# What's the meaning of dimensionality and what is it for this data?

I'm doing my assignment for my "Modeling and Optimization" course, and now I have doubts on the first question:

What is the dimensionality of the data? What are the min, median, max, mean, standard deviation and percentage missing data of each feature?

I can calculate those, but I'm not sure about the "dimensionality" of the data. Here's a sample of my dataset:

Sample  mcg   gvh   alm   mit   erl pox vac   nuc   Class1  Class2
1       0.58  0.61  0.47  0.13  0.5 0   0.48  0.22  MIT     non-CYT
2       0.43  0.67  0.48  0.27  0.5 0   0.53  0.22  MIT     non-CYT
3       0.64  0.62  0.49  0.15  0.5 0   0.53  0.22  MIT     non-CYT
4       0.58  0.44  0.57  0.13  0.5 0   0.54  0.22  NUC     non-CYT
5       0.42  0.44  0.48  0.54  0.5 0   0.48  0.22  MIT     non-CYT
6       0.51  0.4   0.56  0.17  0.5 0.5 0.49  NA    CYT     CYT


I've been told that dimensionality is usually referred to attributes or columns of the dataset. But in this case, does it include Class1 and Class2? and does dimensionality mean, the number of columns or, does it mean the names of columns?

• If the number of "attributes of the dataset" were a valid definition of anything meaningful to statistical analysis or machine learning, then it would be invariant under changes in how the data are represented--but obviously it is not. For instance, Class1 could legitimately be replaced by two columns, in which one indicates whether "MIT" is the value and a second one indicates whether "NUC" is the value. (This is how the data would be internally represented in a regression analysis.) Thus, since it is ill-defined, the "dimensionality" can be practically anything you want it to be. – whuber May 5 '15 at 15:43