Log-Sum Distance Measures and Its Application to Human-Activity Monitoring and Recognition Using Data From Motion Sensors

For the detection of human activities using motion data many techniques employ feature extraction and machine learning. But detection rates and incorrect classification rates require further increase and decrease, respectively. We address both the problems. We propose a novel distance measure, called log-sum distance, for evaluating difference between two sequences of positive numbers. We use the proposed log-sum distance measure to develop algorithms for recognition of human activities from the motion data. The sequences of <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> positive numbers are <italic>residual sum of squares</italic> errors produced from modeling <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> motion time-series with the <italic>multiple linear regression method</italic>. To reduce incorrect classification, we define a threshold test and use it in our proposed novel algorithm. We have defined an optimization function and used it for computing optimal threshold values. Extensive evaluation of our activity detection algorithm with two different sets of data sets show increased activity recognition rates and decreased incorrect classification rates compared with other existing methods. In one data set, the proposed algorithm detects all activities with 100% accuracy and in the another data set, it detects all activities with 99% or higher accuracy. The proposed use of threshold values for classification of activities decreased incorrect classification rates.