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Table 1 System features and calculation

From: Predicting functional performance via classification of lower extremity strength in older adults with exergame-collected data

Features Description Calculation
\({Com}_{{Avg}_{Direction}}\) Average \({\varvec{c}}{\varvec{o}}{\varvec{m}}\) value for movements in each direction, where \({n}_{COM,Direction}\) represents the number of steps for each direction. Four two-dimensional features \((x,y)\) per playthrough \(\frac{{\sum }_{t=1}^{{n}_{COM,Direction}}{\varvec{c}}{\varvec{o}}{\varvec{m}}\left(t\right)}{{n}_{COM,Direction}}\)
\(Direction=Up \leftrightarrow {com}_{y}>0.5, \left|{com}_{x}\right|<0.1\)
\(Direction=Down \leftrightarrow {com}_{y}<-0.5, \left|{com}_{x}\right|<0.1\)
\(Direction=Right \leftrightarrow {com}_{x}>0.5, \left|{com}_{y}\right|<0.1\)
\(Direction=Left \leftrightarrow {com}_{x}<-0.5, \left|{com}_{y}\right|<0.1\)
\({Com}_{{Std}_{Direction}}\) Standard deviation of \({\varvec{c}}{\varvec{o}}{\varvec{m}}\), for each direction, as above. Eight features per playthrough \(\sqrt{\frac{{\sum }_{t=1}^{{n}_{COM,Direction}}{\left({com}_{i}\left(t\right)-{{Com}_{Avg}}_{Direction,i}\right)}^{2}}{{n}_{COM,j}-1}},\)
\(i=x,y, Direction=Up,Down,Left, Right\)
\({Balance}_{Up}, {Balance}_{Down}\) Average value of \({com}_{y}\) for all values where \({com}_{y}>0\) (up) or \({com}_{y}<0\) (down), where \({n}_{COM}\) is the number of \({\varvec{c}}{\varvec{o}}{\varvec{m}}\) samples. Two features per playthrough \(\frac{{\sum }_{t=1}^{{n}_{COM}}{com}_{y}(t)}{{n}_{COM}}:{com}_{y}>0\), \(\frac{{\sum }_{t=1}^{{n}_{COM}}{com}_{y}(t)}{{n}_{COM}}:{com}_{y}<0\)
\({Balance}_{Right}, {Balance}_{Left}\) Average value of \({com}_{x}\) for all values where \({com}_{x}>0\) (right) or \({com}_{x}<0\) (left). Two features per playthrough \(\frac{{\sum }_{t=1}^{{n}_{COM}}{com}_{x}(t)}{{n}_{COM}}:{com}_{x}>0\), \(\frac{{\sum }_{t=1}^{{n}_{COM}}{com}_{x}(t)}{{n}_{COM}}:{com}_{x}<0\)
\({Avg}_{x}, {Avg}_{y}\) Average value of \({com}_{x}\) and \({com}_{y}\). Two features \((x,y)\) per playthrough \(\frac{{\sum }_{t=1}^{{n}_{COM}}{com}_{x}(t)}{{n}_{COM}}\), \(\frac{{\sum }_{t=1}^{{n}_{COM}}{com}_{y}(t)}{{n}_{COM}}\)
\({Max}_{x}, {Max}_{y}\), \({Min}_{x}, {Min}_{y}\) Maximum and minimum value of \({com}_{x}\) and \({com}_{y}\). Two features \((x,y)\) per playthrough \(Max ({com}_{x}\left(t\right),\forall t)\), \(Max ({com}_{y}\left(t\right),\forall t)\),
\(Min ({com}_{x}\left(t\right),\forall t)\),\(Max ({com}_{y}\left(t\right),\forall t)\)
\({Std}_{x}, {Std}_{y}\) Standard deviation of \({com}_{x}\) and \({com}_{y}\). Two features \((x,y)\) per playthrough \(\sqrt{\frac{{\sum }_{t=1}^{{n}_{COM}}{\left({com}_{i}\left(t\right)-{Avg}_{i}\right)}^{2}}{{n}_{COM}-1}}, i=x,y\)
\({If}_{Avg}\), \({If}_{Max}\) Average \(\mathrm{i}f\left(t\right)\) value and maximum for the whole playthrough. Two features per playthrough \(\frac{{\sum }_{t=1}^{{n}_{COM}}if(t)}{{n}_{COM}}\), \(Max (\mathrm{i}f\left(t\right),\forall t)\)
\({If}_{Threshold,i}\) Number of times \(\mathrm{i}f\left(t\right)>i, i=\left[\mathrm{0.5,1},\mathrm{1.5,2}\right].\) Normalized by the total number of samples. Four features per playthrough \(\frac{N (if(\mathrm{t})>i)}{{n}_{COM}}, i=\mathrm{0.5,1},\mathrm{1.5,2}\)
\({If}_{{Sum}_{Avg}}\), \({If}_{{Sum}_{Max}}\) Average value and maximum of the sum of the last 25 values of \(\mathrm{i}f\left(t\right)\) for the whole playthrough. Two features per playthrough \(\frac{{\sum }_{t=1}^{{n}_{COM}}{if}_{Sum}(t)}{{n}_{COM}}, {if}_{Sum}\left(t\right)={\sum }_{i=t-24}^{t}if(\mathrm{t})\), \(Max ({if}_{Sum}(t),\forall t)\)
\({If}_{{Sum}_{Overx}}\) Number of times \({If}_{Sum}\left(t\right)>i,i=\left[\mathrm{0.5,1},\mathrm{1.5,2}\right].\) Normalized by total playthrough time. Four features per playthrough \(\frac{N ({if}_{Sum}(t)>i)}{{n}_{COM}}, i=\mathrm{0.5,1},\mathrm{1.5,2}\)
\({Step}_{Avg}\) Average time between steps, excluding the first step, defining \({Step}_{Time}(i)\) as the time in seconds in which step \(i\) occurred, and \({n}_{Steps}\) as the total number of steps in the playthrough. One feature per playthrough \(\frac{{\sum }_{i=2}^{{n}_{Steps}}{Step}_{Time}\left(i\right)-{Step}_{Time}(i-1)}{{n}_{Steps}}\)
\({Step}_{Std}\) Standard deviation of time between steps, excluding the first step. One feature per playthrough \(\sqrt{\frac{{\sum }_{i=2}^{{n}_{Steps}}{\left({Step}_{Time}\left(i\right)-{Step}_{Time}(i-1)-{Step}_{Avg}\right)}^{2}}{{n}_{Steps}-1}}\)