413,770 research outputs found
Global optimization algorithms for image registration and clustering
Global optimization is a classical problem of finding the minimum or maximum value of an objective function. It has applications in many areas, such as biological image analysis, chemistry, mechanical engineering, financial analysis, deep learning and image processing. For practical applications, it is important to understand the efficiency of global optimization algorithms. This dissertation develops and analyzes some new global optimization algorithms and applies them to practical problems, mainly for image registration and data clustering.
First, the dissertation presents a new global optimization algorithm which approximates the optimum using only function values. The basic idea is to use the points at which the function has been evaluated to decompose the domain into a collection of hyper-rectangles. At each step of the algorithm, it chooses a hyper-rectangle according to a certain criterion and the next function evaluation is at the center of the hyper-rectangle. The dissertation includes a proof that the algorithm converges to the global optimum as the number of function evaluations goes to infinity, and also establishes the convergence rate. Standard test functions are used to experimentally evaluate the algorithm.
The second part focuses on applying algorithms from the first part to solve some practical problems. Image processing tasks often require optimizing over some set of parameters. In the image registration problem, one attempts to determine the best transformation for aligning similar images. Such problems typically require minimizing a dissimilarity measure with multiple local minima. The dissertation describes a global optimization algorithm and applies it to the problem of identifying the best transformation for aligning two images.
Global optimization algorithms can also be applied to the data clustering problem. The basic purpose of clustering is to categorize data into different groups by their similarity. The objective cost functions for clustering usually are non-convex. -means is a popular algorithm which can find local optima quickly but may not obtain global optima. The different starting points for -means can output different local optima. This dissertation describes a global optimization algorithm for approximating the global minimum of the clustering problem.
The third part of the dissertation presents variations of the proposed algorithm that work with different assumptions on the available information, including a version that uses derivatives
XML Matchers: approaches and challenges
Schema Matching, i.e. the process of discovering semantic correspondences
between concepts adopted in different data source schemas, has been a key topic
in Database and Artificial Intelligence research areas for many years. In the
past, it was largely investigated especially for classical database models
(e.g., E/R schemas, relational databases, etc.). However, in the latest years,
the widespread adoption of XML in the most disparate application fields pushed
a growing number of researchers to design XML-specific Schema Matching
approaches, called XML Matchers, aiming at finding semantic matchings between
concepts defined in DTDs and XSDs. XML Matchers do not just take well-known
techniques originally designed for other data models and apply them on
DTDs/XSDs, but they exploit specific XML features (e.g., the hierarchical
structure of a DTD/XSD) to improve the performance of the Schema Matching
process. The design of XML Matchers is currently a well-established research
area. The main goal of this paper is to provide a detailed description and
classification of XML Matchers. We first describe to what extent the
specificities of DTDs/XSDs impact on the Schema Matching task. Then we
introduce a template, called XML Matcher Template, that describes the main
components of an XML Matcher, their role and behavior. We illustrate how each
of these components has been implemented in some popular XML Matchers. We
consider our XML Matcher Template as the baseline for objectively comparing
approaches that, at first glance, might appear as unrelated. The introduction
of this template can be useful in the design of future XML Matchers. Finally,
we analyze commercial tools implementing XML Matchers and introduce two
challenging issues strictly related to this topic, namely XML source clustering
and uncertainty management in XML Matchers.Comment: 34 pages, 8 tables, 7 figure
Similarity Learning for Provably Accurate Sparse Linear Classification
In recent years, the crucial importance of metrics in machine learning
algorithms has led to an increasing interest for optimizing distance and
similarity functions. Most of the state of the art focus on learning
Mahalanobis distances (requiring to fulfill a constraint of positive
semi-definiteness) for use in a local k-NN algorithm. However, no theoretical
link is established between the learned metrics and their performance in
classification. In this paper, we make use of the formal framework of good
similarities introduced by Balcan et al. to design an algorithm for learning a
non PSD linear similarity optimized in a nonlinear feature space, which is then
used to build a global linear classifier. We show that our approach has uniform
stability and derive a generalization bound on the classification error.
Experiments performed on various datasets confirm the effectiveness of our
approach compared to state-of-the-art methods and provide evidence that (i) it
is fast, (ii) robust to overfitting and (iii) produces very sparse classifiers.Comment: Appears in Proceedings of the 29th International Conference on
Machine Learning (ICML 2012
- …