This research is motivated by a long-standing problem of ineffective heuristic initial selection of a class of models, and its structures in modern data mining, machine learning, and other fields. Such heuristics usually are due to insufficient prior knowledge to select a class of models, and inability to represent visually and losslessly the complex high-dimensional data to explore the data for a model class selection. For instance, lossy visualization with different 2-D projections requires an unrealistic review of a vast amount of these projections and the abilities to reconstruct from them the n-D data structures. To make the selection of a class of models faster and more efficient in this paper new closed-contour-coordinate displays are proposed and explored both mathematically and experimentally. Such displays losslessly map all attributes of each n-D data point into a separate 2-D graph/figure. This allows using the unique power of human vision to compare in parallel the hundreds of features of these graphs, and proportionally speed up the selection of an appropriate class of models. This paper includes results of visual data mining for real data sets, including the experimental results of visual feature extraction using this approach. It expands our previous results demonstrated on simulated data and shows the radical advantages of these coordinates vs. parallel coordinates for data dimensions from 20 to 200.