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Video sensor based human activity recognition systems have potential applications in life care and health care areas. The paper presents a system for elderly care by recognizing six abnormal activities; forward fall, backward fall, chest pain, faint, vomit, and headache, selected from the daily life activities of elderly people. Privacy of elderly people is ensured by automatically extracting the binary silhouettes from video activities. Two problems are addressed in this research, which decrease recognition accuracy during the process of abnormal human activity recognition (HAR) system development. First, the problem of continuous changing distance of a moving person from two viewpoints is resolved by using the R-transform. R-transform extracts periodic, scale and translation invariant features from the sequences of activities. Second, the high similarities in postures of different activities is significantly improved by using the kernel discriminant analysis (KDA). KDA increases discrimination between different classes of activities by using non-linear technique. Hidden markov model (HMM) is used for training and recognition of activities. The system is evaluated against linear discriminant analysis (LDA) on the original silhouette features and LDA on the R-transform features. Average recognition rate of 95.8% proves the feasibility of the system for elderly care at home.