Pollutant concentrations and Meteorological data classification by Neural Networks

This paper present an environmental contingency forecasting tool based on Neural Networks (NN). Forecasting tool analyzes every hour and daily Sulphur Dioxide (SO2) concentrations and Meteorological data time series. Pollutant concentrations and meteorological variables are self-organized applying a Self-organizing Map (SOM) NN in different classes. Classes are used in training phase of a General Regression Neural Network (GRNN) classifier to provide an air quality forecast. In this case a time series set obtained from Environmental Monitoring Network (EMN) of the city of Salamanca, Guanajuato, México is used. Results verify the potential of this method versus other statistical classification methods and also variables correlation is solved.

Multi-dimensional classification using Bayesian networks for stationary and evolving streaming data

Hoy en día, con la evolución continua y rápida de las tecnologías de la información y los dispositivos de computación, se recogen y almacenan continuamente grandes volúmenes de datos en distintos dominios y a través de diversas aplicaciones del mundo real. La extracción de conocimiento útil de una cantidad tan enorme de datos no se puede realizar habitualmente de forma manual, y requiere el uso de técnicas adecuadas de aprendizaje automático y de minería de datos. La clasificación es una de las técnicas más importantes que ha sido aplicada con éxito a varias áreas. En general, la clasificación se compone de dos pasos principales: en primer lugar, aprender un modelo de clasificación o clasificador a partir de un conjunto de datos de entrenamiento, y en segundo lugar, clasificar las nuevas instancias de datos utilizando el clasificador aprendido. La clasificación es supervisada cuando todas las etiquetas están presentes en los datos de entrenamiento (es decir, datos completamente etiquetados), semi-supervisada cuando sólo algunas etiquetas son conocidas (es decir, datos parcialmente etiquetados), y no supervisada cuando todas las etiquetas están ausentes en los datos de entrenamiento (es decir, datos no etiquetados). Además, aparte de esta taxonomía, el problema de clasificación se puede categorizar en unidimensional o multidimensional en función del número de variables clase, una o más, respectivamente; o también puede ser categorizado en estacionario o cambiante con el tiempo en función de las características de los datos y de la tasa de cambio subyacente. A lo largo de esta tesis, tratamos el problema de clasificación desde tres perspectivas diferentes, a saber, clasificación supervisada multidimensional estacionaria, clasificación semisupervisada unidimensional cambiante con el tiempo, y clasificación supervisada multidimensional cambiante con el tiempo. Para llevar a cabo esta tarea, hemos usado básicamente los clasificadores Bayesianos como modelos. La primera contribución, dirigiéndose al problema de clasificación supervisada multidimensional estacionaria, se compone de dos nuevos métodos de aprendizaje de clasificadores Bayesianos multidimensionales a partir de datos estacionarios. Los métodos se proponen desde dos puntos de vista diferentes. El primer método, denominado CB-MBC, se basa en una estrategia de envoltura de selección de variables que es voraz y hacia delante, mientras que el segundo, denominado MB-MBC, es una estrategia de filtrado de variables con una aproximación basada en restricciones y en el manto de Markov. Ambos métodos han sido aplicados a dos problemas reales importantes, a saber, la predicción de los inhibidores de la transcriptasa inversa y de la proteasa para el problema de infección por el virus de la inmunodeficiencia humana tipo 1 (HIV-1), y la predicción del European Quality of Life-5 Dimensions (EQ-5D) a partir de los cuestionarios de la enfermedad de Parkinson con 39 ítems (PDQ-39). El estudio experimental incluye comparaciones de CB-MBC y MB-MBC con los métodos del estado del arte de la clasificación multidimensional, así como con métodos comúnmente utilizados para resolver el problema de predicción de la enfermedad de Parkinson, a saber, la regresión logística multinomial, mínimos cuadrados ordinarios, y mínimas desviaciones absolutas censuradas. En ambas aplicaciones, los resultados han sido prometedores con respecto a la precisión de la clasificación, así como en relación al análisis de las estructuras gráficas que identifican interacciones conocidas y novedosas entre las variables. La segunda contribución, referida al problema de clasificación semi-supervisada unidimensional cambiante con el tiempo, consiste en un método nuevo (CPL-DS) para clasificar flujos de datos parcialmente etiquetados. Los flujos de datos difieren de los conjuntos de datos estacionarios en su proceso de generación muy rápido y en su aspecto de cambio de concepto. Es decir, los conceptos aprendidos y/o la distribución subyacente están probablemente cambiando y evolucionando en el tiempo, lo que hace que el modelo de clasificación actual sea obsoleto y deba ser actualizado. CPL-DS utiliza la divergencia de Kullback-Leibler y el método de bootstrapping para cuantificar y detectar tres tipos posibles de cambio: en las predictoras, en la a posteriori de la clase o en ambas. Después, si se detecta cualquier cambio, un nuevo modelo de clasificación se aprende usando el algoritmo EM; si no, el modelo de clasificación actual se mantiene sin modificaciones. CPL-DS es general, ya que puede ser aplicado a varios modelos de clasificación. Usando dos modelos diferentes, el clasificador naive Bayes y la regresión logística, CPL-DS se ha probado con flujos de datos sintéticos y también se ha aplicado al problema real de la detección de código malware, en el cual los nuevos ficheros recibidos deben ser continuamente clasificados en malware o goodware. Los resultados experimentales muestran que nuestro método es efectivo para la detección de diferentes tipos de cambio a partir de los