Modeling Deep Learning Neural Networks With Denotational Mathematics in UbiHealth Environment

Modeling Deep Learning Neural Networks With Denotational Mathematics in UbiHealth Environment

John Sarivougioukas (General Hospital of Athens “G. Gennimatas”, Athens, Greece) and Aristides Vagelatos (CTI&P, Greece)
DOI: 10.4018/IJSSCI.2020070102
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Abstract

Ubiquitous computing environments that are involved in healthcare applications are typically characterized by dynamically changing contexts. The contextual information must be efficiently processed in order to support medical decision making. The ubiquitous computing healthcare ecosystem must be capable of extracting medically valuable characteristics, making precise decisions, and taking medically appropriate actions. In this framework, deep learning networks can be used for data fusion of large and complex sets of information in order to make the appropriate medical diagnoses. The quality of decisions depends on the selection of appropriate network weights, which define a transformation of the given input into a diagnosis. Denotational mathematics provide a promising framework for modeling deep learning networks and adjusting their behavior by adapting their weights for the given input. Furthermore, the fidelity of the network's output can be controlled by applying a regulator to the weights values. The authors show that Denotational Mathematics can serve as a rigorous framework for modeling and controlling deep learning networks, thereby enhancing the quality of medical decision making.
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Introduction

The term UbiHealth (Sarivougioukas et al., 2019) refers to the class of distributed applications in ubiquitous computing (also called UbiComp) environments that support personalized healthcare needs. Such applications are typically met in home healthcare environments (Rodríguez & Favela, 2012). In UbiComp environments, new contextual information emerges and it is dynamically adapted through time. Consequently, new data is constantly generated, requiring adaptive artificial intelligence techniques that are capable of effectively processing the data in order to support the end-users (Shilit & Theimer, 1994). The necessity of the UbiComp environment to be aware in order to effectively support the end-user is also referred as context-awareness (Day, 2001; Abowd et al., 1999). Recently, denotational mathematics (DM) (Wang, 2009a) have been shown to be an elegant framework for modeling UbiHealth environments (Sarivougioukas & Vagelatos, 2014).

In UbiHealth environments, medical cognition can be produced through trained neural networks. Deep learning (Schmidhuber, 2015) has proved to be a valuable tool in extracting the features of occurring instantaneous medical context (LeCun, Bengio & Hinton, 2015). In this framework, direct correspondence is built among the contextual parameters and the weights of the employed network. Moreover, magnitude tolerance for the observed contextual parameters can be transferred to the weights of the network. Thus, properly adapting the weights of the network is essential for ensuring soundness and quality of the network’s output.

In the present paper, DM are proposed for the formal description of Deep Learning Networks (DLNs) (Goodfellow et al., 2016). The modeled DLN is incorporated in an UbiHealth environment for medical diagnoses purposes. This is achieved by considering the DLN in a first-order loop and associating it with a weights regulator. The model assumes the existence of a memory structure that stores network weights related to specific inputs of the network provided by local or remote sensors through the web. The stored weights are evoked from memory and fed into the weights regulator as illustrated in Figure 1. The block diagram presented in Figure 1 provides an overall view of the proposed model. The typical Input, deep learning network (DLN), and the Output blocks are standing up by a memory support, matching, and weights regulator block units. Thus, the received input vectors are matched with the ready-made available vector values required to be provided to the weights regulator where the appropriate and suitable adjustment is performed. The regulator is required in order to support the DLN optimizing the internally applying algorithm of operation which is most suitable for the desired each time application.

The operation of the proposed system assumes the existence of appropriate weights for each set of input signals. The weights regulator monitors the network’s output and fine-tunes the weights in order to improve the quality and accuracy of the output. In other words, the regulator receives the appropriate set of weights that match the corresponding input, and dynamically optimizes it until the desirable output is obtained according to the post-training period.

The benefits gained from the proposed approach are related to the underlying fusion of extended sets of heterogeneous information received from various sources of the UbiHealth ecosystem (Sarivougioukas et al., 2016). The fused information produces medical diagnoses that require appropriate weights of the employed DLN. Thus, for each set of input values there exists a corresponding set of weights resulting in the appropriate diagnoses (network’s output).

Figure 1.

The proposed DLN model

IJSSCI.2020070102.f01

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