Representation of Functional Data in Neural Networks

Functional Data Analysis (FDA) is an extension of traditional data analysis to functional data, for example spectra, temporal series, spatio-temporal images, gesture recognition data, etc. Functional data are rarely known in practice; usually a regular or irregular sampling is known. For this reason, some processing is needed in order to benefit from the smooth character of functional data in the analysis methods. This paper shows how to extend the Radial-Basis Function Networks (RBFN) and Multi-Layer Perceptron (MLP) models to functional data inputs, in particular when the latter are known through lists of input-output pairs. Various possibilities for functional processing are discussed, including the projection on smooth bases, Functional Principal Component Analysis, functional centering and reduction, and the use of differential operators. It is shown how to incorporate these functional processing into the RBFN and MLP models. The functional approach is illustrated on a benchmark of spectrometric data analysis.Comment: Also available online from: http://www.sciencedirect.com/science/journal/0925231

Context Selection on Attributed Graphs for Outlier and Community Detection

Today\u27s applications store large amounts of complex data that combine information of different types. Attributed graphs are an example for such a complex database where each object is characterized by its relationships to other objects and its individual properties. Specifically, each node in an attributed graph may be characterized by a large number of attributes. In this thesis, we present different approaches for mining such high dimensional attributed graphs

Tensor Analysis and Fusion of Multimodal Brain Images

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks that underpin human cognitive processes by analysis of different neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the multimodal, multi-scale nature of neuroimaging data is well reflected by a multi-way (tensor) structure where the underlying processes can be summarized by a relatively small number of components or "atoms". We introduce Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network notation in order to analyze these models. These diagrams not only clarify matrix and tensor EEG and fMRI time/frequency analysis and inverse problems, but also help understand multimodal fusion via Multiway Partial Least Squares and Coupled Matrix-Tensor Factorization. We show here, for the first time, that Granger causal analysis of brain networks is a tensor regression problem, thus allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI recordings shows the potential of the methods and suggests their use in other scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

Artificial intelligence in steam cracking modeling : a deep learning algorithm for detailed effluent prediction

Chemical processes can benefit tremendously from fast and accurate effluent composition prediction for plant design, control, and optimization. The Industry 4.0 revolution claims that by introducing machine learning into these fields, substantial economic and environmental gains can be achieved. The bottleneck for high-frequency optimization and process control is often the time necessary to perform the required detailed analyses of, for example, feed and product. To resolve these issues, a framework of four deep learning artificial neural networks (DL ANNs) has been developed for the largest chemicals production process-steam cracking. The proposed methodology allows both a detailed characterization of a naphtha feedstock and a detailed composition of the steam cracker effluent to be determined, based on a limited number of commercial naphtha indices and rapidly accessible process characteristics. The detailed characterization of a naphtha is predicted from three points on the boiling curve and paraffins, iso-paraffins, olefins, naphthenes, and aronatics (PIONA) characterization. If unavailable, the boiling points are also estimated. Even with estimated boiling points, the developed DL ANN outperforms several established methods such as maximization of Shannon entropy and traditional ANNs. For feedstock reconstruction, a mean absolute error (MAE) of 0.3 wt% is achieved on the test set, while the MAE of the effluent prediction is 0.1 wt%. When combining all networks-using the output of the previous as input to the next-the effluent MAE increases to 0.19 wt%. In addition to the high accuracy of the networks, a major benefit is the negligible computational cost required to obtain the predictions. On a standard Intel i7 processor, predictions are made in the order of milliseconds. Commercial software such as COILSIM1D performs slightly better in terms of accuracy, but the required central processing unit time per reaction is in the order of seconds. This tremendous speed-up and minimal accuracy loss make the presented framework highly suitable for the continuous monitoring of difficult-to-access process parameters and for the envisioned, high-frequency real-time optimization (RTO) strategy or process control. Nevertheless, the lack of a fundamental basis implies that fundamental understanding is almost completely lost, which is not always well-accepted by the engineering community. In addition, the performance of the developed networks drops significantly for naphthas that are highly dissimilar to those in the training set. (C) 2019 THE AUTHORS. Published by Elsevier LTD on behalf of Chinese Academy of Engineering and Higher Education Press Limited Company

Pricing average price advertising options when underlying spot market prices are discontinuous

Advertising options have been recently studied as a special type of guaranteed contracts in online advertising, which are an alternative sales mechanism to real-time auctions. An advertising option is a contract which gives its buyer a right but not obligation to enter into transactions to purchase page views or link clicks at one or multiple pre-specified prices in a specific future period. Different from typical guaranteed contracts, the option buyer pays a lower upfront fee but can have greater flexibility and more control of advertising. Many studies on advertising options so far have been restricted to the situations where the option payoff is determined by the underlying spot market price at a specific time point and the price evolution over time is assumed to be continuous. The former leads to a biased calculation of option payoff and the latter is invalid empirically for many online advertising slots. This paper addresses these two limitations by proposing a new advertising option pricing framework. First, the option payoff is calculated based on an average price over a specific future period. Therefore, the option becomes path-dependent. The average price is measured by the power mean, which contains several existing option payoff functions as its special cases. Second, jump-diffusion stochastic models are used to describe the movement of the underlying spot market price, which incorporate several important statistical properties including jumps and spikes, non-normality, and absence of autocorrelations. A general option pricing algorithm is obtained based on Monte Carlo simulation. In addition, an explicit pricing formula is derived for the case when the option payoff is based on the geometric mean. This pricing formula is also a generalized version of several other option pricing models discussed in related studies.Comment: IEEE Transactions on Knowledge and Data Engineering, 201

Multiscale Image Based Flow Visualization

We present MIBFV, a method to produce real-time, multiscale animations of flow datasets. MIBFV extends the attractive features of the Image-Based Flow Visualization (IBFV) method, i.e. dense flow domain coverage with flow-aligned noise, real-time animation, implementation simplicity, and few (or no) user input requirements, to a multiscale dimension. We generate a multiscale of flow-aligned patterns using an algebraic multigrid method and use them to synthesize the noise textures required by IBFV. We demonstrate our approach with animations that combine multiple scale noise layers, in a global or level-of-detail manner