flujos de datos parcialmente etiquetados y también tiene una buena precisión de la clasificación. Finalmente, la tercera contribución, sobre el problema de clasificación supervisada multidimensional cambiante con el tiempo, consiste en dos métodos adaptativos, a saber, Locally Adpative-MB-MBC (LA-MB-MBC) y Globally Adpative-MB-MBC (GA-MB-MBC). Ambos métodos monitorizan el cambio de concepto a lo largo del tiempo utilizando la log-verosimilitud media como métrica y el test de Page-Hinkley. Luego, si se detecta un cambio de concepto, LA-MB-MBC adapta el actual clasificador Bayesiano multidimensional localmente alrededor de cada nodo cambiado, mientras que GA-MB-MBC aprende un nuevo clasificador Bayesiano multidimensional. El estudio experimental realizado usando flujos de datos sintéticos multidimensionales indica los méritos de los métodos adaptativos propuestos. ABSTRACT Nowadays, with the ongoing and rapid evolution of information technology and computing devices, large volumes of data are continuously collected and stored in different domains and through various real-world applications. Extracting useful knowledge from such a huge amount of data usually cannot be performed manually, and requires the use of adequate machine learning and data mining techniques. Classification is one of the most important techniques that has been successfully applied to several areas. Roughly speaking, classification consists of two main steps: first, learn a classification model or classifier from an available training data, and secondly, classify the new incoming unseen data instances using the learned classifier. Classification is supervised when the whole class values are present in the training data (i.e., fully labeled data), semi-supervised when only some class values are known (i.e., partially labeled data), and unsupervised when the whole class values are missing in the training data (i.e., unlabeled data). In addition, besides this taxonomy, the classification problem can be categorized into uni-dimensional or multi-dimensional depending on the number of class variables, one or more, respectively; or can be also categorized into stationary or streaming depending on the characteristics of the data and the rate of change underlying it. Through this thesis, we deal with the classification problem under three different settings, namely, supervised multi-dimensional stationary classification, semi-supervised unidimensional streaming classification, and supervised multi-dimensional streaming classification. To accomplish this task, we basically used Bayesian network classifiers as models. The first contribution, addressing the supervised multi-dimensional stationary classification problem, consists of two new methods for learning multi-dimensional Bayesian network classifiers from stationary data. They are proposed from two different points of view. The first method, named CB-MBC, is based on a wrapper greedy forward selection approach, while the second one, named MB-MBC, is a filter constraint-based approach based on Markov blankets. Both methods are applied to two important real-world problems, namely, the prediction of the human immunodeficiency virus type 1 (HIV-1) reverse transcriptase and protease inhibitors, and the prediction of the European Quality of Life-5 Dimensions (EQ-5D) from 39-item Parkinson’s Disease Questionnaire (PDQ-39). The experimental study includes comparisons of CB-MBC and MB-MBC against state-of-the-art multi-dimensional classification methods, as well as against commonly used methods for solving the Parkinson’s disease prediction problem, namely, multinomial logistic regression, ordinary least squares, and censored least absolute deviations. For both considered case studies, results are promising in terms of classification accuracy as well as regarding the analysis of the learned MBC graphical structures identifying known and novel interactions among variables. The second contribution, addressing the semi-supervised uni-dimensional streaming classification problem, consists of a novel method (CPL-DS) for classifying partially labeled data streams. Data streams differ from the stationary data sets by their highly rapid generation process and their concept-drifting aspect. That is, the learned concepts and/or the underlying distribution are likely changing and evolving over time, which makes the current classification model out-of-date requiring to be updated. CPL-DS uses the Kullback-Leibler divergence and bootstrapping method to quantify and detect three possible kinds of drift: feature, conditional or dual. Then, if any occurs, a new classification model is learned using the expectation-maximization algorithm; otherwise, the current classification model is kept unchanged. CPL-DS is general as it can be applied to several classification models. Using two different models, namely, naive Bayes classifier and logistic regression, CPL-DS is tested with synthetic data streams and applied to the real-world problem of malware detection, where the new received files should be continuously classified into malware or goodware. Experimental results show that our approach is effective for detecting different kinds of drift from partially labeled data streams, as well as having a good classification performance. Finally, the third contribution, addressing the supervised multi-dimensional streaming classification problem, consists of two adaptive methods, namely, Locally Adaptive-MB-MBC (LA-MB-MBC) and Globally Adaptive-MB-MBC (GA-MB-MBC). Both methods monitor the concept drift over time using the average log-likelihood score and the Page-Hinkley test. Then, if a drift is detected, LA-MB-MBC adapts the current multi-dimensional Bayesian network classifier locally around each changed node, whereas GA-MB-MBC learns a new multi-dimensional Bayesian network classifier from scratch. Experimental study carried out using synthetic multi-dimensional data streams shows the merits of both proposed adaptive methods.

