Low-cost inertial and motion sensors embedded on smartphones have provided a new platform for dynamic activity pattern inference. In this research, a comparison has been conducted on different sensor data, feature spaces and feature selection methods to increase the efficiency and reduce the computation cost of activity recognition on the smartphones. We evaluated a variety of feature spaces and a number of classification algorithms from the area of Machine Learning, including Naive Bayes, Decision Trees, Artificial Neural Networks and Support Vector Machine classifiers. A smartphone app that performs activity recognition is being developed to collect data and send them to a server for activity recognition. Using extensive experiments, the performance of various feature spaces has been evaluated. The results showed that the Bayesian Network classifier yields recognition accuracy of 96.21% using four features while requiring fewer computations.