797 research outputs found
Single molecule localization by constrained optimization
Single Molecule Localization Microscopy (SMLM) enables the acquisition of
high-resolution images by alternating between activation of a sparse subset of
fluorescent molecules present in a sample and localization. In this work, the
localization problem is formulated as a constrained sparse approximation
problem which is resolved by rewriting the pseudo-norm using an
auxiliary term. In the preliminary experiments with the simulated ISBI datasets
the algorithm yields as good results as the state-of-the-art in high-density
molecule localization algorithms.Comment: In Proceedings of iTWIST'18, Paper-ID: 13, Marseille, France,
November, 21-23, 201
Knapsack Problems with Side Constraints
The thesis considers a specific class of resource allocation problems in Combinatorial Optimization: the Knapsack Problems. These are paradigmatic NP-hard problems where a set of items with given profits and weights is available. The aim is to select a subset of the items in order to maximize the total profit without exceeding a known knapsack capacity. In the classical 0-1 Knapsack Problem (KP), each item can be picked at most once.
The focus of the thesis is on four generalizations of KP involving side constraints beyond the capacity bound. More precisely, we provide solution approaches and insights for the following problems: The Knapsack Problem with Setups; the Collapsing Knapsack Problem; the Penalized Knapsack Problem; the Incremental Knapsack Problem.
These problems reveal challenging research topics with many real-life applications. The scientific contributions we provide are both from a theoretical and a practical perspective. On the one hand, we give insights into structural elements and properties of the problems and derive a series of approximation results for some of them. On the other hand, we offer valuable solution approaches for direct applications of practical interest or when the problems considered arise as sub-problems in broader contexts
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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (âefficientâ) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find âquicklyâ (reasonable run-times), with âhighâ probability, provable âgoodâ solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
Top-k Multiclass SVM
Class ambiguity is typical in image classification problems with a large
number of classes. When classes are difficult to discriminate, it makes sense
to allow k guesses and evaluate classifiers based on the top-k error instead of
the standard zero-one loss. We propose top-k multiclass SVM as a direct method
to optimize for top-k performance. Our generalization of the well-known
multiclass SVM is based on a tight convex upper bound of the top-k error. We
propose a fast optimization scheme based on an efficient projection onto the
top-k simplex, which is of its own interest. Experiments on five datasets show
consistent improvements in top-k accuracy compared to various baselines.Comment: NIPS 201
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