César A. Astudillo

Topology-oriented self-organizing maps: a survey

Abstract The self-organizing map (SOM) is a prominent neural network model that has found wide application in a spectrum of domains. Accordingly, it has received widespread attention both from the communities of researchers and practitioners. As a result, several variations of the basic architecture have been devised, specifically in the early years of the SOM’s evolution, which were introduced so as to address various architectural shortcomings or to explore other structures of the basic model. The overall goal of this survey is to present a comprehensive comparison of these networks, in terms of their primitive components and properties. We dichotomize these schemes as being either tree based or non-tree based. We have embarked on this venture with the hope that since the survey is comprehensive and the bibliography extensive, it will be an asset and resource for future researchers.

Imposing tree-based topologies onto self organizing maps

Accepted version of an article from the journal Information Sciences. Definitive published version available on Elsevier Science Direct: http://dx.doi.org/10.1016/j.ins.2011.04.038

The multiple team formation problem using sociometry

The Team Formation problem (TFP) has become a well-known problem in the OR literature over the last few years. In this problem, the allocation of multiple individuals that match a required set of skills as a group must be chosen to maximise one or several social positive attributes.Specifically, the aim of the current research is two-fold. First, two new dimensions of the TFP are added by considering multiple projects and fractions of peoples dedication. This new problem is named the Multiple Team Formation Problem (MTFP).Second, an optimisation model consisting in a quadratic objective function, linear constraints and integer variables is proposed for the problem. The optimisation model is solved by three algorithms: a Constraint Programming approach provided by a commercial solver, a Local Search heuristic and a Variable Neighbourhood Search metaheuristic. These three algorithms constitute the first attempt to solve the MTFP, being a variable neighbourhood local search metaheuristic the most efficient in almost all cases.Applications of this problem commonly appear in real-life situations, particularly with the current and ongoing development of social network analysis. Therefore, this work opens multiple paths for future research. HighlightsOptimisation of human resource allocation in multiple simultaneous projects.Time-fraction allocations are now allowed.Comparison of CP, LS and VNS algorithm performance.Proposal of multiple options for future research.

On Using Adaptive Binary Search Trees to Enhance Self Organizing Maps

We present a strategy by which a Self-Organizing Map (SOM) with an underlying Binary Search Tree (BST) structure can be adaptively re-structured using conditional rotations. These rotations on the nodes of the tree are local and are performed in constant time , guaranteeing a decrease in the Weighted Path Length (WPL) of the entire tree. As a result, the algorithm, referred to as the Tree-based Topology-Oriented SOM with Conditional Rotations (TTO-CONROT), converges in such a manner that the neurons are ultimately placed in the input space so as to represent its stochastic distribution, and additionally, the neighborhood properties of the neurons suit the best BST that represents the data.

Evaluating different families of prediction methods for estimating software project outcomes

We compare classifiers using AUC when predicting software project outcome.Attribute selection using Information Gain improves our classifiers performance.Statistical and ensemble classifiers are robust for predicting project outcome.Random Forest is the most appropriate technique for determining project outcome.Best prediction is achieved with team dynamics, process, and estimation attributes. Software has been developed since the 1960s but the success rate of development projects is still low. Classification models have been used to predict defects and effort estimation, but little work has been done to predict the outcome of these projects. Previous research shows that it is possible to predict outcome using classifiers based on key variables during development, but it is not clear which techniques provide more accurate predictions. We benchmark classifiers from different families to determine the outcome of a software project and identify variables that influence it. A survey-based empirical investigation was used to examine variables contributing to project outcome. Classification models were built and tested to identify the best classifiers for this data by comparing their AUC values. We reduce the dimensionality of the data with Information Gain and build models with the same techniques. We use Information Gain and classification techniques to identify key attributes and their relative importance. We find that four classification techniques provide good results for survey data, regardless of dimensionality reduction. We conclude that Random Forest is the most appropriate technique for predicting project outcome. We identified key attributes which are related to communication, estimation, and process review.

Self-organizing maps whose topologies can be learned with adaptive binary search trees using conditional rotations

Numerous variants of Self-Organizing Maps (SOMs) have been proposed in the literature, including those which also possess an underlying structure, and in some cases, this structure itself can be defined by the user. Although the concepts of growing the SOM and updating it have been studied, the whole issue of using a self-organizing Adaptive Data Structure (ADS) to further enhance the properties of the underlying SOM, has been unexplored. In an earlier work, we impose an arbitrary, user-defined, tree-like topology onto the codebooks, which consequently enforced a neighborhood phenomenon and the so-called tree-based Bubble of Activity (BoA). In this paper, we consider how the underlying tree itself can be rendered dynamic and adaptively transformed. To do this, we present methods by which a SOM with an underlying Binary Search Tree (BST) structure can be adaptively re-structured using Conditional Rotations (CONROT). These rotations on the nodes of the tree are local, can be done in constant time, and performed so as to decrease the Weighted Path Length (WPL) of the entire tree. In doing this, we introduce the pioneering concept referred to as Neural Promotion, where neurons gain prominence in the Neural Network (NN) as their significance increases. We are not aware of any research which deals with the issue of Neural Promotion. The advantage of such a scheme is that the user need not be aware of any of the topological peculiarities of the stochastic data distribution. Rather, the algorithm, referred to as the TTOSOM with Conditional Rotations (TTOCONROT), converges in such a manner that the neurons are ultimately placed in the input space so as to represent its stochastic distribution, and additionally, the neighborhood properties of the neurons suit the best BST that represents the data. These properties have been confirmed by our experimental results on a variety of data sets. We submit that all these concepts are both novel and of a pioneering sort. HighlightsWe merge the concepts of Adaptive Data Structures and Self-Organizing Maps.This new scheme enhances the capabilities of a Tree-based SOM, i.e., the TTOSOM.We attempt to preserve the topology and simultaneously find the Optimal Search Tree.We adapt a tree using the SOMs update rule.Simultaneously, we adapt a BST using rotations that are performed conditionally.