Supervised classification of minimally invasive surgery psychomotor competence based on instruments motion analysis

Background Objective assessment of psychomotor skills has become an important challenge in the training of minimally invasive surgical (MIS) techniques. Currently, no gold standard defining surgical competence exists for classifying residents according to their surgical skills. Supervised classification has been proposed as a means for objectively establishing competence thresholds in psychomotor skills evaluation. This report presents a study comparing three classification methods for establishing their validity in a set of tasks for basic skills’ assessment. Methods Linear discriminant analysis (LDA), support vector machines (SVM), and adaptive neuro-fuzzy inference systems (ANFIS) were used. A total of 42 participants, divided into an experienced group (4 expert surgeons and 14 residents with >10 laparoscopic surgeries performed) and a nonexperienced group (16 students and 8 residents with <10 laparoscopic surgeries performed), performed three box trainer tasks validated for assessment of MIS psychomotor skills. Instrument movements were captured using the TrEndo tracking system, and nine motion analysis parameters (MAPs) were analyzed. The performance of the classifiers was measured by leave-one-out cross-validation using the scores obtained by the participants. Results The mean accuracy performances of the classifiers were 71 % (LDA), 78.2 % (SVM), and 71.7 % (ANFIS). No statistically significant differences in the performance were identified between the classifiers. Conclusions The three proposed classifiers showed good performance in the discrimination of skills, especially when information from all MAPs and tasks combined were considered. A correlation between the surgeons’ previous experience and their execution of the tasks could be ascertained from results. However, misclassifications across all the classifiers could imply the existence of other factors influencing psychomotor competence.

Two Different Approaches of Feature Extraction for Classifying the EEG Signals

The focus of this chapter is to study feature extraction and pattern classification methods from two medical areas, Stabilometry and Electroencephalography (EEG). Stabilometry is the branch of medicine responsible for examining balance in human beings. Balance and dizziness disorders are probably two of the most common illnesses that physicians have to deal with. In Stabilometry, the key nuggets of information in a time series signal are concentrated within definite time periods are known as events. In this chapter, two feature extraction schemes have been developed to identify and characterise the events in Stabilometry and EEG signals. Based on these extracted features, an Adaptive Fuzzy Inference Neural network has been applied for classification of Stabilometry and EEG signals.

Modelización del registro y proceso de datos espectrales, referidos a superficies líticas, en un ámbito arqueológico.

