Learning Using Concave and Convex Kernels: Applications in Predicting Quality of Sleep and Level of Fatigue in Fibromyalgia

Abstract

Fibromyalgia is a medical condition characterized by widespread muscle pain and tenderness and is often accompanied by fatigue and alteration in sleep, mood, and memory. Poor sleep quality and fatigue, as prominent characteristics of fibromyalgia, have a direct impact on patient behavior and quality of life. As such, the detection of extreme cases of sleep quality and fatigue level is a prerequisite for any intervention that can improve sleep quality and reduce fatigue level for people with fibromyalgia and enhance their daytime functionality. In this study, we propose a new supervised machine learning method called Learning Using Concave and Convex Kernels (LUCCK). This method employs similarity functions whose convexity or concavity can be configured so as to determine a model for each feature separately, and then uses this information to reweight the importance of each feature proportionally during classification. The data used for this study was collected from patients with fibromyalgia and consisted of blood volume pulse (BVP), 3-axis accelerometer, temperature, and electrodermal activity (EDA), recorded by an Empatica E4 wristband over the courses of several days, as well as a self-reported survey. Experiments on this dataset demonstrate that the proposed machine learning method outperforms conventional machine learning approaches in detecting extreme cases of poor sleep and fatigue in people with fibromyalgia.

Keywords: Empatica E4; Learning Using Concave and Convex Kernels; fibromyalgia; self-reported survey.

Figure A1

$Q\left(x\right)={(1+{\lambda }_1{x}^2)}^{-1/{\lambda }_1}$ with for ${\lambda }_1=0.4,0.8,\cdots ,4$ (blue curves) and ${\lambda }_1=0$ (red curve).

Figure A2

$Q\left(\mathbf{x}\right)={(1+x_1^2)}^{-1}{(1+x_2^2)}^{-1}=\alpha$ with $0<\alpha <1$.

Figure A3

$Q\left(\mathbf{x}\right)={(1+2x_1^2)}^{-\frac{1}{2}}{(1+x_2^2)}^{-1}=\alpha$ with $0<\alpha <1$.

Figure 1

Schematic Diagram of the Proposed Processing System for BVP, accelerometer, EDA and temperature signals.