Enabling Explainable Fusion in Deep Learning with Fuzzy Integral Neural Networks

Information fusion is an essential part of numerous engineering systems and biological functions, e.g., human cognition. Fusion occurs at many levels, ranging from the low-level combination of signals to the high-level aggregation of heterogeneous decision-making processes. While the last decade has witnessed an explosion of research in deep learning, fusion in neural networks has not observed the same revolution. Specifically, most neural fusion approaches are ad hoc, are not understood, are distributed versus localized, and/or explainability is low (if present at all). Herein, we prove that the fuzzy Choquet integral (ChI), a powerful nonlinear aggregation function, can be represented as a multi-layer network, referred to hereafter as ChIMP. We also put forth an improved ChIMP (iChIMP) that leads to a stochastic gradient descent-based optimization in light of the exponential number of ChI inequality constraints. An additional benefit of ChIMP/iChIMP is that it enables eXplainable AI (XAI). Synthetic validation experiments are provided and iChIMP is applied to the fusion of a set of heterogeneous architecture deep models in remote sensing. We show an improvement in model accuracy and our previously established XAI indices shed light on the quality of our data, model, and its decisions.Comment: IEEE Transactions on Fuzzy System

Fuzzy Interval-Valued Multi Criteria Based Decision Making for Ranking Features in Multi-Modal 3D Face Recognition

Soodamani Ramalingam, 'Fuzzy interval-valued multi criteria based decision making for ranking features in multi-modal 3D face recognition', Fuzzy Sets and Systems, In Press version available online 13 June 2017. This is an Open Access paper, made available under the Creative Commons license CC BY 4.0 https://creativecommons.org/licenses/by/4.0/This paper describes an application of multi-criteria decision making (MCDM) for multi-modal fusion of features in a 3D face recognition system. A decision making process is outlined that is based on the performance of multi-modal features in a face recognition task involving a set of 3D face databases. In particular, the fuzzy interval valued MCDM technique called TOPSIS is applied for ranking and deciding on the best choice of multi-modal features at the decision stage. It provides a formal mechanism of benchmarking their performances against a set of criteria. The technique demonstrates its ability in scaling up the multi-modal features.Peer reviewedProo

Efficient Data Driven Multi Source Fusion

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

Explainable parts-based concept modeling and reasoning

State-of-the-art artificial intelligence (AI) learning algorithms heavily rely on deep learning methods that exploit correlation between inputs and outputs. While effective, these methods typically provide little insight to the reasoning process used by the machine, which makes it difficult for human users to understand the process, trust the decisions made by the system, and control emergent behaviors in the system. One method to fix this is eXplainable AI (XAI), which aims to create algorithms that perform well while also providing explanations to users about the reasoning process to mitigate the problems outlined above. In this thesis, I focus on advancing the research around XAI techniques by introducing systems that provide explanations through the use of partsbased concept modeling and reasoning. Instead of correlating input to output, I correlate input to sub-parts or features of the overall concept being learned by the system. These features are used to model and reason about a concept using an explicitly defined structure. These structures provide explanations to the user by nature of how they are defined. Specifically, I introduce a shallow and deep Adaptive Neuro-Fuzzy Inference System (ANFIS) that can reason in noisy and uncertain contexts. ANFIS provides explanations in the form of learned rules that combine features to determine the overall output concept. I apply this system to real geospatial parts-based reasoning problems and evaluate the performance and explainability of the algorithm. I discover some drawbacks to the ANFIS system as traditionally defined due to dead and diminishing gradients. This leads me to focus on how to model parts-based concepts and their inherent uncertainty in other ways, namely through Spatially Attributed Relation Graphs (SARGs). I incorporate human feedback to refine the machine learning of concepts using SARGs. Finally, I present future directions for research to build on the progress presented in this thesis.Includes bibliographical references

Feature and Decision Level Fusion Using Multiple Kernel Learning and Fuzzy Integrals

The work collected in this dissertation addresses the problem of data fusion. In other words, this is the problem of making decisions (also known as the problem of classification in the machine learning and statistics communities) when data from multiple sources are available, or when decisions/confidence levels from a panel of decision-makers are accessible. This problem has become increasingly important in recent years, especially with the ever-increasing popularity of autonomous systems outfitted with suites of sensors and the dawn of the ``age of big data.\u27\u27 While data fusion is a very broad topic, the work in this dissertation considers two very specific techniques: feature-level fusion and decision-level fusion. In general, the fusion methods proposed throughout this dissertation rely on kernel methods and fuzzy integrals. Both are very powerful tools, however, they also come with challenges, some of which are summarized below. I address these challenges in this dissertation. Kernel methods for classification is a well-studied area in which data are implicitly mapped from a lower-dimensional space to a higher-dimensional space to improve classification accuracy. However, for most kernel methods, one must still choose a kernel to use for the problem. Since there is, in general, no way of knowing which kernel is the best, multiple kernel learning (MKL) is a technique used to learn the aggregation of a set of valid kernels into a single (ideally) superior kernel. The aggregation can be done using weighted sums of the pre-computed kernels, but determining the summation weights is not a trivial task. Furthermore, MKL does not work well with large datasets because of limited storage space and prediction speed. These challenges are tackled by the introduction of many new algorithms in the following chapters. I also address MKL\u27s storage and speed drawbacks, allowing MKL-based techniques to be applied to big data efficiently. Some algorithms in this work are based on the Choquet fuzzy integral, a powerful nonlinear aggregation operator parameterized by the fuzzy measure (FM). These decision-level fusion algorithms learn a fuzzy measure by minimizing a sum of squared error (SSE) criterion based on a set of training data. The flexibility of the Choquet integral comes with a cost, however---given a set of N decision makers, the size of the FM the algorithm must learn is 2N. This means that the training data must be diverse enough to include 2N independent observations, though this is rarely encountered in practice. I address this in the following chapters via many different regularization functions, a popular technique in machine learning and statistics used to prevent overfitting and increase model generalization. Finally, it is worth noting that the aggregation behavior of the Choquet integral is not intuitive. I tackle this by proposing a quantitative visualization strategy allowing the FM and Choquet integral behavior to be shown simultaneously