La determinación del origen de un material utilizado por el hombre en la prehistoria es de suma importancia en el ámbito de la arqueología. En los últimos años, los estudios de procedencia han utilizado técnicas que suelen ser muy precisas pero con el inconveniente de ser metodologías de carácter destructivo. El fenómeno de la minería a gran escala es una de las características que acompaña al Neolítico, de ahí que la revolución correspondiente a este periodo sea una de las etapas más importantes para la humanidad. El yacimiento arqueológico de Casa Montero es una mina de sílex neolítica ubicada en la Península Ibérica, de gran importancia por su antigüedad y su escala productiva. Este sitio arqueológico corresponde a una cantera de explotación de rocas silícicas desarrollada en el periodo neolítico en la que solamente se han encontrado los desechos de la extracción minera, lo cual incrementa la variabilidad de las muestras analizadas, de las que se desconoce su contexto económico, social y cultural. Es de gran interés arqueológico saber por qué esos grupos neolíticos explotaban de forma tan intensiva determinados tipos de material y cuál era el destino de la cadena productiva del sílex. Además, por ser una excavación de rescate, que ha tenido que procesar varias toneladas de material, en un tiempo relativamente corto, requiere de métodos expeditivos de clasificación y manejo de dicho material. Sin embargo,la implementación de cualquier método de clasificación debe evitar la alteración o modificación de la muestra,ya que,estudios previos sobre caracterización de rocas silícicas tienen el inconveniente de alterar parcialmente el objeto de estudio. Por lo que el objetivo de esta investigación fue la modelización del registro y procesamiento de datos espectrales adquiridos de rocas silícicas del yacimiento arqueológico de Casa Montero. Se implementó la metodología para el registro y procesamiento de datos espectrales de materiales líticos dentro del contexto arqueológico. Lo anterior se ha conseguido con la aplicación de modelos de análisis espectral, algoritmos de suavizado de firmas espectrales, reducción de la dimensionalidad de las características y la aplicación de métodos de clasificación, tanto de carácter vectorial como raster. Para la mayoría de los procedimientos se ha desarrollado una aplicación informática validada tanto por los propios resultados obtenidos como comparativamente con otras aplicaciones. Los ensayos de evaluación de la metodología propuesta han permitido comprobar la eficacia de los métodos. Por lo que se concluye que la metodología propuesta no solo es útil para materiales silícicos, sino que se puede generalizar en aquellos procesos donde la caracterización espectral puede ser relevante para la clasificación de materiales que no deban ser alterados, además, permite aplicarla a gran escala, dado que los costes de ejecución son mínimos si se comparan con los de métodos convencionales. Así mismo, es de destacar que los métodos propuestos, representan la variabilidad del material y permiten relacionarla con el estado del yacimiento, según su contenido respecto de las tipologías de la cadena operativa. ABSTRACT: The determination of the origin of a material used by man in prehistory is very important in the field of archaeology. In recent years the provenance studies have used techniques that tend to be very precise but with the drawback of being destructive methodologies. The phenomenon of mining on a large scale is a feature that accompanies the Neolithic period; the Neolithic revolution is one of the most important periods of humanity. The archaeological site of Casa Montero is a Neolithic flint mine located in the Iberian Peninsula of great importance for its antiquity and its scale. This archaeological site corresponds to a quarry exploitation of silicic rocks developed in the Neolithic period, in which only found debris from mining, which increases the variability of the samples analyzed, including their economic, social and cultural context is unknown. It is of great archaeological interest to know why these Neolithic groups exploited as intensive certain types of material and what the final destination of flint was in the productive chain. In addition, being an excavation of rescue that had to process several tons of material in a relatively short time requires expeditious methods of classification and handling of the material. However, the implementation of any method of classification should avoid the alteration or modification of the sample, since previous studies on characterization of silicic rocks have the disadvantage of destroying or partially modify the object of study. So the objective of this research wasthe modeling of the registration and processing of acquired spectral data of silicic rocks of the archaeological site of Casa Montero. The methodology implemented for modeling the registration and processing of existing spectral data of lithic materials within the archaeological context, was presented as an alternative to the conventional classification methods (methods destructive and expensive) or subjective methods that depend on the experience of the expert. The above has been achieved with the implementation of spectral analysis models, smoothing of spectral signatures and the dimensionality reduction algorithms. Trials of validation of the proposed methodology allowed testing the effectiveness of the methods in what refers to the spectral characterization of siliceous materials of Casa Montero. Is remarkable the algorithmic contribution of the signal filtering, improve of quality and reduction of the dimensionality, as well the proposal of using raster structures for efficient storage and analysis of spectral information. For which it is concluded that the proposed methodology is not only useful for siliceous materials, but it can be generalized in those processes where spectral characterization may be relevant to the classification of materials that must not be altered, also allows to apply it on a large scale, given that the implementation costs are minimal when compared with conventional methods.

