How can one visualize data points in N dimensional space?

READ ~ 30min breaks this down well in http://Up%20and%20Down%20the%20Ladder%20Of%20Abstraction. The goal is to create a view or set of views that maintains a tangible link to what it represents.

There are a lot of visualization techniques. http://en.wikipedia.org/wiki/Parallel_coordinates http://en.wikipedia.org/wiki/Chernoff_face http://en.wikipedia.org/wiki/Star_plot and many others. Also, you can always resort to visualizing everything in 2d. NC2 different plots, showing plot between every pair of dimensions.

Since our brain is limited to 3 dimensional perception, you have to use one of these tricks: Dimensional reduction: use any method to reduce the dimensions of your samples to the most significant ones. As stated by , the PCA is a technique that used often. Projection: project your N dimensional sample space into many 3 or 2 dimensional representations. Adding dimensions: you can actually represent more than three dimensions if you use colors, multiple plots, animations... Overall, use a combination of the tricks listed above. Good luck visualizing your data. If you have enjoyed reading this answer, make sure to follow me here:

First reduce the number of dimensions to 2 or 3 using https://en.wikipedia.org/wiki/Principal_component_analysis, then visualize the data with scatter plot or heat map.

You may want to use some technique for dimensionality reduction. For instance, one that is particularly well suited for the visualization of high-dimensional datasets: http://lvdmaaten.github.io/tsne/. As you can see, they have implementations in many different programming language. You can play with it. There are more options: http://www.multifactordimensionalityreduction.org/, http://www.epistasis.org/, etc... Here is a link from Wikipedia that shortly explains the MDR processe: https://en.wikipedia.org/wiki/Multifactor_dimensionality_reduction

I built a completely abstract 3D model which is a guidance and a set of subtlest components, using simplest math. Like if a point is X, what is the structure to build other points or guiding lines. Some self-similarity as a functional component included. I hadn't bother wether it's matches others' understanding it not at that point. I just built something which felt natural to me as a base for comparison. I then started applying found X points, which are conclusions made from previous model application, in time, which is 4th, reusing the model at various scales. Eventually X points serve as a wave guiding elements and can be reverse engineered via wave equations to re-allocate the points. This sounds complicated so the trick is to get comfortable with applying and then just trust it. With practice (in time) you can observe points matching with multi factor authentication. That in turn moves you forward. I haven't yet found a technology to visualize the model itself myself (apart from the verbal description) so I use light properties as a computational medium to capture a result. Also it might be helpful to consider points to form groups, when needed.