Smart home technology is a better choice for the people to care about security, comfort and power saving as well. It is required to develop technologies that recognize the Activities of Daily Living (ADLs) of the residents at home and detect the abnormal behavior in the individual's patterns. Data mining techniques such as Frequent pattern mining (FPM), High Utility Pattern (HUP) Mining were used to find those activity patterns from the collected sensor data. But applying the above technique for Activity Recognition from the temporal sensor data stream is highly complex and challenging task. So, a new approach is proposed for activity recognition from sensor data stream which is achieved by constructing Frequent Pattern Stream tree (FPS - tree). FPS is a sliding window based approach to discover the recent activity patterns over time from data streams. The proposed work aims at identifying the frequent pattern of the user from the sensor data streams which are later modeled for activity recognition. The proposed FPM algorithm uses a data structure called Linked Sensor Data Stream (LSDS) for storing the sensor data stream information which increases the efficiency of frequent pattern mining algorithm through both space and time. The experimental results show the efficiency of the proposed algorithm and this FPM is further extended for applying for power efficiency using HUP to detect the high usage of power consumption of residents at smart home.