoothness of a
function on one space to its lifting to the other space via the landmarks. We
develop novel mathematical tools that enable us to study these seemingly
different problems in a unified manner.

9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn