How should I approach a situtation when I try to apply some ML algorithm (classification, to be more specific, SVM in particular) over some high dimensional input, and the r
Some suggestions:
Project data (just for visualization) to a lower-dimensional space (using PCA or MDS or whatever makes sense for your data)
Try to understand why learning fails. Do you think it overfits? Do you think you have enough data? Is it possible there isn't enough information in your features to solve the task you are trying to solve? There are ways to answer each of these questions without visualizing the data.
Also, if you tell us what the task is and what your SVM output is, there may be more specific suggestions people could make.