Can we say data science focuses on the science of data, while Data mining concerned with the process?
What of machine learning aspect of it?
More or less your answer is a good approximation. Machine learning is a family of algorithms, you can develop just the tools in an abstract way (pure machine learning) or you can use it in a particular dataset.
For example, having a dataset, you can apply this algorithms to get hidden patters in your data (this is the relationship with data mining) or to build a model to predict or classify new data (this is the relationship with data science in general) .
Data mining is all about examining the large database which are previously exists and to examining it in a meaningful way to generate useful information.
Data science is a combination of data inference, algorithm development, and technology in order to solve analytically complex problems.
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