  Data-intensive applications impact many domains, and their steadily
increasing size and complexity demands high-performance, highly usable
environments. We integrate a set of ideas developed in various data science and
data engineering frameworks. They employ a set of operators on specific data
abstractions that include vectors, matrices, tensors, graphs, and tables. Our
key concepts are inspired from systems like MPI, HPF (High-Performance
Fortran), NumPy, Pandas, Spark, Modin, PyTorch, TensorFlow, RAPIDS(NVIDIA), and
OneAPI (Intel). Further, it is crucial to support different languages in
everyday use in the Big Data arena, including Python, R, C++, and Java. We note
the importance of Apache Arrow and Parquet for enabling language agnostic high
performance and interoperability. In this paper, we propose High-Performance
Tensors, Matrices and Tables (HPTMT), an operator-based architecture for
data-intensive applications, and identify the fundamental principles needed for
performance and usability success. We illustrate these principles by a
discussion of examples using our software environments, Cylon and Twister2 that
embody HPTMT.
