Walking fingerprinting

Abstract

We consider the problem of predicting an individual's identity from accelerometry data collected during walking. In a previous paper, we transformed the accelerometry time series into an image by constructing the joint distribution of the acceleration and lagged acceleration for a vector of lags. Predictors derived by partitioning this image into grid cells were used in logistic regression to predict individuals. Here, we (a) implement machine learning methods for prediction using the grid cell-derived predictors; (b) derive inferential methods to screen for the most predictive grid cells while adjusting for correlation and multiple comparisons; and (c) develop a novel multivariate functional regression model that avoids partitioning the predictor space. Prediction methods are compared on two open source acceleometry data sets collected from: (a) 32 individuals walking on a $1.06$ km path; and (b) six repetitions of walking on a 20 m path on two occasions at least 1 week apart for 153 study participants. In the 32-individual study, all methods achieve at least 95% rank-1 accuracy, while in the 153-individual study, accuracy varies from 41% to 98%, depending on the method and prediction task. Methods provide insights into why some individuals are easier to predict than others.

Keywords: accelerometry; biometrics; functional data.

Figure 1.

Eight 3-s intervals shown from different study participants. Data are a single time series obtained as the sum of squares of observed accelerations along the three axes. The left panels provide the information about the identity of study participants, whereas the right panels do not. The questions are (a) among the individuals shown in the right plots, is there any individual whose data are displayed in the left panels? and (b) if yes, then which ones? The answer to the riddle is provided at the end of the discussion and in the acknowledgements.

Figure 2.

Subset of the empirical joint distribution of acceleration and lag acceleration for Subject 19 in the IU data. The pairs $\{v_{ij}(s-u),v_{ij}(s)\}$ are plotted for $u=1,15,30,45$ centiseconds (columns) and $j=1,2$ s (rows).

Figure 3.

Predictor extraction for Subject 19. The values of $X_{ijc}$ for Subject 19 in the IU data are shown for $u=1,15,30,45$ (columns) and $j=1,2$ (rows). The white number in each grid cell is the value of $X_{ijc}$ for that cell. For example, $X_{i=19,j=2,c=[0.75,1.00),[0.75,1.00)}=61$ and is shown in the bottom-left corner of the plot. Only a subset of the grid cells is shown as the other grid cells have no observations for these two seconds.

Figure 4.

Classification metrics over varying number of seconds in testing data. First row: rank-1 accuracies; Second row: rank-5 accuracies. Each column corresponds to different data and prediction tasks. The lines show how accuracy for each model changes as the number of seconds averaged over in the testing data is increased.

Figure 5.

Significant grid cells from image partitioning, Subject 143 ZJU Session 1. (a) Grid cells that are significant in distinguishing Subject 143 from the other subjects in the ZJU S1 task. (b) Grid cells that are significant after adjusting for correlation and multiplicity. (a) Unadjusted and (b) Correlation and Multiplicity Adjusted.

Figure 6.

Comparison of data from well and poorly predicted subjects. Panel (a) demonstrates a subset of the joint distribution for subject 5 (left) and subject 79 (right) in session 1 (top row) and session 2 (bottom row). The images are similar between sessions and these individuals were correctly identified in session 2 from their session 1 data. Panel (b) shows the same subset of the joint distribution for subject 3 (left) and subject 136 (right) in session 1 (top row) and session 2 (bottom row). The images do not look similar, and hence these individuals were not correctly predicted in the ZJU S1S2 task.