346 research outputs found

    Efficient binary fuzzy measure representation and Choquet integral learning

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    The Choquet integral (ChI), a parametric function for information aggregation, is parameterized by the fuzzy measure (FM), which has 2N real-valued variables for N inputs. However, the ChI incurs huge storage and computational burden due to its exponential complexity relative to N and, as a result, its calculation, storage, and learning becomes intractable for even modest sizes (e.g., N = 15). Inspired by empirical observations in multi-sensor fusion and the more general need to mitigate the storage, computational, and learning limitations, we previously explored the binary ChI (BChI) relative to the binary fuzzy measure (BFM). The BChI is a natural _t for many applications and can be used to approximate others. Previously, we investigated different properties of the BChI and we provided an initial representation. In this article, we propose a new efficient learning algorithm for the BChI, called EBChI, by utilizing the BFM properties that add at most one variable per training instance. Furthermore, we provide an efficient representation of the BFM (EBFM) scheme that further reduces the number of variables required for storage and computation, thus enabling the use of the BChI for \big N". Finally, we conduct experiments on synthetic data that demonstrate the efficiency of our proposed techniques

    Efficient Data Driven Multi Source Fusion

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    Data/information fusion is an integral component of many existing and emerging applications; e.g., remote sensing, smart cars, Internet of Things (IoT), and Big Data, to name a few. While fusion aims to achieve better results than what any one individual input can provide, often the challenge is to determine the underlying mathematics for aggregation suitable for an application. In this dissertation, I focus on the following three aspects of aggregation: (i) efficient data-driven learning and optimization, (ii) extensions and new aggregation methods, and (iii) feature and decision level fusion for machine learning with applications to signal and image processing. The Choquet integral (ChI), a powerful nonlinear aggregation operator, is a parametric way (with respect to the fuzzy measure (FM)) to generate a wealth of aggregation operators. The FM has 2N variables and N(2N − 1) constraints for N inputs. As a result, learning the ChI parameters from data quickly becomes impractical for most applications. Herein, I propose a scalable learning procedure (which is linear with respect to training sample size) for the ChI that identifies and optimizes only data-supported variables. As such, the computational complexity of the learning algorithm is proportional to the complexity of the solver used. This method also includes an imputation framework to obtain scalar values for data-unsupported (aka missing) variables and a compression algorithm (lossy or losselss) of the learned variables. I also propose a genetic algorithm (GA) to optimize the ChI for non-convex, multi-modal, and/or analytical objective functions. This algorithm introduces two operators that automatically preserve the constraints; therefore there is no need to explicitly enforce the constraints as is required by traditional GA algorithms. In addition, this algorithm provides an efficient representation of the search space with the minimal set of vertices. Furthermore, I study different strategies for extending the fuzzy integral for missing data and I propose a GOAL programming framework to aggregate inputs from heterogeneous sources for the ChI learning. Last, my work in remote sensing involves visual clustering based band group selection and Lp-norm multiple kernel learning based feature level fusion in hyperspectral image processing to enhance pixel level classification

