A fusion method for multi-valued data Papčo, Martin; Rodríguez-Martínez, Iosu; Fumanal-Idocin, Javier ...
Information fusion,
July 2021, 2021-07-00, Volume:
71
Journal Article
Peer reviewed
Open access
In this paper we propose an extension of the notion of deviation-based aggregation function tailored to aggregate multidimensional data. Our objective is both to improve the results obtained by other ...methods that try to select the best aggregation function for a particular set of data, such as penalty functions, and to reduce the temporal complexity required by such approaches. We discuss how this notion can be defined and present three illustrative examples of the applicability of our new proposal in areas where temporal constraints can be strict, such as image processing, deep learning and decision making, obtaining favourable results in the process.
•We have expanded the target of deviation-based functions to the multivariable case.•We provide a new construction method for this type of deviation-based functions.•Our approach is not restricted to aggregating values of the unit interval.•Temporal complexity is lower than that of alternatives such as penalty functions.•Our method can be applied in image reduction, deep learning or decision making.
The 2019 coronavirus disease outbreak, caused by the severe acute respiratory syndrome type-2 virus (SARS-CoV-2), was declared a pandemic in March 2020. Since its emergence to the present day, this ...disease has brought multiple countries to the brink of health care collapse during several waves of the disease. One of the most common tests performed on patients is chest x-ray imaging. These images show the severity of the patient’s illness and whether it is indeed covid or another type of pneumonia. Automated assessment of this type of imaging could alleviate the time required for physicians to treat and diagnose each patient. To this end, in this paper we propose the use of Convolutional Neural Networks (CNNs) to carry out this process. The aim of this paper is twofold. Firstly, we present a pipeline adapted to this problem, covering all steps from the preprocessing of the datasets to the generation of classification models based on CNNs. Secondly, we have focused our study on the modification of the information fusion processes of this type of architectures, in the pooling layers. We propose a number of aggregation theory functions that are suitable to replace classical processes and have shown their benefits in past applications, and study their performance in the context of the x-ray classification problem. We find that replacing the feature reduction processes of CNNs leads to drastically different behaviours of the final model, which can be beneficial when prioritizing certain metrics such as precision or recall.
•Convolutional Neural Networks are effective for detecting SARS-CoV-2 on x-ray images.•Intermediate extracted features can be fused through different aggregation functions.•Grouping functions are harder to train but can offer better classification accuracy.•An early restart policy eases training models which make use of grouping functions.
Traditionally, Convolutional Neural Networks make use of the maximum or arithmetic mean in order to reduce the features extracted by convolutional layers in a downsampling process known as pooling. ...However, there is no strong argument to settle upon one of the two functions and, in practice, this selection turns to be problem dependent. Further, both of these options ignore possible dependencies among the data. We believe that a combination of both of these functions, as well as of additional ones which may retain different information, can benefit the feature extraction process. In this work, we replace traditional pooling by several alternative functions. In particular, we consider linear combinations of order statistics and generalizations of the Sugeno integral, extending the latter’s domain to the whole real line and setting the theoretical base for their application. We present an alternative pooling layer based on this strategy which we name “CombPool” layer. We replace the pooling layers of three different architectures of increasing complexity by CombPool layers, and empirically prove over multiple datasets that linear combinations outperform traditional pooling functions in most cases. Further, combinations with either the Sugeno integral or one of its generalizations usually yield the best results, proving a strong candidate to apply in most architectures.
Restricted equivalence functions are well-known functions to compare two numbers in the interval between 0 and 1. Despite the numerous works studying the properties of restricted equivalence ...functions and their multiple applications as support for different similarity measures, an extension of these functions to an n-dimensional space is absent from the literature. In this paper, we present a novel contribution to the restricted equivalence function theory, allowing to compare multivalued elements. Specifically, we extend the notion of restricted equivalence functions from <inline-formula><tex-math notation="LaTeX">L</tex-math></inline-formula> to <inline-formula><tex-math notation="LaTeX">L^{n}</tex-math></inline-formula> and present a new similarity construction on <inline-formula><tex-math notation="LaTeX">L^{n}</tex-math></inline-formula>. Our proposal is tested in the context of color image anisotropic diffusion as an example of one of its many applications.
