Tensor Type Calculus

Tensor type calculus focuses on developing efficient and robust methods for representing, manipulating, and analyzing multi-dimensional data structures called tensors. Current research emphasizes developing novel tensor operations (like broadcast products), designing efficient algorithms for tensor decomposition (e.g., using Tucker, PARAFAC, or Tensor Train decompositions) and regularization (e.g., ℓ₁-norm and ℓ₂,ₚ-norm), and applying these techniques to diverse problems including denoising, dimensionality reduction, and machine learning tasks like regression and neural network optimization. This field is significant because it offers powerful tools for handling the increasingly prevalent high-dimensional data in various scientific domains and practical applications, leading to improved accuracy, efficiency, and privacy in data analysis and machine learning.