We present a method, including tool support, for bibliometric mining of trends in large and dynamic research areas. The method is applied to the machine learning research area for the years 2013 to 2022. A total number of 398,782 documents from Scopus were analyzed. A taxonomy containing 26 research directions within machine learning was defined by four experts with the help of a Python program and existing taxonomies. The trends in terms of productivity, growth rate, and citations were analyzed for the research directions in the taxonomy. Our results show that the two directions, Applications and Algorithms, are the largest, and that the direction Convolutional Neural Networks is the one that grows the fastest and has the highest average number of citations per document. It also turns out that there is a clear correlation between the growth rate and the average number of citations per document, i.e., documents in fast-growing research directions have more citations. The trends for machine learning research in four geographic regions (North America, Europe, the BRICS countries, and The Rest of the World) were also analyzed. The number of documents during the time period considered is approximately the same for all regions. BRICS has the highest growth rate, and, on average, North America has the highest number of citations per document. Using our tool and method, we expect that one could perform a similar study in some other large and dynamic research area in a relatively short time.