A New Estimator of Intrinsic Dimension Based on the Multipoint Morisita Index

The size of datasets has been increasing rapidly both in terms of number of variables and number of events. As a result, the empty space phenomenon and the curse of dimensionality complicate the extraction of useful information. But, in general, data lie on non-linear manifolds of much lower dimension than that of the spaces in which they are embedded. In many pattern recognition tasks, learning these manifolds is a key issue and it requires the knowledge of their true intrinsic dimension. This paper introduces a new estimator of intrinsic dimension based on the multipoint Morisita index. It is applied to both synthetic and real datasets of varying complexities and comparisons with other existing estimators are carried out. The proposed estimator turns out to be fairly robust to sample size and noise, unaffected by edge effects, able to handle large datasets and computationally efficient

Interest rates mapping

The present study deals with the analysis and mapping of Swiss franc interest rates. Interest rates depend on time and maturity, defining term structure of the interest rate curves (IRC). In the present study IRC are considered in a two-dimensional feature space - time and maturity. Geostatistical models and machine learning algorithms (multilayer perceptron and Support Vector Machines) were applied to produce interest rate maps. IR maps can be used for the visualisation and patterns perception purposes, to develop and to explore economical hypotheses, to produce dynamic asses-liability simulations and for the financial risk assessments. The feasibility of an application of interest rates mapping approach for the IRC forecasting is considered as well.Comment: 8 pages, 8 figures. Presented at Applications of Physics in Financial Analysis conference (APFA6), Lisbon, Portugal, 200

Multi-scale support vector algorithms for hot spot detection and modelling

The algorithmic approach to data modelling has developed rapidly these last years, in particular methods based on data mining and machine learning have been used in a growing number of applications. These methods follow a data-driven methodology, aiming at providing the best possible generalization and predictive abilities instead of concentrating on the properties of the data model. One of the most successful groups of such methods is known as Support Vector algorithms. Following the fruitful developments in applying Support Vector algorithms to spatial data, this paper introduces a new extension of the traditional support vector regression (SVR) algorithm. This extension allows for the simultaneous modelling of environmental data at several spatial scales. The joint influence of environmental processes presenting different patterns at different scales is here learned automatically from data, providing the optimum mixture of short and large-scale models. The method is adaptive to the spatial scale of the data. With this advantage, it can provide efficient means to model local anomalies that may typically arise in situations at an early phase of an environmental emergency. However, the proposed approach still requires some prior knowledge on the possible existence of such short-scale patterns. This is a possible limitation of the method for its implementation in early warning systems. The purpose of this paper is to present the multi-scale SVR model and to illustrate its use with an application to the mapping of Cs137 activity given the measurements taken in the region of Briansk following the Chernobyl acciden

Data-driven topo-climatic mapping with machine learning methods

Automatic environmental monitoring networks enforced by wireless communication technologies provide large and ever increasing volumes of data nowadays. The use of this information in natural hazard research is an important issue. Particularly useful for risk assessment and decision making are the spatial maps of hazard-related parameters produced from point observations and available auxiliary information. The purpose of this article is to present and explore the appropriate tools to process large amounts of available data and produce predictions at fine spatial scales. These are the algorithms of machine learning, which are aimed at non-parametric robust modelling of non-linear dependencies from empirical data. The computational efficiency of the data-driven methods allows producing the prediction maps in real time which makes them superior to physical models for the operational use in risk assessment and mitigation. Particularly, this situation encounters in spatial prediction of climatic variables (topo-climatic mapping). In complex topographies of the mountainous regions, the meteorological processes are highly influenced by the relief. The article shows how these relations, possibly regionalized and non-linear, can be modelled from data using the information from digital elevation models. The particular illustration of the developed methodology concerns the mapping of temperatures (including the situations of Föhn and temperature inversion) given the measurements taken from the Swiss meteorological monitoring network. The range of the methods used in the study includes data-driven feature selection, support vector algorithms and artificial neural network

Long-range fluctuations and multifractality in connectivity density time series of a wind speed monitoring network

This paper studies the daily connectivity time series of a wind speed-monitoring network using multifractal detrended fluctuation analysis. It investigates the long-range fluctuation and multifractality in the residuals of the connectivity time series. Our findings reveal that the daily connectivity of the correlation-based network is persistent for any correlation threshold. Further, the multifractality degree is higher for larger absolute values of the correlation threshol

Resonance equals reducibility for A-hypergeometric systems

Classical theorems of Gel'fand et al., and recent results of Beukers, show that non-confluent Cohen-Macaulay A-hypergeometric systems have reducible monodromy representation if and only if the continuous parameter is A-resonant. We remove both the confluence and Cohen-Macaulayness conditions while simplifying the proof.Comment: 9 pages, final versio

Learning wind fields with multiple kernels

This paper presents multiple kernel learning (MKL) regression as an exploratory spatial data analysis and modelling tool. The MKL approach is introduced as an extension of support vector regression, where MKL uses dedicated kernels to divide a given task into sub-problems and to treat them separately in an effective way. It provides better interpretability to non-linear robust kernel regression at the cost of a more complex numerical optimization. In particular, we investigate the use of MKL as a tool that allows us to avoid using ad-hoc topographic indices as covariables in statistical models in complex terrains. Instead, MKL learns these relationships from the data in a non-parametric fashion. A study on data simulated from real terrain features confirms the ability of MKL to enhance the interpretability of data-driven models and to aid feature selection without degrading predictive performances. Here we examine the stability of the MKL algorithm with respect to the number of training data samples and to the presence of noise. The results of a real case study are also presented, where MKL is able to exploit a large set of terrain features computed at multiple spatial scales, when predicting mean wind speed in an Alpine regio

