Batch effect confounding leads to strong bias in performance estimates obtained by cross-validation.

BACKGROUND: With the large amount of biological data that is currently publicly available, many investigators combine multiple data sets to increase the sample size and potentially also the power of their analyses. However, technical differences ("batch effects") as well as differences in sample composition between the data sets may significantly affect the ability to draw generalizable conclusions from such studies. FOCUS: The current study focuses on the construction of classifiers, and the use of cross-validation to estimate their performance. In particular, we investigate the impact of batch effects and differences in sample composition between batches on the accuracy of the classification performance estimate obtained via cross-validation. The focus on estimation bias is a main difference compared to previous studies, which have mostly focused on the predictive performance and how it relates to the presence of batch effects. DATA: We work on simulated data sets. To have realistic intensity distributions, we use real gene expression data as the basis for our simulation. Random samples from this expression matrix are selected and assigned to group 1 (e.g., 'control') or group 2 (e.g., 'treated'). We introduce batch effects and select some features to be differentially expressed between the two groups. We consider several scenarios for our study, most importantly different levels of confounding between groups and batch effects. METHODS: We focus on well-known classifiers: logistic regression, Support Vector Machines (SVM), k-nearest neighbors (kNN) and Random Forests (RF). Feature selection is performed with the Wilcoxon test or the lasso. Parameter tuning and feature selection, as well as the estimation of the prediction performance of each classifier, is performed within a nested cross-validation scheme. The estimated classification performance is then compared to what is obtained when applying the classifier to independent data.

Semi-supervised remote sensing image classification with cluster kernels

A semisupervised support vector machine is presented for the classification of remote sensing images. The method exploits the wealth of unlabeled samples for regularizing the training kernel representation locally by means of cluster kernels. The method learns a suitable kernel directly from the image and thus avoids assuming a priori signal relations by using a predefined kernel structure. Good results are obtained in image classification examples when few labeled samples are available. The method scales almost linearly with the number of unlabeled samples and provides out-of-sample predictions.

Analysis, modelling and classification of geospatial data using machine learning

The research considers the problem of spatial data classification using machine learning algorithms: probabilistic neural networks (PNN) and support vector machines (SVM). As a benchmark model simple k-nearest neighbor algorithm is considered. PNN is a neural network reformulation of well known nonparametric principles of probability density modeling using kernel density estimator and Bayesian optimal or maximum a posteriori decision rules. PNN is well suited to problems where not only predictions but also quantification of accuracy and integration of prior information are necessary. An important property of PNN is that they can be easily used in decision support systems dealing with problems of automatic classification. Support vector machine is an implementation of the principles of statistical learning theory for the classification tasks. Recently they were successfully applied for different environmental topics: classification of soil types and hydro-geological units, optimization of monitoring networks, susceptibility mapping of natural hazards. In the present paper both simulated and real data case studies (low and high dimensional) are considered. The main attention is paid to the detection and learning of spatial patterns by the algorithms applied.

