A self–stabilizing algorithm for finding weighted centroid in trees

In this paper we present some modification of the Blair and Manne algorithm for finding the center of a tree network in the distributed, self-stabilizing environment. Their algorithm finds n/2 -separator of a tree. Our algorithm finds weighted centroid, which is direct generalization of the former one for tree networks with positive weights on nodes. Time complexity of both algorithms is O(n2), where n is the number of nodes in the network

Local feature weighting in nearest prototype classification

The distance metric is the corner stone of nearest neighbor (NN)-based methods, and therefore, of nearest prototype (NP) algorithms. That is because they classify depending on the similarity of the data. When the data is characterized by a set of features which may contribute to the classification task in different levels, feature weighting or selection is required, sometimes in a local sense. However, local weighting is typically restricted to NN approaches. In this paper, we introduce local feature weighting (LFW) in NP classification. LFW provides each prototype its own weight vector, opposite to typical global weighting methods found in the NP literature, where all the prototypes share the same one. Providing each prototype its own weight vector has a novel effect in the borders of the Voronoi regions generated: They become nonlinear. We have integrated LFW with a previously developed evolutionary nearest prototype classifier (ENPC). The experiments performed both in artificial and real data sets demonstrate that the resulting algorithm that we call LFW in nearest prototype classification (LFW-NPC) avoids overfitting on training data in domains where the features may have different contribution to the classification task in different areas of the feature space. This generalization capability is also reflected in automatically obtaining an accurate and reduced set of prototypes.Publicad

Evolutionary design of nearest prototype classifiers

In pattern classification problems, many works have been carried out with the aim of designing good classifiers from different perspectives. These works achieve very good results in many domains. However, in general they are very dependent on some crucial parameters involved in the design. These parameters have to be found by a trial and error process or by some automatic methods, like heuristic search and genetic algorithms, that strongly decrease the performance of the method. For instance, in nearest prototype approaches, main parameters are the number of prototypes to use, the initial set, and a smoothing parameter. In this work, an evolutionary approach based on Nearest Prototype Classifier (ENPC) is introduced where no parameters are involved, thus overcoming all the problems that classical methods have in tuning and searching for the appropiate values. The algorithm is based on the evolution of a set of prototypes that can execute several operators in order to increase their quality in a local sense, and with a high classification accuracy emerging for the whole classifier. This new approach has been tested using four different classical domains, including such artificial distributions as spiral and uniform distibuted data sets, the Iris Data Set and an application domain about diabetes. In all the cases, the experiments show successfull results, not only in the classification accuracy, but also in the number and distribution of the prototypes achieved.Publicad

An overview of the main machine learning models - from theory to algorithms

Dissertation presented as the partial requirement for obtaining a Master's degree in Data Science and Advanced AnalyticsIn the context of solving highly complex problems, Artificial Intelligence shows an exponential growth over the past years allowing the Machine Learning to augment and sometimes to outperform the human learning. From driverless cars to automatic recommendation on Netflix, we are surrounded by AI, even if we do not notice it. Furthermore, companies have recently adopted new frameworks in their routines which are mainly composed by algorithms able to solve complex problems in a short period of time. The growth of AI technologies has been absolutely stunning and yes, it is only possible because a sub-field of AI called Machine Learning is growing even faster. In a small scale, Machine Learning may be seen as a simple system able to find patterns on data and learn from it. However, it is precisely that learning process that in a large scale will allow machines to mimic the human behavior and perform tasks that would eventually require human intelligence. Just for us to have an idea, according to Forbes the global Machine Learning market was evaluated in $1.7B in 2017 and it is expected to reach almost$21B in 2024. Naturally, Machine Learning has become an attractive and profitable scientific area that demands continuous learning since there is always something new being discovered. During the last decades, a huge number of algorithms have been proposed by the research community, which sometimes may cause some confusion of how and when to use each one of them. That is exactly what is pretended in this thesis, over the next chapters we are going to review the main Machine Learning models and their respective advantages/disadvantages

