A Unified Framework for Behaviour Monitoring and Abnormality Detection for Smart Home

Algorithm 1

Algorithm for X-means clustering.

(1) Set the maximum number of clusters to be .

(2) Repeat the steps (3) to (6) for k₀ =2 to

(3) For K=k₀ apply K-means clustering

(4) Label the divided clusters as C₁,C₂,C₃…

(5) Repeat the steps (4.a) to (4.c) for

(5.a) For every cluster , generate two new centroids

from original centroid

(by transforming the initial value of centroid in

two different directions along a randomly chosen

value of vector by an amount equals to their

cluster size.)

(5.b) Apply K means with K=2. Label the divided

clusters ,

(5.c) Apply the model selection test BIC to check if two

clusters better than original single cluster in each

case. Replace each centroid based on the criteria

of model selection.

Where p - no. of observations, k - clusters and - log probability.

(5.d) Let BIC_C represents –score of children clusters

and BIC_P –score of parent cluster

(5.e) If BIC_C>BIC_P, the two-divided clusters are

accepted, and the division is continued;

(5.f) If BIC_C<BIC_P the two-divided clusters are

discarded, and the original cluster is kept;

(6) If the condition of convergence is not fulfilled, go to

Step (2). Otherwise, Stop.