Mult-class differentiation of cannabis seedlings in a forensic context

This article presents an experimental study about the classification ability of several classifiers for multi-classclassification of cannabis seedlings. As the cultivation of drug type cannabis is forbidden in Switzerland lawenforcement authorities regularly ask forensic laboratories to determinate the chemotype of a seized cannabisplant and then to conclude if the plantation is legal or not. This classification is mainly performed when theplant is mature as required by the EU official protocol and then the classification of cannabis seedlings is a timeconsuming and costly procedure. A previous study made by the authors has investigated this problematic [1]and showed that it is possible to differentiate between drug type (illegal) and fibre type (legal) cannabis at anearly stage of growth using gas chromatography interfaced with mass spectrometry (GC-MS) based on therelative proportions of eight major leaf compounds. The aims of the present work are on one hand to continueformer work and to optimize the methodology for the discrimination of drug- and fibre type cannabisdeveloped in the previous study and on the other hand to investigate the possibility to predict illegal cannabisvarieties. Seven classifiers for differentiating between cannabis seedlings are evaluated in this paper, namelyLinear Discriminant Analysis (LDA), Partial Least Squares Discriminant Analysis (PLS-DA), Nearest NeighbourClassification (NNC), Learning Vector Quantization (LVQ), Radial Basis Function Support Vector Machines(RBF SVMs), Random Forest (RF) and Artificial Neural Networks (ANN). The performance of each method wasassessed using the same analytical dataset that consists of 861 samples split into drug- and fibre type cannabiswith drug type cannabis being made up of 12 varieties (i.e. 12 classes). The results show that linear classifiersare not able to manage the distribution of classes in which some overlap areas exist for both classificationproblems. Unlike linear classifiers, NNC and RBF SVMs best differentiate cannabis samples both for 2-class and12-class classifications with average classification results up to 99% and 98%, respectively. Furthermore, RBFSVMs correctly classified into drug type cannabis the independent validation set, which consists of cannabisplants coming from police seizures. In forensic case work this study shows that the discrimination betweencannabis samples at an early stage of growth is possible with fairly high classification performance fordiscriminating between cannabis chemotypes or between drug type cannabis varieties.

Kernel-based mapping of orographic rainfall enhancement in the Swiss Alps as detected by weatherradar

In this paper, we develop a data-driven methodology to characterize the likelihood of orographic precipitation enhancement using sequences of weather radar images and a digital elevation model (DEM). Geographical locations with topographic characteristics favorable to enforce repeatable and persistent orographic precipitation such as stationary cells, upslope rainfall enhancement, and repeated convective initiation are detected by analyzing the spatial distribution of a set of precipitation cells extracted from radar imagery. Topographic features such as terrain convexity and gradients computed from the DEM at multiple spatial scales as well as velocity fields estimated from sequences of weather radar images are used as explanatory factors to describe the occurrence of localized precipitation enhancement. The latter is represented as a binary process by defining a threshold on the number of cell occurrences at particular locations. Both two-class and one-class support vector machine classifiers are tested to separate the presumed orographic cells from the nonorographic ones in the space of contributing topographic and flow features. Site-based validation is carried out to estimate realistic generalization skills of the obtained spatial prediction models. Due to the high class separability, the decision function of the classifiers can be interpreted as a likelihood or susceptibility of orographic precipitation enhancement. The developed approach can serve as a basis for refining radar-based quantitative precipitation estimates and short-term forecasts or for generating stochastic precipitation ensembles conditioned on the local topography.

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 region.

Multiple Kernel Learning of Environmental Data. Case study: Analysis and Mapping of Wind Fields

The paper presents the Multiple Kernel Learning (MKL) approach as a modelling and data exploratory tool and applies it to the problem of wind speed mapping. Support Vector Regression (SVR) is used to predict spatial variations of the mean wind speed from terrain features (slopes, terrain curvature, directional derivatives) generated at different spatial scales. Multiple Kernel Learning is applied to learn kernels for individual features and thematic feature subsets, both in the context of feature selection and optimal parameters determination. An empirical study on real-life data confirms the usefulness of MKL as a tool that enhances the interpretability of data-driven models.

Applying machine learning methods to avalanche forecasting

Avalanche forecasting is a complex process involving the assimilation of multiple data sources to make predictions over varying spatial and temporal resolutions. Numerically assisted forecasting often uses nearest neighbour methods (NN), which are known to have limitations when dealing with high dimensional data. We apply Support Vector Machines to a dataset from Lochaber, Scotland to assess their applicability in avalanche forecasting. Support Vector Machines (SVMs) belong to a family of theoretically based techniques from machine learning and are designed to deal with high dimensional data. Initial experiments showed that SVMs gave results which were comparable with NN for categorical and probabilistic forecasts. Experiments utilising the ability of SVMs to deal with high dimensionality in producing a spatial forecast show promise, but require further work.