Cognition and maths in children referred for ADHD assessment

Attention Deficit Hyperactivity Disorder (ADHD) is a lifelong neurodevelopmental disorder. ADHD symptoms manifest as persistent inattention, hyperactivity, and/or impulsivity. Children with ADHD also show pervasive difficulties in cognitive processes including Executive Functions, memory, and processing speed – processes hypothesised to underpin academic success. Many children with ADHD struggle with maths, as demonstrated by lower levels of attainment and higher incidence of maths learning difficulties. Maths abilities predict a range of outcomes in adulthood and therefore represent a particularly important area of investigation in this population. However, much of the previous research relies on broad attainment tests to explore maths performance. Such tests risk masking more intricate sources of maths difficulties. Specifically, three maths components are proposed to support broad maths achievement in children: factual knowledge, conceptual understanding, and procedural skill. These skills have not yet been explored comprehensively in children with ADHD. Not all children with ADHD show difficulties with maths and some perform similarly to their neurotypical peers. The source of this within group variability has previously been attributed to differences in behavioural symptom presentations, such as inattention. Given that behavioural manifestations are closely linked to differences in neurocognitive abilities, which are also notoriously diverse in ADHD, cognitive mechanisms could offer a better explanation for heterogeneity in maths performance. Keeping the componential nature of maths skills in mind, the broad aim of this thesis was to conduct a comprehensive investigation into their relationship with behavioural and cognitive processes in a clinical ADHD population. Exploring how performance across these components relates to behavioural and cognitive functioning in ADHD can help inform pathways of risk for maths difficulties and act as a steppingstone to devising educational interventions. Following the General Introduction, Chapter 2 includes a systematic review of existing literature addressing the association between previously implicated cognitive processes and maths performance in ADHD. To date, studies on the relationship between cognition and maths in ADHD have not been systematically reviewed making it difficult to appraise research in this area. The results showed a positive association between cognition and maths performance in this population. However, very few studies met inclusion criteria and those that did, only assessed a limited number of relevant cognitive domains. The results of this chapter demonstrate a lack of research into the relationship between cognition and maths in clinical ADHD and, via quality appraisal, highlight key methodological considerations for future research. Chapter 3 contains the General Methodology which explores the methodological decisions employed for the remaining study chapters such as participant inclusion and materials used. This chapter also provides information on procedures used, ethics, participant characteristics, missing data, sample size, and data preparation. Chapter 4 comprises a comprehensive investigation of cognition, behaviour, and maths in 44 drug naïve children on the waiting list for ADHD evaluation at Child and Adolescent Mental Health Services. The results showed that cognition, rather than ADHD symptoms, correlated with both standardised maths attainment scores and more specific components of maths skills. In particular, verbal, and visuospatial aspects of memory functioning showed the strongest associations with maths across the board. This suggests that cognitive processes, rather than clinical ADHD symptoms, are more informative for maths performance in children with clinically high ADHD symptoms and represent viable targets for future research on maths interventions. This chapter also demonstrated high rates of co-occurrence with other neurodevelopmental disorders which must be considered when characterising ADHD samples. Chapter 5 built on the richness of the clinical characterisation in the preceding chapter, which found that around half of the sample showed motor difficulties indicative of Developmental Coordination Disorder (DCD). Specifically, this study divided the sample into two groups – one with high ADHD and DCD symptoms (ADHD + co-occurring motor difficulties) and one who scored lower on the DCD assessment screener (ADHD-only). The results showed that these groups were comparable in terms of maths performance and in many of the cognitive tasks. However, the ADHD + co-occurring motor difficulties group showed significantly poorer performance on visuospatial WM than the ADHD-only group. This highlighted visuospatial WM as a clinically informative and distinguishing feature of children with concurrently high DCD symptoms. Overall, the strength of associations between cognitive processes and maths skills did not differ. This further pointed to cognitive dimensions as more informative mechanisms in relation to maths, than that of diagnostic symptomatology. The final study chapter, Chapter 6, compared a traditional categorical grouping approach (i.e., clinical ADHD vs no clinical ADHD diagnosis) to that of a data-driven grouping approach (i.e., groups based on children’s cognitive data). This chapter demonstrated that a categorical diagnostic approach was not informative of children’s maths outcomes. By contrast, the data-driven approaches, which grouped children using relevant cognitive performance, generated meaningful cognitive subgroups which could be differentiated on their maths, as well as intelligence scores. This suggests that cognitive patterns of performance, rather than children’s diagnostic outcomes, are more informative for identifying meaningful groups of struggling learners. Collectively, the current thesis is the first to provide a comprehensive investigation of maths skills in a clinically referred and drug naïve sample of children with high ADHD symptoms. Throughout this thesis, practical and theoretical implications for future work in ADHD are discussed