EFM: evolutionary fuzzy model for dynamic activities recognition using a smartphone accelerometer

Abstract

Activity recognition is an emerging field of research that enables a large number of human-centric applications in the u-healthcare domain. Currently, there are major challenges facing this field, including creating devices that are unobtrusive and handling uncertainties associated with dynamic activities. In this paper, we propose a novel Evolutionary Fuzzy Model (EFM) to measure the uncertainties associated with dynamic activities and relax the domain knowledge constraints which are imposed by domain experts during the development of fuzzy systems. Based on the time and frequency domain features, we define the fuzzy sets and estimate the natural grouping of data through expectation maximization of the likelihoods. A Genetic Algorithm (GA) is investigated and designed to determine the optimal fuzzy rules. To evaluate the EFM, we performed experiments on seven daily life activities of ten human subjects. Our experiments show significant improvement of 9 % in class-accuracy and 11 % in the F-measures of recognized activities compared to existing counterparts. The practical solution to dynamic activity recognition problems is expected to be an EFM, due to EFM’s utilization of smartphones and natural way of handling uncertainties.

Appendix

In this section, we present details of the parameters for Gaussian membership estimation for expectation maximization algorithms, which are used for computing μ _k and δ _k . The log-likelihood of the observed data Y={Y _m }, m=1,…,M is calculated as:

$$ l (\varTheta )=\sum_{m=1}^{M} \mathrm{log}p_{mix} (Y_{m}|\varTheta ) $$

(12)

Expectation Step (E-Step)

(13)

To fit an observed set of data points {Y _m }, the mixing portion “w _mk ” and the components “K” that generated each data point “Y _m ” is unknown. The objective is to find the parameter vector θ _k =[μ _k ,δ _k ].

Inserting (13) into (12) gives,

$$l (\varTheta )=\sum_{m=1}^{M}\log \sum_{k=1}^{K}p (Y_{m}\ |\ \theta_{k} )w_{mk} $$

For Expectation step, use Jensen’s inequality,

At the Maximization step (M-Step)

$$ \nabla_{\theta _{k}}\sum_{m=1}^{M} \sum_{l=1}^{K}w_{mk}\mathrm{log}p (Y_{m}\ |\ \theta_{l} ) $$

(14)

At maximum, the partial derivations w.r.t. all parameters vanish:

$$ \nabla_{\theta _{k}}l (\varTheta )=\sum _{m=1}^{M}\frac{w_{mk}}{p (Y_{m}\ |\ \theta_{k} )}\ \nabla_{\theta _{k}}p (Y_{m}\ |\ \theta_{k} ) $$

(15)

In order to find the parameters of accelerometer data, our problem is a similar problem to the one dimensional Gaussian mixture, where we do not know the variances or mixture portions either. The parameter vector is θ _k =[μ _k ,δ _k ] is computed as:

$$ p (Y_{m}\ \vert \ \theta_{k})= \frac{1}{\sqrt{2\pi \delta_{k}^{2}}} \exp \biggl\{-\frac{ (Y_{m}-\mu_{k} )^{2}}{2\delta_{k}^{2}} \biggr\} $$

(16)

The Expectation step is easily defined by inserting (16) into (13). For Maximization, inserting (16) into (15) and taking the derivative w.r.t. μ _k gives,

(17)

Taking the derivative w.r.t. δ _k

(18)

Equations (17) and (18) are required parameters for the Gaussian membership function.