Analysis and spatial modeling of the indoor radon Swiss data

The present research deals with an important public health threat, which is the pollution created by radon gas accumulation inside dwellings. The spatial modeling of indoor radon in Switzerland is particularly complex and challenging because of many influencing factors that should be taken into account. Indoor radon data analysis must be addressed from both a statistical and a spatial point of view. As a multivariate process, it was important at first to define the influence of each factor. In particular, it was important to define the influence of geology as being closely associated to indoor radon. This association was indeed observed for the Swiss data but not probed to be the sole determinant for the spatial modeling. The statistical analysis of data, both at univariate and multivariate level, was followed by an exploratory spatial analysis. Many tools proposed in the literature were tested and adapted, including fractality, declustering and moving windows methods. The use of Quan-tité Morisita Index (QMI) as a procedure to evaluate data clustering in function of the radon level was proposed. The existing methods of declustering were revised and applied in an attempt to approach the global histogram parameters. The exploratory phase comes along with the definition of multiple scales of interest for indoor radon mapping in Switzerland. The analysis was done with a top-to-down resolution approach, from regional to local lev¬els in order to find the appropriate scales for modeling. In this sense, data partition was optimized in order to cope with stationary conditions of geostatistical models. Common methods of spatial modeling such as Κ Nearest Neighbors (KNN), variography and General Regression Neural Networks (GRNN) were proposed as exploratory tools. In the following section, different spatial interpolation methods were applied for a par-ticular dataset. A bottom to top method complexity approach was adopted and the results were analyzed together in order to find common definitions of continuity and neighborhood parameters. Additionally, a data filter based on cross-validation was tested with the purpose of reducing noise at local scale (the CVMF). At the end of the chapter, a series of test for data consistency and methods robustness were performed. This lead to conclude about the importance of data splitting and the limitation of generalization methods for reproducing statistical distributions. The last section was dedicated to modeling methods with probabilistic interpretations. Data transformation and simulations thus allowed the use of multigaussian models and helped take the indoor radon pollution data uncertainty into consideration. The catego-rization transform was presented as a solution for extreme values modeling through clas-sification. Simulation scenarios were proposed, including an alternative proposal for the reproduction of the global histogram based on the sampling domain. The sequential Gaussian simulation (SGS) was presented as the method giving the most complete information, while classification performed in a more robust way. An error measure was defined in relation to the decision function for data classification hardening. Within the classification methods, probabilistic neural networks (PNN) show to be better adapted for modeling of high threshold categorization and for automation. Support vector machines (SVM) on the contrary performed well under balanced category conditions. In general, it was concluded that a particular prediction or estimation method is not better under all conditions of scale and neighborhood definitions. Simulations should be the basis, while other methods can provide complementary information to accomplish an efficient indoor radon decision making.

How early can we predict Alzheimer's disease using computational anatomy?

Computational anatomy with magnetic resonance imaging (MRI) is well established as a noninvasive biomarker of Alzheimer's disease (AD); however, there is less certainty about its dependency on the staging of AD. We use classical group analyses and automated machine learning classification of standard structural MRI scans to investigate AD diagnostic accuracy from the preclinical phase to clinical dementia. Longitudinal data from the Alzheimer's Disease Neuroimaging Initiative were stratified into 4 groups according to the clinical status-(1) AD patients; (2) mild cognitive impairment (MCI) converters; (3) MCI nonconverters; and (4) healthy controls-and submitted to a support vector machine. The obtained classifier was significantly above the chance level (62%) for detecting AD already 4 years before conversion from MCI. Voxel-based univariate tests confirmed the plausibility of our findings detecting a distributed network of hippocampal-temporoparietal atrophy in AD patients. We also identified a subgroup of control subjects with brain structure and cognitive changes highly similar to those observed in AD. Our results indicate that computational anatomy can detect AD substantially earlier than suggested by current models. The demonstrated differential spatial pattern of atrophy between correctly and incorrectly classified AD patients challenges the assumption of a uniform pathophysiological process underlying clinically identified AD.

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 networks.

