Linked Questions

103 votes
2 answers
250k views

Why do we need to normalize data before principal component analysis (PCA)? [duplicate]

I'm doing principal component analysis on my dataset and my professor told me that I should normalize the data before doing the analysis. Why? What would happen If I did PCA without normalization? ...
user avatar
  • 5,317
4 votes
1 answer
2k views

SVD for PCA: Why would one standardize the data matrix? [duplicate]

As explained in amoeba's beautiful answer here one can use a singular value decomposition of the data matrix, $\mathbf{X} = \mathbf{USV}^\top$, to do a principal component analysis, if it is assumed ...
user avatar
  • 41
1 vote
2 answers
661 views

Does standardization compromises Principal Component Analysis? [duplicate]

I've been dealing with PCA over the past week and I ended up with a requirement for performing PCA (in Python Machine Learning Book by Sebastian Raschka): Note that the PCA directions are highly ...
user avatar
  • 331
-1 votes
1 answer
3k views

Why is PCA normalization necessary? [duplicate]

I have read a lot of threads concerning this question but I still seem not to understand the reason we normalize data for PCA. If we normalize the data, every feature is on the same scale. To make use ...
user avatar
  • 21
1 vote
1 answer
2k views

Principal component analysis- covariance or correlation matrix [duplicate]

I am doing a PCA on 24 satisfaction variables from a survey. Respondents indicate their levels of satisfaction towards different aspects of the service. These variables are all measured in same unit,...
user avatar
  • 15
2 votes
0 answers
2k views

Why subtracting the means in PCA, but not dividing by standard deviations? [duplicate]

I know this can vary, but in the standard setup, when calculating principal components (PCs), we begin by subtracting the means of each feature (dimension), but we do not divide by the standard ...
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1 vote
1 answer
1k views

Does one need to standardize data before PCA even if all the variables are measured in the same units? [duplicate]

I have been learning about PCA and SVD. And I know that to standardize the features before PCA is necessary. But I came across the book rating matrix, which makes me confused about what ...
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  • 31
2 votes
1 answer
799 views

Variable standardization / scaling for PCA when all dimensions already have same scale [duplicate]

Often when PCA is performed on exam results where all variables (dimensions) have the same $0$ to $100$ scale, scaling is none the less applied. For different scales I can see the purpose of it, but ...
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0 votes
1 answer
562 views

Standardization before PCA with data in same units and similar interval? [duplicate]

We have 16 variables which are indices produced by calculations based on ratio (unitless in fact). Some examples of the ranges of our variables are (0.450-0.750), (0.000 - 0.800) and (0.000 - 1.000). ...
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2 votes
0 answers
553 views

How can it be that almost all the variance is explained by the first PC? [duplicate]

I have a data matrix $X$ and I perform a PCA on this data with: ...
user avatar
  • 373
0 votes
1 answer
337 views

Data normalization prior to PCA? [duplicate]

I want to get some intuition on normalization prior to feature selection with PCA. I'm sure z-normalization is a bad idea, since it normalizes the variances to 1 for each feature, PCA will be ...
user avatar
  • 1,132
0 votes
1 answer
284 views

Correlation Matrix or Covariance Matrix in PCA [duplicate]

I have 4 metrics, three of them measured on the scale 0 to 1, and one measured on the scale 0 to 6. When I stored my data, I converted the fourth one by dividing it by 10, so that I can get values ...
user avatar
  • 157
0 votes
0 answers
166 views

Scale before PCA [duplicate]

I'm using PCA from sckit-learn and I'm getting some results which I'm trying to interpret, so I ran into question - should I subtract the mean (or perform standardization) before using PCA, or is this ...
user avatar
0 votes
0 answers
104 views

Why is scaling the data needed before principal component analysis (PCA) [duplicate]

I recognize that there are many questions on Cross Validated about scaling and PCA, but, after reading all of them, I still can't find the answer to my question. Several people have said that the ...
user avatar
  • 495
0 votes
0 answers
69 views

Is it possible that PCA works better without data scaling? [duplicate]

I am a beginner. I have a dataset of 1700 samples with 4 features and I have to perform Hierarchical Clustering (the agglomerative version) and I need to decide whether or not to scale the data and ...
user avatar
  • 1

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