Using Jaccard Distance Measure for Unsupervised Activity Recognition with Smartphone Accelerometers

Abstract

The rapid popularity of smartphones has led to a growing research interest in human activity recognition (HAR) with the mobile devices. Accelerometer is the most commonly used sensor of smartphone for HAR. Many supervised HAR methods have been developed. However, it is very difficult to collect the annotated or labeled training data for HAR. So, developing of effective unsupervised methods for HAR is very necessary. The accuracy of an unsupervised method, such as clustering, can be greatly affected by the similarity or distance measures, because the learning process of clustering method is completely depending on the similarity between objects. Although Euclidean distance measure is commonly used in unsupervised activity recognition, it is not suitable for measuring distance when the number of features is very large, which is usually the case in HAR. Jaccard distance is a distance measure based on mutual information theory and can better represent the differences between nonnegative feature vectors than Euclidean distance. It can also work well with a large number of features. In this work, the Jaccard distance measure is applied to HAR for the first time. In the experiments, the results of the Jaccard distance measure and the Euclidean distance measure are compared, using three different feature extraction methods which include time-domain, frequency-domain and mixed-domain feature extractions. To comprehensively analyze the experimental results, two different evaluation methods are used: (a) C-Index before clustering, (b) FM-index after using five different clustering methods which are Spectral Cluster, Single-Linkage, Ward-Linkage, Average-Linkage, and K-Medoids. Experiments show that, almost for every combination of the feature extraction methods and the evaluation methods, the Jaccard distance measure is consistently better than the Euclidean distance measure for unsupervised HAR.