A Novel Self Organizing Map Which Utilizes Imposed Tree-Based Topologies

In this paper we propose a strategy, the Tree-based Topology-Oriented SOM (TTO-SOM) by which we can impose an arbitrary, user-defined, tree-like topology onto the codebooks. Such an imposition enforces a neighborhood phenomenon which is based on the user-defined tree, and consequently renders the so-called bubble of activity to be drastically different from the ones defined in the prior literature. The map learnt as a consequence of training with the TTO-SOM is able to infer both the distribution of the data and its structured topology interpreted via the perspective of the user-defined tree. The TTO-SOM also reveals multi-resolution capabilities, which are helpful for representing the original data set with different numbers of points, whithout the necessity of recomputing the whole tree. The ability to extract an skeleton, which is a “stick-like” representation of the image in a lower dimensional space, is discussed as well. These properties have been confirmed by our experimental results on a variety of data sets.

Assessing Wheat Traits by Spectral Reflectance: Do We Really Need to Focus on Predicted Trait-Values or Directly Identify the Elite Genotypes Group?

Phenotyping, via remote and proximal sensing techniques, of the agronomic and physiological traits associated with yield potential and drought adaptation could contribute to improvements in breeding programs. In the present study, 384 genotypes of wheat (Triticum aestivum L.) were tested under fully irrigated (FI) and water stress (WS) conditions. The following traits were evaluated and assessed via spectral reflectance: Grain yield (GY), spikes per square meter (SM2), kernels per spike (KPS), thousand-kernel weight (TKW), chlorophyll content (SPAD), stem water soluble carbohydrate concentration and content (WSC and WSCC, respectively), carbon isotope discrimination (Δ13C), and leaf area index (LAI). The performances of spectral reflectance indices (SRIs), four regression algorithms (PCR, PLSR, ridge regression RR, and SVR), and three classification methods (PCA-LDA, PLS-DA, and kNN) were evaluated for the prediction of each trait. For the classification approaches, two classes were established for each trait: The lower 80% of the trait variability range (Class 1) and the remaining 20% (Class 2 or elite genotypes). Both the SRIs and regression methods performed better when data from FI and WS were combined. The traits that were best estimated by SRIs and regression methods were GY and Δ13C. For most traits and conditions, the estimations provided by RR and SVR were the same, or better than, those provided by the SRIs. PLS-DA showed the best performance among the categorical methods and, unlike the SRI and regression models, most traits were relatively well-classified within a specific hydric condition (FI or WS), proving that classification approach is an effective tool to be explored in future studies related to genotype selection.

Metric Space Searching Based on Random Bisectors and Binary Fingerprints

We present a novel index for approximate searching in metric spaces based on random bisectors and binary fingerprints. The aim is to deal with scenarios where the main memory available is small. The method was tested on synthetic and real-world metric spaces. Our results show that our scheme outperforms the standard permutant-based index in scenarios where memory is scarce.

Fast BMU Search in SOMs Using Random Hyperplane Trees

One of the most prominent Neural Networks (NNs) reported in the literature is the Kohonen’s Self-Organizing Map (SOM). In spite of all its desirable capabilities and the scores of reported applications, it, unfortunately, possesses some fundamental drawbacks. Two of these handicaps are the quality of the map learned and the time required to train it. The most demanding phase of the algorithm involves determining the so-called Best Matching Unit (BMU), which requires time that is proportional to the number of neurons in the NN. The focus of this paper is to reduce the time needed for this tedious task, and to attempt to obtain an approximation of the BMU is as little as logarithmic time. To achieve this, we depend heavily on the work of [3,6], where the authors focused on how to accurately learn the data distribution connecting the neurons on a self-organizing tree, and how the learning algorithm, called the Tree-based Topology-Oriented SOM (TTOSOM), can be useful for data clustering [3,6] and classification [5]. We briefly state how we intend to reduce the training time for identifying the BMU efficiently. First, we show how a novel hyperplane-based partitioning scheme can be used to accelerate the task. Unlike the existing hyperplane-based partitioning methods reported in the literature, our algorithm can avoid ill-conditioned scenarios. It is also capable of considering data points that are dynamic. We demonstrate how these hyperplanes can be recursively defined, represented and computed, so as to recursively divide the hyper-space into two halves. As far as we know, the use of random hyperplanes to identify the BMU is both pioneering and novel.