Figure 7.

Visualising the switching AR posterior state probabilities for data from a single walking test. The log of the input state probabilities $p_{z_1},\dots ,p_{z_T}$ is projected into 2D using linear discriminant analysis (LDA), and projections are denoted with $p_{z_t}^{*}$ where the $p_{z_t}$ is a $K^{+}$ dimensional vector and $p_{z_t}^{*}$ is 2D. Input projections are labeled with adherence (red) and violation (blue). The “linear” structure can be explained with the fact that typically, a data point $x_t$ is associated with high probability to only one of the $K^{+}$ AR states in the behavioral segmentation (and low probability for the remaining AR states) so that the input vector $p_{z_t}$ is sparse. The decision boundary of the multinomial naive Bayes classifier is also projected (using the same LDA coefficients) into 2D (black line). A few outlier projections $p_{z_t}^{*}$ are outside the plot axis limits, but they do not significantly affect the decision boundary and yet reduce the visual interpretability of the projection of the bulk of the data.