Machine learning algorithms and traditional data mining process usually require a large volume of data to train the algorithm-specific models, with little or no user feedback during the model building process. Such a »big data» based automatic learning strategy is sometimes unrealistic for applications where data collection or processing is very expensive or difficult, such as in clinical trials. Furthermore, expert knowledge can be very valuable in the model building process in some fields such as biomedical sciences. In this paper, we propose a new visual analytics approach to interactive machine learning and visual data mining. In this approach, multi-dimensional data visualization techniques are employed to facilitate user interactions with the machine learning and mining process. This allows dynamic user feedback in different forms, such as data selection, data labeling, and data correction, to enhance the efficiency of model building. In particular, this approach can significantly reduce the amount of data required for training an accurate model, and therefore can be highly impactful for applications where large amount of data is hard to obtain. The proposed approach is tested on two application problems: the handwriting recognition (classification) problem and the human cognitive score prediction (regression) problem. Both experiments show that visualization supported interactive machine learning and data mining can achieve the same accuracy as an automatic process can with much smaller training data sets.