Video-based human activity recognition systems have potential contributions to various applications such as smart homes and healthcare services. In this work, we present a novel depth video-based translation and scaling invariant human activity recognition (HAR) system utilizing R transformation of depth silhouettes. To perform HAR in indoor settings, an invariant HAR method is critical to freely perform activities anywhere in a camera view without translation and scaling problems of human body silhouettes. We obtain such invariant features via R transformation on depth silhouettes. Furthermore, in R transforming depth silhouettes, shape information of human body reflected in depth values is encoded into the features. In R transformation, 2D feature maps are computed first through Radon transform of each depth silhouette followed by computing 1D feature profile through R transform to get the translation and scaling invariant features. Then, we apply Principle Component Analysis (PCA) for dimension reduction and Linear Discriminant Analysis (LDA) to make the features more prominent, compact and robust. Finally, Hidden Markov Models (HMMs) are used to train and recognize different human activities. Our proposed system shows superior recognition rate over the conventional approaches, reaching up to the mean recognition rate of 93.16% for six typical human activities whereas the conventional PC and IC-based depth silhouettes achieved only 74.83% and 86.33%, while binary silhouettes-based R transformation approach achieved 67.08% respectively. Our experimental results show that the proposed method is robust, reliable, and efficient in recognizing the daily human activities.