Machine Learning

Machine Learning can be defined in various ways related to a scientific domain concerned with the design and development of theoretical and implementation tools that allow building systems with some Human Like intelligent behavior. Machine learning addresses more specifically the ability to improve automatically through experience

Safe sets, network majority on weighted trees

Let G = (V, E) be a graph and let w : V → ℝ>0 be a positive weight function on the vertices of G. For every subset X of V, let w(X) ≔ ∑v∈Gw(v). A non-empty subset ∑ is a weighted safe set if, for every component C of the subgraph induced by S and every component D of G/S, we have w(C) ≥ w(D) whenever there is an edge between C and D. If the subgraph G(S) induced by a weighted safe set S is connected, then the set S is called a weighted connected safe set. In this article, we show that the problem of computing the minimum weight of a safe set is NP-hard for trees, even if the underlying tree is restricted to be a star, but it is polynomially solvable for paths. We also give an O(n log n) time 2-approximation algorithm for finding a weighted connected safe set with minimum weight in a weighted tree. Then, as a generalization of the concept of a minimum safe set, we define the concept of a parameterized infinite family of proper central subgraphs on weighted trees, whose polar ends are the vertex set of the tree and the centroid points. We show that each of these central subgraphs includes a centroid point. © 2017 Wiley Periodicals, Inc

Data-based melody generation through multi-objective evolutionary computation

Genetic-based composition algorithms are able to explore an immense space of possibilities, but the main difficulty has always been the implementation of the selection process. In this work, sets of melodies are utilized for training a machine learning approach to compute fitness, based on different metrics. The fitness of a candidate is provided by combining the metrics, but their values can range through different orders of magnitude and evolve in different ways, which makes it hard to combine these criteria. In order to solve this problem, a multi-objective fitness approach is proposed, in which the best individuals are those in the Pareto front of the multi-dimensional fitness space. Melodic trees are also proposed as a data structure for chromosomic representation of melodies and genetic operators are adapted to them. Some experiments have been carried out using a graphical interface prototype that allows one to explore the creative capabilities of the proposed system. An Online Supplement is provided and can be accessed at http://dx.doi.org/10.1080/17459737.2016.1188171, where the reader can find some technical details, information about the data used, generated melodies, and additional information about the developed prototype and its performance.This work was supported by the Spanish Ministerio de Educación, Cultura y Deporte [FPU fellowship AP2012-0939]; and the Spanish Ministerio de Economía y Competitividad project TIMuL supported by UE FEDER funds [No. TIN2013–48152–C2–1–R]

Continual learning from stationary and non-stationary data

Continual learning aims at developing models that are capable of working on constantly evolving problems over a long-time horizon. In such environments, we can distinguish three essential aspects of training and maintaining machine learning models - incorporating new knowledge, retaining it and reacting to changes. Each of them poses its own challenges, constituting a compound problem with multiple goals. Remembering previously incorporated concepts is the main property of a model that is required when dealing with stationary distributions. In non-stationary environments, models should be capable of selectively forgetting outdated decision boundaries and adapting to new concepts. Finally, a significant difficulty can be found in combining these two abilities within a single learning algorithm, since, in such scenarios, we have to balance remembering and forgetting instead of focusing only on one aspect. The presented dissertation addressed these problems in an exploratory way. Its main goal was to grasp the continual learning paradigm as a whole, analyze its different branches and tackle identified issues covering various aspects of learning from sequentially incoming data. By doing so, this work not only filled several gaps in the current continual learning research but also emphasized the complexity and diversity of challenges existing in this domain. Comprehensive experiments conducted for all of the presented contributions have demonstrated their effectiveness and substantiated the validity of the stated claims

Center location problems on tree graphs with subtree-shaped customers

We consider the p-center problem on tree graphs where the customers are modeled as continua subtrees. We address unweighted and weighted models as well as distances with and without addends. We prove that a relatively simple modification of Handler’s classical linear time algorithms for unweighted 1- and 2-center problems with respect to point customers, linearly solves the unweighted 1- and 2-center problems with addends of the above subtree customer model. We also develop polynomial time algorithms for the p-center problems based on solving covering problems and searching over special domains