Effectiveness of landmark analysis for establishing locality in p2p networks

Locality to other nodes on a peer-to-peer overlay network can be established by means of a set of landmarks shared among the participating nodes. Each node independently collects a set of latency measures to landmark nodes, which are used as a multi-dimensional feature vector. Each peer node uses the feature vector to generate a unique scalar index which is correlated to its topological locality. A popular dimensionality reduction technique is the space filling Hilbert’s curve, as it possesses good locality preserving properties. However, there exists little comparison between Hilbert’s curve and other techniques for dimensionality reduction. This work carries out a quantitative analysis of their properties. Linear and non-linear techniques for scaling the landmark vectors to a single dimension are investigated. Hilbert’s curve, Sammon’s mapping and Principal Component Analysis have been used to generate a 1d space with locality preserving properties. This work provides empirical evidence to support the use of Hilbert’s curve in the context of locality preservation when generating peer identifiers by means of landmark vector analysis. A comparative analysis is carried out with an artificial 2d network model and with a realistic network topology model with a typical power-law distribution of node connectivity in the Internet. Nearest neighbour analysis confirms Hilbert’s curve to be very effective in both artificial and realistic network topologies. Nevertheless, the results in the realistic network model show that there is scope for improvements and better techniques to preserve locality information are required

Index Information Algorithm with Local Tuning for Solving Multidimensional Global Optimization Problems with Multiextremal Constraints

Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust nonconvex subregions are considered. Both the objective function and the constraints may be partially defined. To solve such problems an algorithm is proposed, that uses Peano space-filling curves and the index scheme to reduce the original problem to a H\"{o}lder one-dimensional one. Local tuning on the behaviour of the objective function and constraints is used during the work of the global optimization procedure in order to accelerate the search. The method neither uses penalty coefficients nor additional variables. Convergence conditions are established. Numerical experiments confirm the good performance of the technique.Comment: 29 pages, 5 figure

Deterministic global optimization using space-filling curves and multiple estimates of Lipschitz and Holder constants

In this paper, the global optimization problem $\min_{y\in S} F(y)$ with $S$ being a hyperinterval in $\Re^N$ and $F(y)$ satisfying the Lipschitz condition with an unknown Lipschitz constant is considered. It is supposed that the function $F(y)$ can be multiextremal, non-differentiable, and given as a `black-box'. To attack the problem, a new global optimization algorithm based on the following two ideas is proposed and studied both theoretically and numerically. First, the new algorithm uses numerical approximations to space-filling curves to reduce the original Lipschitz multi-dimensional problem to a univariate one satisfying the H\"{o}lder condition. Second, the algorithm at each iteration applies a new geometric technique working with a number of possible H\"{o}lder constants chosen from a set of values varying from zero to infinity showing so that ideas introduced in a popular DIRECT method can be used in the H\"{o}lder global optimization. Convergence conditions of the resulting deterministic global optimization method are established. Numerical experiments carried out on several hundreds of test functions show quite a promising performance of the new algorithm in comparison with its direct competitors.Comment: 26 pages, 10 figures, 4 table

Binääridatan visualisointi

Tässä opinnäytetyössä tarkastellaan visualisoinnin käyttöä takaisinmallinnuksen työkaluna. Takaisinmallinnuksessa käsitellään usein suuria määriä tietoa, jota on vaikea ymmärtää ilman abstraktiota. Työssä todetaan, että eri visualisointien avulla voidaan tunnistaa tietorakenteita tuntemattomasta datasta tehokkaasti. Jotkin visualisoinnin keinot todetaan toimivan eri tunnis-tamisen osa-alueissa paremmin kuin toiset

Generating alphaalpha -dense curves in non-convex sets to solve a class of non-smooth constrained global optimization

This paper deals with the dimensionality reduction approach to study multi-dimensional constrained global optimization problems where the objective function is non-differentiable over a general compact set $D$ of $mathbb{R}^{n}$ and H"{o}lderian. The fundamental principle is to provide explicitly a parametric representation $x_{i}=ell _{i}(t),1leq ileq n$ of $alpha$-dense curve $ell_{alpha }$ in the compact $D$, for $t$ in an interval $mathbb{I}$ of $mathbb{R}$, which allows to convert the initial problem to a one dimensional H"{o}lder unconstrained one. Thus, we can solve the problem by using an efficient algorithm available in the case of functions depending on a single variable. A relation between the parameter $alpha$ of the curve $ell _{alpha }$ and the accuracy of attaining the optimal solution is given. Some concrete $alpha$ dense curves in a non-convex feasible region $D$ are constructed. The numerical results show that the proposed approach is efficient.</p

Local and deep texture features for classification of natural and biomedical images

Developing efficient feature descriptors is very important in many computer vision applications including biomedical image analysis. In the past two decades and before the popularity of deep learning approaches in image classification, texture features proved to be very effective to capture the gradient variation in the image. Following the success of the Local Binary Pattern (LBP) descriptor, many variations of this descriptor were introduced to further improve the ability of obtaining good classification results. However, the problem of image classification gets more complicated when the number of images increases as well as the number of classes. In this case, more robust approaches must be used to address this problem. In this thesis, we address the problem of analyzing biomedical images by using a combination of local and deep features. First, we propose a novel descriptor that is based on the motif Peano scan concept called Joint Motif Labels (JML). After that, we combine the features extracted from the JML descriptor with two other descriptors called Rotation Invariant Co-occurrence among Local Binary Patterns (RIC-LBP) and Joint Adaptive Medina Binary Patterns (JAMBP). In addition, we construct another descriptor called Motif Patterns encoded by RIC-LBP and use it in our classification framework. We enrich the performance of our framework by combining these local descriptors with features extracted from a pre-trained deep network called VGG-19. Hence, the 4096 features of the Fully Connected 'fc7' layer are extracted and combined with the proposed local descriptors. Finally, we show that Random Forests (RF) classifier can be used to obtain superior performance in the field of biomedical image analysis. Testing was performed on two standard biomedical datasets and another three standard texture datasets. Results show that our framework can beat state-of-the-art accuracy on the biomedical image analysis and the combination of local features produce promising results on the standard texture datasets.Includes bibliographical reference