# PCA principal component analysis standardized data

• cutesteph
In summary, the conversation discusses the benefits of using standardized data and the correlation matrix compared to converting data into similar units. The use of the correlation matrix allows for normalization of data within each group, while converting units can lead to different results. The definition of "normalizing" the data is replacing it with the z-score, and the professor may have used this method to show the potential differences in results between the two approaches. However, the mathematical definition of "better" would need to be defined in order to determine which method is truly more effective.

#### cutesteph

Why is better to use the standardized data using the correlation matrix than say converting data into just similar units. Like say I had data that measured car speeds measured in seconds for some data and the other data measured in minutes. Why would it be better just to measure the data using the correlation matrix to normalize data than to just covert all the times to say meters traveled per second.

Why would it be better just to measure the data using the correlation matrix to normalize data than to just covert all the times to say meters traveled per second.
I don't understand this sentence, but in general data analysis requires all data to have the same units.

I mean like say we are looking are car race data like from 1/4 a mile 1 mile are in seconds, while data for a 10 mile and a 50 mile race are in minutes. Can't you use normalize data using the correlation matrix within each group like 1/4 mile race even though it is in seconds to a 10 mile race even though it is in minutes? My professor analyzed data that way in a lecture and compared it to a method to just covert all units to meters per second and just take the covariance matrix of that.

cutesteph said:
Why would it be better just to measure the data using the correlation matrix to normalize data than to just covert all the times to say meters traveled per second.

What is your definition of "normalizing" the data? Does it amount to replacing the data on each axis by the "z-score" of the data?

Yes. It would be which would be equivalent to using the correlation matrix in lieu of the covariance matrix for PCA. I just not sure exactly why would it be better to use that method than to just chance the units to the same units of say in my example meters per second for each different race length.

cutesteph said:
I just not sure exactly why would it be better to use that method than to just chance the units to the same units of say in my example meters per second for each different race length.

We'd have to define what "better" means mathematically to investigate that question.

Perhaps the professor was illustrating that you can get different answers if you convert units and do PCA than if you do PCA and convert the units in the principal components afterwards. That difference doesn't mean that one way is always better or worse than the other.