# Predicting Activities of Daily Living with Spatio-Temporal Information
## 1 Introduction  
Almost every country in the world is experiencing a growing and aging population. The smart home is considered a viable solution to address living problems, typically the elderly or those with diminished cognitive capabilities. An important part of the functioning of smart homes is to monitor user daily activities and detect any alarming situations (e.g., skipping meals several days in a row). Sensors attached to objects of daily use (e.g., fridge, light, etc.) are often deployed in the smart home to collect information about user daily activities. These sensors are activated when the user performs their activities (e.g., opening the fridge, turning on the light, etc.). The recognition system uses the sensory outputs from the home to learn about user activity patterns and predict the next probable event. The majority of the probabilistic graphical models such as the hidden Markov model and its variants, and deep learning methods for activity recognition, can predict where the user will go next or what activity is the user doing given the sequence of sensor readings [1; 2; 3; 4; 5]. However, for a smart home to react intelligently and support its users, the recognition system should not only recognize their activities but also have the ability to reason, e.g., at what time and in which room did a particular event occur. Knowing the contexts of the user such as when and where a particular event occurred are important for detecting any unusual or abnormal events and issue warnings to caregivers or family members. For example, the recognition system learns that the user always goes to bed at 10 p.m. If something is happening after 10 p.m. then it is more likely that the user is sleeping. If the user were in the kitchen doing laundry at 1 a.m., this would be something that the recognition systemwill recognize as unusual. Both space and time play an important role in activity recognition, and to represent and fuse all this information in the smart home poses a challenge. An individual's pattern of daily activities is likely the same everyday. For example, a morning routine could consist of making the bed, grooming, making coffee and having breakfast. It turns out that compression can be used to identify repeated 'patterns' that represent user activities. To illustrate how compression can be used in this study, we first describe the form in which we expect the data to appear. When the user performs an activity in the smart home, each user-interaction event contains information about (1) the time when the activity is performed, (2) the location of where the activity is performed and (3) the sensor that is being activated. Each user-interaction event is annotated (usually by the user themselves) with an activity name and a label stating the starts and ends of an activity. Table 1 shows an example of activity events in a smart home. Since each activity event consists of information about time and location, this information can be incorporated when compressing the data stream. This paper extends the prediction by partial matching (PPM), an adaptive statistical data compression technique, to include spatial and temporal information. Our aim in this paper is to improve the activity recognition process by incorporating spatial and temporal context information, as illustrated in Figure 1. In particular, this paper aims to answer questions such as 'where will the user most likely be at a given time' or 'given that the user is in a particular location at a given time, what activity is the user most likely doing'. Evaluation was performed on three publicly available smart-home datasets.