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.
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