Due to their high adaptability to varied settings and effective optimization algorithm, Convolutional Neural Networks (CNNs) have set the state-of-the-art on image processing jobs for the previous ...decade. CNNs work in a sequential fashion, alternating between extracting significant features from an input image and aggregating these features locally through “pooling” functions, in order to produce a more compact representation.
Functions like the arithmetic mean or, more typically, the maximum are commonly used to perform this downsampling operation. Despite the fact that many studies have been devoted to the development of alternative pooling algorithms, in practice, “max-pooling” still equals or exceeds most of these possibilities, and has become the standard for CNN construction.
In this paper we focus on the properties that make the maximum such an efficient solution in the context of CNN feature downsampling and propose its replacement by grouping functions, a family of functions that share those desirable properties. In order to adapt these functions to the context of CNNs, we present (a,b)-grouping functions, an extension of grouping functions to work with real valued data. We present different construction methods for (a,b)-grouping functions, and demonstrate their empirical applicability for replacing max-pooling by using them to replace the pooling function of many well-known CNN architectures, finding promising results.
•Grouping pooling generalizes maximum pooling while considering all inputs.•Aggregation functions extended to a real domain (a, b) can act as pooling operator.•Different methods for constructing (a, b)-grouping functions are presented.•(a, b)-grouping poolings improve the gradient flow of max-pooling.
Fusion functions and their most important subclass, aggregation functions, have been successfully applied in fuzzy modeling. However, there are practical problems, such as classification via ...Convolutional Neural Networks (CNNs), where the data to be aggregated are not modeling membership degrees in the unit interval. In this scenario, systems could benefit from the application of operators defined in domains different from 0,1, although, presenting similar behavior of some aggregation functions whose subclasses are currently defined only in the fuzzy context (e.g., overlap functions and t-norms). So, the main objective of this paper is to present a general framework to characterize classes of fusion functions with floating domains, called (a,b)-fusion functions, defined on any closed real interval a,b, based on classes of core fusion functions defined on 0,1. The fundamental aspect of this framework is that the properties of a core fusion function are preserved in the context of the analogous (a,b)-fusion function. Construction methods are presented, and some properties are studied. We also introduce a framework to define fusion functions in which the inputs come from an interval a,b but the output is mapped on a possibly different interval c,d. Finally, we present an illustrative example in image classification via CNNs.
Aggregation operators are unvaluable tools when different pieces of information have to be taken into account with respect to the same object. They allow to obtain a unique outcome when different ...evaluations are available for the same element/object. In this contribution we assume that the opinions are not given in form of isolated values, but intervals. We depart from two “classical” aggregation functions and define a new operator for aggregating intervals based on the two original operators. We study under what circumstances this new function is well defined and we provide a general characterization for monotonicity. We also study the behaviour of this operator when the departing functions are the most common aggregation operators. We also provide an illustrative example demonstrating the practical application of the theoretical contribution to ensemble deep learning models.
In this paper we propose an extension of the notion of deviation-based aggregation function tailored to aggregate multidimensional data. Our objective is both to improve the results obtained by other ...methods that try to select the best aggregation function for a particular set of data, such as penalty functions, and to reduce the temporal complexity required by such approaches. We discuss how this notion can be defined and present three illustrative examples of the applicability of our new proposal in areas where temporal constraints can be strict, such as image processing, deep learning and decision making, obtaining favourable results in the process.
To the authors' knowledge, liver damage after liver radioembolization with yttrium90-labeled microspheres has never been studied specifically.
Using a complete set of data recorded prospectively ...among all patients without previous chronic liver disease treated by radioembolization at the authors' institution from September 2003 to July 2006, patterns of liver damage were identified and possible risk factors were analyzed.
In all, 20% of patients developed a distinct clinical picture that appeared 4 to 8 weeks after treatment and was characterized by jaundice and ascites. Veno-occlusive disease was the histologic hallmark observed in the most severe cases. This form of sinusoidal obstruction syndrome was not observed among patients who never received chemotherapy or in those in whom a single hepatic lobe was treated. Relevant to treatment planning, a possible risk factor was a higher treatment dose in relation to the targeted liver volume. A transjugular intrahepatic stent shunt improved liver function in 2 patients with impending liver failure, although 1 of them eventually died from it.
Radioembolization of liver tumors, particularly after antineoplastic chemotherapy, may result in an uncommon but potentially life-threatening form of hepatic sinusoidal obstruction syndrome that presents clinically with jaundice and ascites.
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