Modeling ADLs with Timed HMMs

Here are some results for using HMM's to recognize ADLs. First about the data set:

This was the dataset that Matthai first recorded at his house. It consists of 17 non-researchers performing 12 activities one from each of 12 classes. The 12 classes were chosen randomly from a total set of 14 classes, so in each user trace there are 2 classes not represented. The classes of activities performed correspond to ADLs on the form that Intel scrounged up that care-givers fill out during home-care visits.

Each user wore an RFID antenna glove and performed their activities in a house that was tagged with 108 RFID tags. The sequence of activities has no information as they were randomly ordered. Each activity was performed atomically with no interruptions. Here are some statistics related to the data:

Here is a graph of the activity durations:

Here is the aggregate of all of those durations approximated by a gamma function

To model this domain with HMMs I segmented each of the traces into their 12 composite activities. I calculated P(RFID objects given activity) for each activity including the possibility of a "nothing" observation. Then I constructed an HMM in which there was one node for each activity. Each node has a self-transition whose probability was calculated based on mean activity duration. Each node also had 13 uniformly distributed out-transitions to the other activity nodes. The HMM started with a uniform prior over all of the activities. I then performed 17 fold cross-validation on the user traces and determined the viterbi path through the state space that corresponded to left out user trace. Here are the results: