# Linear Regression Model with Many Features - Real Life Example

I am learning Machine Learning (Linear Regression) from Prof. Andrew Ng's lecture. While listening when to use normal equation vs gradient descent, he says when our features number is very high (like $10^6$) then to use gradient descent.

Everything is clear to me, but I wonder that can someone give me real life examples where we use such such huge number of features?

• Where does the notion that there's a need to compute $(X^TX)^{-1}$ come from? That's not a good idea at all. – Glen_b Apr 20 '14 at 22:10
• Document classification, bioinformatics (microarray data, genomics, PPI networks, ...), web data mining (Twitter, Facebook, Google, ...), ... – Marc Claesen Apr 20 '14 at 22:16

Another example - image recognition. Imagine that you have just a 512 x 512 gray-scale image - it means that without additional pre-processing you already have $2^{18}$ features - with each pixel being a feature.
Genetic analysis is another common example. Most mammals have genomes with a number of protein-coding genes in the order of $$10^4$$, but there's lots of other coding regions (for different kinds of RNA that are not used for protein synthesis directly), too. Additionally, some experimental/methodological procedures bases on sequencing slice the genome into millions ($$10^6$$) of bins and measure certain molecular features for these bins (like DNA methylation or CpG-islands).