Algorithm 1. Pseudocode of the 2SpamH algorithm which has two stages: (1) prototype selection in the feature space of device use and sensor activity levels to label data points as “missing” or “non-missing” with some confidence based on a threshold, and (2) a k-nearest neighbors (KNN) approach to label non-prototype data points in the feature space based on their proximity to the labeled prototypes. The algorithm returns “missing” labels for all data points.
2SpamH Algorithm
Input: Sensor activity matrix $\mathit{W}$, Device usage matrix $\mathit{Z}$, Prototype selection percentiles $\{{\theta }_{lower},{\theta }_{upper}\}$, Number of nearest neighbors $k$
Output: Missing label matrix $\mathit{M}$
Stage 1: Prototype Selection
1.	Perform PCA on $\mathit{Z}$ and $\mathit{W}$ to obtain the principal components:
	$C^Z=PCA\left(\mathit{Z}\right),C^W=PCA\left(\mathit{W}\right)$
	where $C^Z$ and $C^W$ are vectors of length T of the first principal components of $\mathit{Z}$ and $\mathit{W}$. If ncol($\mathit{Z}$) = 1, then $C^Z=\mathit{Z}$; if ncol($\mathit{W}$) = 1, then $C^W$= $\mathit{W}$.
2.	Construct the feature space $F$ as the set of points $f_t=(C_t^Z,C_t^W)$ for each t:
	$F=\left\{f_t\right|t=1,\dots ,T\}$
	where $f_t=(C_t^Z,C_t^W)$ represents the coordinates of the tth data point in the constructed feature space.
3.	Compute the lower and upper quantiles for $C^Z$ and $C^W$:
	$q_{lower}^Z,q_{upper}^Z=Q(C^Z,{\theta }_{lower}),Q(C^Z,{\theta }_{upper})$
	$q_{lower}^W,q_{upper}^W=Q(C^W,{\theta }_{lower}),Q(C^W,{\theta }_{upper})$
4.	Identify the set of missing prototypes in the feature space $F$:
	$P_{missing}=\{f_t\in F|C_t^Z<q_{lower}^{Z}and{C}_t^W<q_{lower}^W\}$
5.	Identify the set of non-missing prototypes in the feature space F:
	$P_{non\text{-}missing}=\{f_t\in F|C_t^Z>q_{upper}^{Z}and{C}_t^W<q_{upper}^W\}$
6.	For each data point $f_t\in F$:
7.	Assign labels to rows of $\mathit{M}$ based on whether data points fall within the prototype regions:
	$M_{t,:}=\left\{\begin{array}{cc}\mathrm{M}\mathrm{i}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}& \mathrm{i}\mathrm{f}{f}_t\in P_{missing}\\ \mathrm{Non}\text{-}\mathrm{missing}& \mathrm{i}\mathrm{f}{f}_t\in P_{non\text{-}missing}\\ \mathrm{N}\mathrm{A}& \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}\right.$
Stage 2: Labeling Unlabeled Data Using KNN
8.	For each unlabeled data point $f_{t^{\prime }}\in F$ that was not assigned a label in Stage 1:
9.	Implement KNN with $K=k$ and Euclidean distance function           $d\left(f_t,f_{t^{\prime }}\right)=\sqrt{({\left(C_t^Z-{C_t^Z}^{\prime }\right)}^2+{\left(C_t^W-{C_t^W}^{\prime }\right)}^2)}$ to label the remaining unlabeled data points:           $M_{t^{\prime },:}:=\mathrm{K}\mathrm{N}\mathrm{N}\left(f_{t^{\prime }}\right|P_{missing},P_{non\text{-}missing},k)$
Return: Missing label matrix $\mathit{M}.$