# Predicting Activities of Daily Living with Spatio-Temporal Information
## 2 Related Work  
The work of [PERSON], [PERSON] and [PERSON] [6] is among the earlier work that used compression for activity recognition. They partitioned the home into different zones, where each zone is represented by a symbol. A dictionary of user movements is trained using the LZ78 compression algorithm. They then applied prediction by partial matching (PPM) to predict user next location based on the phrases in the dictionary. [PERSON] and [PERSON] [7] proposed a sequential prediction algorithm called Active LeZi, to predict the user's next action based on an observed sequence of user-home interactions. Similar to the approach taken in [6], they built a representation of user-home interactions with LZ78 and used PPM to calculate the probability of the next most probable action.  
In the work of [PERSON], [PERSON] and [PERSON] [8], they introduced an adaptive sequence prediction algorithm that generates a finite-order Markov model and makes predictions based on PPM. To better capture the boundary between two opposite events, they applied an episode evaluation criteria that makes use of sensor ON and OFF states to indicate the start and end of an episode. An enhancement to this work is seen in [9] where they used a prefix tree-based data model to learn and predict user actions.  
A variation to the work described above is the work of [PERSON], [PERSON] and [PERSON] [10]. They used compression as an unsupervised learning method to identify activities in an unlabeled sensor stream. The sensor stream is represented as a sequence of characters. The Lempel-Ziv-Welch dictionary-based compression algorithm and edit distance are used to identify repeated sequences from sensor readings that represent user activities.  
Most of these studies attempt to infer user activities from a sequence of sensor readings to either predict the user's next location or action. Our work differs from these studies as the spatio-temporal information and user activities are represented in tuples. The PPM model is built on these tuples and the trained model is used to make prediction.  
There are works that used PPM to predict user locations using GPS trajectories. In the work of [PERSON], [PERSON] and [PERSON] [11], they combined Markov model and PPM for predicting route and destination. PPM is used to learn about the road segments traversed by the user, while Markov model is used to model the transitions between locations. When predicting user route and destination, Markov model first predicts the next user location based on current location, and the routes and destination are retrieved from PPM. [PERSON] and [PERSON] [12] extends the PPM algorithm to include temporal and location information to predict user next location based on movement traces obtained from wireless access points. Our work is closely related to the work proposed in [12]. The main difference lies in the way the PPM is trained. Our approach trained the PPM based on user-interaction events rather than on the entire sequence of movement traces.  
Another variation to the methods pointed out above is to use frequent pattern mining. [PERSON] et al. [13] mined frequent temporal patterns from a sequence of user actions. The mined patterns are used to characterize activities. [PERSON] [14] combined association rule mining and expectation-maximization clustering to discover temporal features and relations of activities from sensor-based data. However, these methods do not use any spatial information to infer user activities. In the work of [PERSON] et al. [15], they attempt to extract spatial and temporal features from sensor data. They first applied \(k\)-means to cluster the temporal features and then used spatial features, which include a set of sensors and their frequency, to build a prediction model in each temporal cluster. Such methods, however, require the temporal features obtained from sensor readings to be clustered first before any classification can be performed.