. Author manuscript; available in PMC: 2017 Jul 1.

Published in final edited form as: IEEE J Biomed Health Inform. 2015 Aug 17;20(4):1188–1194. doi: 10.1109/JBHI.2015.2445754

TABLE IV.

Statistical activity features (μ is the mean of the activity performance features p of size n).

Statistical features

Definition

Formula

Variance

Variance is the measure of spread.

Var (p) = \sum_{k = 1}^{n} {(p_{i} - μ)}^{2}

Autocorrelation

Autocorrelation(AC) is the similarity between observations that are displaced in time. We calculate autocorrelation at lag 1.

AC-lag1 (p) = \frac{\sum_{i = 1}^{n - 1} (p_{i} - μ) (p_{i} + 1 - μ)}{\sum_{n = 1}^{n} {(p_{i} - μ)}^{2}}

Skewness

Skewness measures the degree of asymmetry in the distribution of values.

skewnewess (p) = \frac{\frac{1}{n} \sum_{i = 1}^{n} {(p_{i} - μ)}^{3}}{{(\frac{1}{n} \sum_{i = 1}^{n} {(p_{i} - μ)}^{2})}^{3 / 2}}

Kurtosis

Kurtosis measures the amount of peakedness of the distribution toward the mean.

kurtosis (p) = \frac{\frac{1}{n} \sum_{i = 1}^{n} {(p_{i} - μ)}^{4}}{{(\frac{1}{n} \sum_{i = 1}^{n} {(p_{i} - μ)}^{2})}^{3}}

Change

Change characterizes the amount of change in an individual’s activity performance over time.

Algorithm 2