In modern healthcare, sensing technologies such as IoT empower the quality of assisted living service by knowing what a resident is doing in real-time. Using extreme connectivity and cloud computing in a smart home, where a collection of sensors is installed, the sensors sample continuously from the movements of the resident as well as ambient data from the surrounding inside the house. Automatic human activity recognition of the resident's activities is one of the key components of assisted living in smart home. For monitoring in-home safety, the ability in recognizing abnormal activities such as accident, falling, acute disease attack (e.g. asthma, stroke, etc.), fainting, wobbling, is particularly important. The detection and machine learning process must be both accurate and fast, to cope with the real-time activity recognition. To this end, a novel streamlined sensor data processing method is proposed called Evolutionary Expand-and-Contract Instance-based Learning algorithm (EEAC-IBL). The multivariate data stream is first expanded into many subspaces, then the subspaces which are corresponding to the characteristics of the features are selected and condensed into a significant feature subset. The selection operates scholastically instead of deterministically by evolutionary optimization which approximates the best subgroup. Followed by data stream mining, the machine learning for activity recognition is done on the fly. This approach is unique and suitable for such extreme connectivity scenario where precise feature selection is not required, and the relative importance of each feature among the sensor data changes over time. This stochastic approximation method is fast and accurate, offering an alternative to traditional machine learning method for smart home activity recognition application. Our experimental results show computing advantages over other classical approaches.