    Learning nonlinear monotone classifiers using the Choquet Integral

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    In der jĂŒngeren Vergangenheit hat das Lernen von Vorhersagemodellen, die eine monotone Beziehung zwischen Ein- und Ausgabevariablen garantieren, wachsende Aufmerksamkeit im Bereich des maschinellen Lernens erlangt. Besonders fĂŒr flexible nichtlineare Modelle stellt die GewĂ€hrleistung der Monotonie eine große Herausforderung fĂŒr die Umsetzung dar. Die vorgelegte Arbeit nutzt das Choquet Integral als mathematische Grundlage fĂŒr die Entwicklung neuer Modelle fĂŒr nichtlineare Klassifikationsaufgaben. Neben den bekannten Einsatzgebieten des Choquet-Integrals als flexible Aggregationsfunktion in multi-kriteriellen Entscheidungsverfahren, findet der Formalismus damit Eingang als wichtiges Werkzeug fĂŒr Modelle des maschinellen Lernens. Neben dem Vorteil, Monotonie und FlexibilitĂ€t auf elegante Weise mathematisch vereinbar zu machen, bietet das Choquet-Integral Möglichkeiten zur Quantifizierung von Wechselwirkungen zwischen Gruppen von Attributen der Eingabedaten, wodurch interpretierbare Modelle gewonnen werden können. In der Arbeit werden konkrete Methoden fĂŒr das Lernen mit dem Choquet Integral entwickelt, welche zwei unterschiedliche AnsĂ€tze nutzen, die Maximum-Likelihood-SchĂ€tzung und die strukturelle Risikominimierung. WĂ€hrend der erste Ansatz zu einer Verallgemeinerung der logistischen Regression fĂŒhrt, wird der zweite mit Hilfe von Support-Vektor-Maschinen realisiert. In beiden FĂ€llen wird das Lernproblem imWesentlichen auf die Parameter-Identifikation von Fuzzy-Maßen fĂŒr das Choquet Integral zurĂŒckgefĂŒhrt. Die exponentielle Anzahl von Freiheitsgraden zur Modellierung aller Attribut-Teilmengen stellt dabei besondere Herausforderungen im Hinblick auf LaufzeitkomplexitĂ€t und Generalisierungsleistung. Vor deren Hintergrund werden die beiden AnsĂ€tze praktisch bewertet und auch theoretisch analysiert. Zudem werden auch geeignete Verfahren zur KomplexitĂ€tsreduktion und Modellregularisierung vorgeschlagen und untersucht. Die experimentellen Ergebnisse sind auch fĂŒr anspruchsvolle Referenzprobleme im Vergleich mit aktuellen Verfahren sehr gut und heben die NĂŒtzlichkeit der Kombination aus Monotonie und FlexibilitĂ€t des Choquet Integrals in verschiedenen AnsĂ€tzen des maschinellen Lernens hervor

    Efficient Multi-Resolution Fusion for Remote Sensing Data with Label Uncertainty

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    Multi-modal sensor data fusion takes advantage of complementary or reinforcing information from each sensor and can boost overall performance in applications such as scene classification and target detection. This paper presents a new method for fusing multi-modal and multi-resolution remote sensor data without requiring pixel-level training labels, which can be difficult to obtain. Previously, we developed a Multiple Instance Multi-Resolution Fusion (MIMRF) framework that addresses label uncertainty for fusion, but it can be slow to train due to the large search space for the fuzzy measures used to integrate sensor data sources. We propose a new method based on binary fuzzy measures, which reduces the search space and significantly improves the efficiency of the MIMRF framework. We present experimental results on synthetic data and a real-world remote sensing detection task and show that the proposed MIMRF-BFM algorithm can effectively and efficiently perform multi-resolution fusion given remote sensing data with uncertainty.Comment: 4 pages, 3 figures, 2 tables; Accepted to International Geoscience and Remote Sensing Symposium (IGARSS) 2023; Code available at https://github.com/hvak/MIMRF-BF

    Choquistic Regression: Generalizing Logistic Regression using the Choquet Integral

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    In this paper, we propose a generalization of logistic regression based on the Choquet integral. The basic idea of our approach, referred to as choquistic regression, is to replace the linear function of predictor variables, which is commonly used in logistic regression to model the log odds of the positive class, by the Choquet integral. Thus, it becomes possible to capture non-linear dependencies and interactions among predictor variables while preserving two important properties of logistic regression, namely the comprehensibility of the model and the possibility to ensure its monotonicity in individual predictors. In experimental studies with real and benchmark data, choquistic regression consistently improves upon standard logistic regression in terms of predictive accuracy

    An Overview of Classifier Fusion Methods

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    A number of classifier fusion methods have been recently developed opening an alternative approach leading to a potential improvement in the classification performance. As there is little theory of information fusion itself, currently we are faced with different methods designed for different problems and producing different results. This paper gives an overview of classifier fusion methods and attempts to identify new trends that may dominate this area of research in future. A taxonomy of fusion methods trying to bring some order into the existing “pudding of diversities” is also provided

    An Overview of Classifier Fusion Methods

    Get PDF
    A number of classifier fusion methods have been recently developed opening an alternative approach leading to a potential improvement in the classification performance. As there is little theory of information fusion itself, currently we are faced with different methods designed for different problems and producing different results. This paper gives an overview of classifier fusion methods and attempts to identify new trends that may dominate this area of research in future. A taxonomy of fusion methods trying to bring some order into the existing “pudding of diversities” is also provided
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