A survey of feature selection in Internet traffic characterization

In the last decade, the research community has focused on new classification methods that rely on statistical characteristics of Internet traffic, instead of pre-viously popular port-number-based or payload-based methods, which are under even bigger constrictions. Some research works based on statistical characteristics generated large fea-ture sets of Internet traffic; however, nowadays it?s impossible to handle hun-dreds of features in big data scenarios, only leading to unacceptable processing time and misleading classification results due to redundant and correlative data. As a consequence, a feature selection procedure is essential in the process of Internet traffic characterization. In this paper a survey of feature selection methods is presented: feature selection frameworks are introduced, and differ-ent categories of methods are briefly explained and compared; several proposals on feature selection in Internet traffic characterization are shown; finally, future application of feature selection to a concrete project is proposed.

Application of Decision Theory methods for a Community of Madrid Soil classification case

A land classification method was designed for the Community of Madrid (CM), which has lands suitable for either agriculture use or natural spaces. The process started from an extensive previous CM study that contains sets of land attributes with data for 122 types and a minimum-requirements method providing a land quality classification (SQ) for each land. Borrowing some tools from Operations Research (OR) and from Decision Science, that SQ has been complemented by an additive valuation method that involves a more restricted set of 13 representative attributes analysed using Attribute Valuation Functions to obtain a quality index, QI, and by an original composite method that uses a fuzzy set procedure to obtain a combined quality index, CQI, that contains relevant information from both the SQ and the QI methods.

Classification of Satellite Images by means of Fuzzy Rules generated by a Genetic Algorithm

The data acquired by Remote Sensing systems allow obtaining thematic maps of the earth's surface, by means of the registered image classification. This implies the identification and categorization of all pixels into land cover classes. Traditionally, methods based on statistical parameters have been widely used, although they show some disadvantages. Nevertheless, some authors indicate that those methods based on artificial intelligence, may be a good alternative. Thus, fuzzy classifiers, which are based on Fuzzy Logic, include additional information in the classification process through based-rule systems. In this work, we propose the use of a genetic algorithm (GA) to select the optimal and minimum set of fuzzy rules to classify remotely sensed images. Input information of GA has been obtained through the training space determined by two uncorrelated spectral bands (2D scatter diagrams), which has been irregularly divided by five linguistic terms defined in each band. The proposed methodology has been applied to Landsat-TM images and it has showed that this set of rules provides a higher accuracy level in the classification process

Multiscale object-based classification of satellite images merging multispectral information with panchromatic textural features

Once admitted the advantages of object-based classification compared to pixel-based classification; the need of simple and affordable methods to define and characterize objects to be classified, appears. This paper presents a new methodology for the identification and characterization of objects at different scales, through the integration of spectral information provided by the multispectral image, and textural information from the corresponding panchromatic image. In this way, it has defined a set of objects that yields a simplified representation of the information contained in the two source images. These objects can be characterized by different attributes that allow discriminating between different spectral&textural patterns. This methodology facilitates information processing, from a conceptual and computational point of view. Thus the vectors of attributes defined can be used directly as training pattern input for certain classifiers, as for example artificial neural networks. Growing Cell Structures have been used to classify the merged information.

Text categorization methods for automatic estimation of verbal intelligence

In this paper we investigate whether conventional text categorization methods may suffice to infer different verbal intelligence levels. This research goal relies on the hypothesis that the vocabulary that speakers make use of reflects their verbal intelligence levels. Automatic verbal intelligence estimation of users in a spoken language dialog system may be useful when defining an optimal dialog strategy by improving its adaptation capabilities. The work is based on a corpus containing descriptions (i.e. monologs) of a short film by test persons yielding different educational backgrounds and the verbal intelligence scores of the speakers. First, a one-way analysis of variance was performed to compare the monologs with the film transcription and to demonstrate that there are differences in the vocabulary used by the test persons yielding different verbal intelligence levels. Then, for the classification task, the monologs were represented as feature vectors using the classical TF–IDF weighting scheme. The Naive Bayes, k-nearest neighbors and Rocchio classifiers were tested. In this paper we describe and compare these classification approaches, define the optimal classification parameters and discuss the classification results obtained.

