## 4 Conclusions  
Human activity recognition (HAR) is a common time series classification task, which requires high accuracy with high processing speed in real-time applications. LSTM networks are widely used in time series classification problems, whereas they require big training data and high-dimensional feature vectors to get optimum performance, which dramatically increase the training duration and reduces the processing speed. Dimension reduction methods are generally employed to process LSTMs in low dimensional feature space, which usually yields low performance. In previous study [10], LSTM showed dramatically the worst performance with low dimensional feature vectors among the other machine learning classifiers, which are not deep learning-based methods. The reason for that was the discrimination power of the feature vectors constructed using the 3D joint angles in global coordinate system was very weak to get high accuracy in LSTM network. In order to boost the performance of LSTMs in low dimensional feature space, in this paper, a novel egocentric  
Figure 10: Graph of accuracies of previous and proposed method in varying discrete cosine transform (DCT) vector sizes.  
coordinate system is presented. Based on the body relative direction of the users in the camera vision, proposed method provides a scale and rotation invariant human activity recognition system, which employs LSTM network with low-dimensional 3D posture data. In the proposed framework, Kinect depth sensor is employed to obtain skeleton joints. Since angles are used, proposed system is already scale invariant. In order to provide rotation invariance, body relative direction in egocentric coordinates is calculated. The 3D vector between right hip and left hip is used to get the horizontal axis and its cross product with the vertical axis of global coordinate system assumed to be the depth axis of the proposed local coordinate system. Instead of using 3D joint angles, 8 number of limbs and their corresponding 3D angles with \(X\), \(Y\), and \(Z\) axes of the proposed coordinate system are employed as the feature vector. In terms of dimension reduction, averaging filter, HWT (Haar wavelet transform) and DCT (discrete cosine transform) are employed with varying kernel sizes. Sliding kernel's functionality is achieved using a specific queue data structure. Finally, extracted features are trained and tested with LSTM (long short-term memory) network which is an artificial recurrent neural network (RNN) architecture. Experimental results indicate that DCT compression has the minimum loss of information among other dimension reduction methods and proposed framework dramatically increases the discrimination power of feature vectors. Using the proposed egocentric coordinate system, LSTM achieves outstanding results with 83.9% accuracy with an optimum DCT compression rate of 90%. Additionally, a benchmarking study is performed with the previous study's method [10] in which the highest accuracy is obtained with 61.6% where rotation invariance is satisfied while rotating by the 45 degrees of freedom in training session. Benchmarking results show that proposed method overwhelms the previous method dramatically (approximately 30% in accuracy) and yields excellent results. As the future work, other attempts to obtain different source of coordinate input will be tested instead of using the Kinect camera, e.g., such as from CCTV real time video without a depth sensor.  
This research received no external funding.  
This research was supported by the Kyungsung University Research Grants in 2019 and Brain Busan 21+ 2020.  
The author declares no conflict of interest.