18,921 research outputs found
On morphological hierarchical representations for image processing and spatial data clustering
Hierarchical data representations in the context of classi cation and data
clustering were put forward during the fties. Recently, hierarchical image
representations have gained renewed interest for segmentation purposes. In this
paper, we briefly survey fundamental results on hierarchical clustering and
then detail recent paradigms developed for the hierarchical representation of
images in the framework of mathematical morphology: constrained connectivity
and ultrametric watersheds. Constrained connectivity can be viewed as a way to
constrain an initial hierarchy in such a way that a set of desired constraints
are satis ed. The framework of ultrametric watersheds provides a generic scheme
for computing any hierarchical connected clustering, in particular when such a
hierarchy is constrained. The suitability of this framework for solving
practical problems is illustrated with applications in remote sensing
Graph ambiguity
In this paper, we propose a rigorous way to define the concept of ambiguity in the domain of graphs. In past studies, the classical definition of ambiguity has been derived starting from fuzzy set and fuzzy information theories. Our aim is to show that also in the domain of the graphs it is possible to derive a formulation able to capture the same semantic and mathematical concept. To strengthen the theoretical results, we discuss the application of the graph ambiguity concept to the graph classification setting, conceiving a new kind of inexact graph matching procedure. The results prove that the graph ambiguity concept is a characterizing and discriminative property of graphs. (C) 2013 Elsevier B.V. All rights reserved
Convex Graph Invariant Relaxations For Graph Edit Distance
The edit distance between two graphs is a widely used measure of similarity
that evaluates the smallest number of vertex and edge deletions/insertions
required to transform one graph to another. It is NP-hard to compute in
general, and a large number of heuristics have been proposed for approximating
this quantity. With few exceptions, these methods generally provide upper
bounds on the edit distance between two graphs. In this paper, we propose a new
family of computationally tractable convex relaxations for obtaining lower
bounds on graph edit distance. These relaxations can be tailored to the
structural properties of the particular graphs via convex graph invariants.
Specific examples that we highlight in this paper include constraints on the
graph spectrum as well as (tractable approximations of) the stability number
and the maximum-cut values of graphs. We prove under suitable conditions that
our relaxations are tight (i.e., exactly compute the graph edit distance) when
one of the graphs consists of few eigenvalues. We also validate the utility of
our framework on synthetic problems as well as real applications involving
molecular structure comparison problems in chemistry.Comment: 27 pages, 7 figure
FlashProfile: A Framework for Synthesizing Data Profiles
We address the problem of learning a syntactic profile for a collection of
strings, i.e. a set of regex-like patterns that succinctly describe the
syntactic variations in the strings. Real-world datasets, typically curated
from multiple sources, often contain data in various syntactic formats. Thus,
any data processing task is preceded by the critical step of data format
identification. However, manual inspection of data to identify the different
formats is infeasible in standard big-data scenarios.
Prior techniques are restricted to a small set of pre-defined patterns (e.g.
digits, letters, words, etc.), and provide no control over granularity of
profiles. We define syntactic profiling as a problem of clustering strings
based on syntactic similarity, followed by identifying patterns that succinctly
describe each cluster. We present a technique for synthesizing such profiles
over a given language of patterns, that also allows for interactive refinement
by requesting a desired number of clusters.
Using a state-of-the-art inductive synthesis framework, PROSE, we have
implemented our technique as FlashProfile. Across tasks over large
real datasets, we observe a median profiling time of only s.
Furthermore, we show that access to syntactic profiles may allow for more
accurate synthesis of programs, i.e. using fewer examples, in
programming-by-example (PBE) workflows such as FlashFill.Comment: 28 pages, SPLASH (OOPSLA) 201
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