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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?

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    $\begingroup$ 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. $\endgroup$ – whuber♦ May 5 '15 at 15:43
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Your assumption is correct, and you are also noticing subtleties. In a perfect world, the number of columns is the number of dimensions of a data set. However, some columns are similar, some are correlated, some are duplicates in some way, some are junk, some are useless, etc. so the actual number of dimensions can be unknown. Its a knotty problem. In your case I would go with your first assumption.

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  • $\begingroup$ So in this case would you say, Class1 and Class2 are also dimensions too? $\endgroup$ – Farid Nouri Neshat May 5 '15 at 15:08
  • $\begingroup$ In a perfect world are they independent of each other? ie separate pieces of information? individual variables? $\endgroup$ – mandata May 5 '15 at 15:12
  • $\begingroup$ This is yeast data? $\endgroup$ – mandata May 5 '15 at 15:14
  • $\begingroup$ Yes, I think. I believe they are actually dependent on other variables. $\endgroup$ – Farid Nouri Neshat May 5 '15 at 15:15
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Dimensionality is the number of columns of data which is basically the attributes of data like name, age, sex and so on. While classification or clustering the data, we need to decide what all dimensionalities/columns we want to use to get meaning information.

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