Difference between big data and high dimensional data What do big data and high dimensional data mean? Is high dimensional data a special case of big data? What are the complications that arise in the analysis of high dimensional and big data each? 
 A: Big data implies large numbers of data points, while high-dimensional data implies many dimensions/variables/features/columns. 
It's possible to have a dataset with many dimensions and few points, or many points with few dimensions. But if you have high-dimensional datasets with few data points, you're unlikely to be able to learn much from it. So high-dimensional data is generally going to be big data as well. 
The converse is not true - big data does not need many dimensions for you to learn from it. But if you are only working with a few dimensions, it's probably not as necessary to collect a large number of data points to do your analysis. Note that there are important exceptions to this - noisy measurements, high frequency spatial or temporal data, and so on. 
So it's probably generally true that giant datasets with many points also happen to have many variables/dimensions as well. In other words, the terms mean different things, but big data is usually high-dimensional data and vice versa.

Regarding the complications associated with each, here is a very incomplete answer: big data poses computational challenges (loading data in memory, for example), while analysis of high-dimensional data falls prey to the curse of dimensionality.
