Motivated by the importance of studying the relationship between habits of students and their academic performance, daily activities of undergraduate participants have been tracked with smartwatches and smartphones. Smartwatches collect data together with an Android application that interacts with the users who provide the labeling of their own activities. The tracked activities include eating, running, sleeping, classroom-session, exam, job, homework, transportation, watching TV-Series, and reading. The collected data were stored in a server for activity recognition with supervised machine learning algorithms. The methodology for the concept proof includes the extraction of features with the discrete wavelet transform from gyroscope and accelerometer signals to improve the classification accuracy. The results of activity recognition with Random Forest were satisfactory (86.9%) and support the relationship between smartwatch sensor signals and daily-living activities of students which opens the possibility for developing future experiments with automatic activity-labeling, and so forth to facilitate activity pattern recognition to propose a recommendation system to enhance the academic performance of each student.

In this paper, fractional calculus principles are considered to implement fractional derivative gradient optimizers for the Tensorflow backend. The performance of these fractional derivative optimizers is compared with that of other well-known ones. Our experiments consider some human activity recognition (HAR) datasets, and the results show that there is a subtle difference between the performance of the proposed method and other existing ones. The main conclusion is that fractional derivative gradient descent optimizers could help to improve the performance of training and validation tasks and opens the possibility to include more fractional calculus concepts to neural networks applied to HAR.

Machine learning is a branch of artificial intelligence that dates back more than 50 years. It is currently experiencing a boom in research and technological development. With the rise of machine learning, the need to propose improved optimizers has become more acute, leading to the search for new gradient-based optimizers. In this paper, the ancient concept of fractional derivatives has been applied to some optimizers available in PyTorch. A comparative study is presented to show how the fractional versions of gradient optimizers could improve their performance on generative adversarial networks (GAN) and natural language applications with Bidirectional Encoder Representations from Transformers (BERT). The results are encouraging for both state-of-the art algorithms, GAN and BERT, and open up the possibility of exploring further applications of fractional calculus in machine learning.

A novel morphing activation function is proposed, motivated by the wavelet theory and the use of wavelets as activation functions. Morphing refers to the gradual change of shape to mimic several apparently unrelated activation functions. The shape is controlled by the fractional order derivative, which is a trainable parameter to be optimized in the neural network learning process. Given the morphing activation function, and taking only integer-order derivatives, efficient piecewise polynomial versions of several existing activation functions are obtained. Experiments show that the performance of polynomial versions PolySigmoid, PolySoftplus, PolyGeLU, PolySwish, and PolyMish is similar or better than their counterparts Sigmoid, Softplus, GeLU, Swish, and Mish. Furthermore, it is possible to learn the best shape from the data by optimizing the fractional-order derivative with gradient descent algorithms, leading to the study of a more general formula based on fractional calculus to build and adapt activation functions with properties useful in machine learning.