Search results for "Linear Algebra."
showing 10 items of 552 documents
Kernel-Based Framework for Multitemporal and Multisource Remote Sensing Data Classification and Change Detection
2008
The multitemporal classification of remote sensing images is a challenging problem, in which the efficient combination of different sources of information (e.g., temporal, contextual, or multisensor) can improve the results. In this paper, we present a general framework based on kernel methods for the integration of heterogeneous sources of information. Using the theoretical principles in this framework, three main contributions are presented. First, a novel family of kernel-based methods for multitemporal classification of remote sensing images is presented. The second contribution is the development of nonlinear kernel classifiers for the well-known difference and ratioing change detectio…
Perspectives and reflections on teaching linear algebra
2020
Abstract This paper presents ‘expert opinions’ on what should be taught in a first-year linear algebra course at university; the aim is to gain a generic picture and general guiding principles for such a course. Drawing on a Delphi method, 14 university professors—called ‘experts’ in this study—addressed the following questions: What should be on a first-year linear algebra undergraduate course for engineering and/or mathematics students? How could such courses be taught? What tools (if any) are essential to these two groups of students? The results of the investigation, these experts’ opinions, mainly concern what should be in a linear algebra course (e.g. problem-solving and applications)…
Automatic left ventricle volume calculation with explainability through a deep learning weak-supervision methodology
2021
[EN] Background and objective: Magnetic resonance imaging is the most reliable imaging technique to assess the heart. More specifically there is great importance in the analysis of the left ventricle, as the main pathologies directly affect this region. In order to characterize the left ventricle, it is necessary to extract its volume. In this work we present a neural network architecture that is capable of directly estimating the left ventricle volume in short axis cine Magnetic Resonance Imaging in the end-diastolic frame and provide a segmentation of the region which is the basis of the volume calculation, thus offering explain-ability to the estimated value. Methods: The network was des…
Intertwining operators between different Hilbert spaces: connection with frames
2009
In this paper we generalize a strategy recently proposed by the author concerning intertwining operators. In particular we discuss the possibility of extending our previous results in such a way to construct (almost) isospectral self-adjoint operators living in different Hilbert spaces. Many examples are discussed in details. Many of them arise from the theory of frames in Hilbert spaces, others from the so-called g-frames.
A Comparison of Advanced Regression Algorithms for Quantifying Urban Land Cover
2014
Quantitative methods for mapping sub-pixel land cover fractions are gaining increasing attention, particularly with regard to upcoming hyperspectral satellite missions. We evaluated five advanced regression algorithms combined with synthetically mixed training data for quantifying urban land cover from HyMap data at 3.6 and 9 m spatial resolution. Methods included support vector regression (SVR), kernel ridge regression (KRR), artificial neural networks (NN), random forest regression (RFR) and partial least squares regression (PLSR). Our experiments demonstrate that both kernel methods SVR and KRR yield high accuracies for mapping complex urban surface types, i.e., rooftops, pavements, gras…
Minor Cutting Edge Wear in Finish Turning Operations
1999
In finish turning operation, it has already shown, that for the sake of control the dimensional accuracy and the micro-geometry of the worked surface, the wear parameters employed in rough turning operations are not suitable. In the present work the study of wear in fmish turning operations, is carried out, employing a particular groove survey methodology, already proposed in a previous paper, that is based on the techniques of acquirement and processing of images. In order to verify the applicability of the proposed technique two kind of alumina-based inserts and two kind of sintered carbide inserts have been tested. The experimental tests have confirmed the validity of the technique in th…
Structured Output SVM for Remote Sensing Image Classification
2011
Traditional kernel classifiers assume independence among the classification outputs. As a consequence, each misclassification receives the same weight in the loss function. Moreover, the kernel function only takes into account the similarity between input values and ignores possible relationships between the classes to be predicted. These assumptions are not consistent for most of real-life problems. In the particular case of remote sensing data, this is not a good assumption either. Segmentation of images acquired by airborne or satellite sensors is a very active field of research in which one tries to classify a pixel into a predefined set of classes of interest (e.g. water, grass, trees,…
Manifold Learning with High Dimensional Model Representations
2020
Manifold learning methods are very efficient methods for hyperspectral image (HSI) analysis but, unless specifically designed, they cannot provide an explicit embedding map readily applicable to out-of-sample data. A common assumption to deal with the problem is that the transformation between the high input dimensional space and the (typically low) latent space is linear. This is a particularly strong assumption, especially when dealing with hyperspectral images due to the well-known nonlinear nature of the data. To address this problem, a manifold learning method based on High Dimensional Model Representation (HDMR) is proposed, which enables to present a nonlinear embedding function to p…
The Elephant in the Machine: Proposing a New Metric of Data Reliability and its Application to a Medical Case to Assess Classification Reliability
2020
In this paper, we present and discuss a novel reliability metric to quantify the extent a ground truth, generated in multi-rater settings, as a reliable basis for the training and validation of machine learning predictive models. To define this metric, three dimensions are taken into account: agreement (that is, how much a group of raters mutually agree on a single case)
Application of model quality evaluation to systems biology
2008
Application of model quality evaluation to the quasispecies models is presented. These models are useful for the analysis of the DNA and RNA evolution and for the description of the population dynamics of viruses and bacteria. An estimate of the parameters together with their interval of variability is computed and the quality evaluation is tested on the basis of the model prediction error capability.