Visual process maps: a visualization tool for discovering habits in smart homes

Abstract

Models of human habits in smart spaces can be expressed by using a multitude of representations whose readability influences the possibility of being validated by human experts. The visual analysis by domain experts allows to identify stages of human habits that could be automatized or simplified by redesigning the environment. In this paper, we present a visual analysis pipeline for graphically visualizing human habits, starting from the sensor log of a smart space,. We apply techniques borrowed from the area of business process automation and mining on a version of the sensor log preprocessed in order to translate raw sensor measurements into human actions. The proposed method is employed to automatically extract models to be reused for ambient intelligence. A user evaluation demonstrates the effectiveness of the approach, and compares it with respect to a relevant state-of-the-art visual tool, namely Situvis.

Appendix A: Jaccard similarity measure

In this paper, we use the Jaccard similarity factor in three different variants: (i) the weighted algorithm on the same subset of nodes, (ii) the weighted algorithm on the same subset of edges, and (iii) a non weighted version (i.e., considering only the graph structure or topology) that, on the same subset of nodes, computes how many edges are in common.

The weighted version is as it follows: given two graphs $G_1$ and $G_2$ with the same nodes (i.e., the same event types), the weighted Jaccard similarity $J(G_1,G_2)$ between the two graphs is given by:

$$\begin{aligned} J(G_1,G_2) = \frac{{\sum _{i}^{}{\sum _{j}^{}{min(G_1(n_i, n_j), G_2(n_i, n_j))}}+\sum _{i}^{}{min(G_1(n_i), G_2(n_i))}}}{{\sum _{i}^{}{\sum _{j}^{}{max(G_1(n_i, n_j), G_2(n_i, n_j))}}+\sum _{i}^{}{max(G_1(n_i), G_2(n_i))}}} \end{aligned}$$

(1)

where $G_k(n_i, n_j)$ is the weight assigned to the arc from $n_i$ to $n_j$ in $G_k$ (if the arc is absent the weight is 0), $G_k(n_i)$ is the weight assigned to node $n_i$ in graph $G_k$, and min (resp. max) are binary operators returning the minimum (resp. the maximum) between two operands. By definition the value of J is always a positive real number minor or equal to 1.

Conversely the non weighted Jaccard coefficient is defined as it follows: given two graphs $G_1 = \left\langle E_1, V_1 \right\rangle$ and $G_2 = \left\langle E_2, V_2 \right\rangle$ with $E_i$ and $V_i$ respectively the set of the edges and the set of the nodes of graph $G_i$, the Jaccard similarity coefficient J between them is computed as $J = {{E_1 \cap E_2}\over {E1 \cup E_2}}$, on $V_1 \cap V_2$. In other terms, on common sub-graph’s nodes between the two graphs, Jaccard coefficient J indicates if there are the same connections between the same nodes of the graphs.