Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral Clustering, Spanning Forest, and Bayesian Forest Process   Spectral clustering algorithms are very popular. Starting from a pairwise
similarity matrix, spectral clustering gives a partition of data that
approximately minimizes the total similarity scores across clusters. Since
there is no need to model how data are distributed within each cluster, such a
method enjoys algorithmic simplicity and robustness in clustering non-Gaussian
data such as those near manifolds. Nevertheless, several important questions
are unaddressed, such as how to estimate the similarity scores and cluster
assignment probabilities, as important uncertainty estimates in clustering. In
this article, we propose to solve these problems with a discovered generative
modeling counterpart. Our clustering model is based on a spanning forest graph
that consists of several disjoint spanning trees, with each tree corresponding
to a cluster. Taking a Bayesian approach, we assign proper densities on the
root and leaf nodes, and we prove that the posterior mode is almost the same as
spectral clustering estimates. Further, we show that the associated generative
process, named "forest process", is a continuous extension to the classic urn
process, hence inheriting many nice properties such as having unbounded support
for the number of clusters and being amenable to existing partition probability
function; at the same time, we carefully characterize their differences. We
demonstrate a novel application in joint clustering of multiple-subject
functional magnetic resonance imaging scans of the human brain.

31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph