Dimensionality and hige dimensional data: definition, examples, curse of..

Posted 2021-03-14 dulun

Dimensionality in statistics refers to how many attributes a dataset has. For example, healthcare data is notorious for having vast amounts of variables (e.g. blood pressure, weight, cholesterol level). In an ideal world, this data could be represented in a spreadsheet, with one column representing each dimension. In practice, this is difficult to do, in part because many variables are inter-related (like weight and blood pressure).

Note: Dimensionality means something slightly different in other areas of mathematics and science. For example, in physics, dimensionality can usually be expressed in terms of fundamental dimensions like mass, time, or length. In matrix algebra, two units of measure have the same dimensionality if both statements are true:

1. A function exists that maps one variable onto another variable.
2. The inverse of the function in (1) does the reverse.

High Dimensional Data

High Dimensional means that the number of dimensions is staggeringly惊人地 high — so high that calculations become extremely difficult. With high dimensional data, the number of features can exceed the number of observations. For example, microarrays, which measure gene expression, can contain tens of hundreds of samples. Each sample can contain tens of thousands of genes.

1. What is the dimension of time series. 

As far as I considered, one time series is two dimensions. 

Is a time series high dimensional because it is multivariate or because of length?