A new feature extraction method for signal classification applied to cat spinal cord signals

In the spinal cord of the anesthetized cat, spontaneous cord dorsum potentials (CDPs) appear synchronously along the lumbo-sacral segments. These CDPs have different shapes and magnitudes. Previous work has indicated that some CDPs appear to be specially associated with the activation of spinal pathways that lead to primary afferent depolarization and presynaptic inhibition. Visual detection and classification of these CDPs provides relevant information on the functional organization of the neural networks involved in the control of sensory information and allows the characterization of the changes produced by acute nerve and spinal lesions. We now present a novel feature extraction approach for signal classification, applied to CDP detection. The method is based on an intuitive procedure. We first remove by convolution the noise from the CDPs recorded in each given spinal segment. Then, we assign a coefficient for each main local maximum of the signal using its amplitude and distance to the most important maximum of the signal. These coefficients will be the input for the subsequent classification algorithm. In particular, we employ gradient boosting classification trees. This combination of approaches allows a faster and more accurate discrimination of CDPs than is obtained by other methods.

Fusion of probabilistic knowledge-based classification rules and learning automata for automatic recognition of digital images

In this paper, the fusion of probabilistic knowledge-based classification rules and learning automata theory is proposed and as a result we present a set of probabilistic classification rules with self-learning capability. The probabilities of the classification rules change dynamically guided by a supervised reinforcement process aimed at obtaining an optimum classification accuracy. This novel classifier is applied to the automatic recognition of digital images corresponding to visual landmarks for the autonomous navigation of an unmanned aerial vehicle (UAV) developed by the authors. The classification accuracy of the proposed classifier and its comparison with well-established pattern recognition methods is finally reported.

Automatic blood glucose classification for gestational diabetes with feature selection: decision trees vs neural networks

Automatic blood glucose classification may help specialists to provide a better interpretation of blood glucose data, downloaded directly from patients glucose meter and will contribute in the development of decision support systems for gestational diabetes. This paper presents an automatic blood glucose classifier for gestational diabetes that compares 6 different feature selection methods for two machine learning algorithms: neural networks and decision trees. Three searching algorithms, Greedy, Best First and Genetic, were combined with two different evaluators, CSF and Wrapper, for the feature selection. The study has been made with 6080 blood glucose measurements from 25 patients. Decision trees with a feature set selected with the Wrapper evaluator and the Best first search algorithm obtained the best accuracy: 95.92%.

Region-dependent vehicle classification using PCA features

Video-based vehicle detection is the focus of increasing interest due to its potential towards collision avoidance. In particular, vehicle verification is especially challenging due to the enormous variability of vehicles in size, color, pose, etc. In this paper, a new approach based on supervised learning using Principal Component Analysis (PCA) is proposed that addresses the main limitations of existing methods. Namely, in contrast to classical approaches which train a single classifier regardless of the relative position of the candidate (thus ignoring valuable pose information), a region-dependent analysis is performed by considering four different areas. In addition, a study on the evolution of the classification performance according to the dimensionality of the principal subspace is carried out using PCA features within a SVM-based classification scheme. Indeed, the experiments performed on a publicly available database prove that PCA dimensionality requirements are region-dependent. Hence, in this work, the optimal configuration is adapted to each of them, rendering very good vehicle verification results.

Multi-dimensional classification with super-classes

The multi-dimensional classification problem is a generalisation of the recently-popularised task of multi-label classification, where each data instance is associated with multiple class variables. There has been relatively little research carried out specific to multi-dimensional classification and, although one of the core goals is similar (modelling dependencies among classes), there are important differences; namely a higher number of possible classifications. In this paper we present method for multi-dimensional classification, drawing from the most relevant multi-label research, and combining it with important novel developments. Using a fast method to model the conditional dependence between class variables, we form super-class partitions and use them to build multi-dimensional learners, learning each super-class as an ordinary class, and thus explicitly modelling class dependencies. Additionally, we present a mechanism to deal with the many class values inherent to super-classes, and thus make learning efficient. To investigate the effectiveness of this approach we carry out an empirical evaluation on a range of multi-dimensional datasets, under different evaluation metrics, and in comparison with high-performing existing multi-dimensional approaches from the literature. Analysis of results shows that our approach offers important performance gains over competing methods, while also exhibiting tractable running time.