Kernel-based Mapping of Meteorological Fields in Complex Orography

Due to the advances in sensor networks and remote sensing technologies, the acquisition and storage rates of meteorological and climatological data increases every day and ask for novel and efficient processing algorithms. A fundamental problem of data analysis and modeling is the spatial prediction of meteorological variables in complex orography, which serves among others to extended climatological analyses, for the assimilation of data into numerical weather prediction models, for preparing inputs to hydrological models and for real time monitoring and short-term forecasting of weather.In this thesis, a new framework for spatial estimation is proposed by taking advantage of a class of algorithms emerging from the statistical learning theory. Nonparametric kernel-based methods for nonlinear data classification, regression and target detection, known as support vector machines (SVM), are adapted for mapping of meteorological variables in complex orography.With the advent of high resolution digital elevation models, the field of spatial prediction met new horizons. In fact, by exploiting image processing tools along with physical heuristics, an incredible number of terrain features which account for the topographic conditions at multiple spatial scales can be extracted. Such features are highly relevant for the mapping of meteorological variables because they control a considerable part of the spatial variability of meteorological fields in the complex Alpine orography. For instance, patterns of orographic rainfall, wind speed and cold air pools are known to be correlated with particular terrain forms, e.g. convex/concave surfaces and upwind sides of mountain slopes.Kernel-based methods are employed to learn the nonlinear statistical dependence which links the multidimensional space of geographical and topographic explanatory variables to the variable of interest, that is the wind speed as measured at the weather stations or the occurrence of orographic rainfall patterns as extracted from sequences of radar images. Compared to low dimensional models integrating only the geographical coordinates, the proposed framework opens a way to regionalize meteorological variables which are multidimensional in nature and rarely show spatial auto-correlation in the original space making the use of classical geostatistics tangled.The challenges which are explored during the thesis are manifolds. First, the complexity of models is optimized to impose appropriate smoothness properties and reduce the impact of noisy measurements. Secondly, a multiple kernel extension of SVM is considered to select the multiscale features which explain most of the spatial variability of wind speed. Then, SVM target detection methods are implemented to describe the orographic conditions which cause persistent and stationary rainfall patterns. Finally, the optimal splitting of the data is studied to estimate realistic performances and confidence intervals characterizing the uncertainty of predictions.The resulting maps of average wind speeds find applications within renewable resources assessment and opens a route to decrease the temporal scale of analysis to meet hydrological requirements. Furthermore, the maps depicting the susceptibility to orographic rainfall enhancement can be used to improve current radar-based quantitative precipitation estimation and forecasting systems and to generate stochastic ensembles of precipitation fields conditioned upon the orography.

Machine learning for spatial environmental data. Theory, applications and software

The book presents the state of the art in machine learning algorithms (artificial neural networks of different architectures, support vector machines, etc.) as applied to the classification and mapping of spatially distributed environmental data. Basic geostatistical algorithms are presented as well. New trends in machine learning and their application to spatial data are given, and real case studies based on environmental and pollution data are carried out. The book provides a CD-ROM with the Machine Learning Office software, including sample sets of data, that will allow both students and researchers to put the concepts rapidly to practice.

Improving a leaves automatic recognition process using PCA

In this work we present a simulation of a recognition process with perimeter characterization of a simple plant leaves as a unique discriminating parameter. Data coding allowing for independence of leaves size and orientation may penalize performance recognition for some varieties. Border description sequences are then used, and Principal Component Analysis (PCA) is applied in order to study which is the best number of components for the classification task, implemented by means of a Support Vector Machine (SVM) System. Obtained results are satisfactory, and compared with [4] our system improves the recognition success, diminishing the variance at the same time.

Multi-source composite kernels for urban image classification

This letter presents advanced classification methods for very high resolution images. Efficient multisource information, both spectral and spatial, is exploited through the use of composite kernels in support vector machines. Weighted summations of kernels accounting for separate sources of spectral and spatial information are analyzed and compared to classical approaches such as pure spectral classification or stacked approaches using all the features in a single vector. Model selection problems are addressed, as well as the importance of the different kernels in the weighted summation.