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Results tagged with pca
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user 11852
Principal component analysis (PCA) is a linear dimensionality reduction technique. It reduces a multivariate dataset to a smaller set of constructed variables preserving as much information (as much variance) as possible. These variables, called principal components, are linear combinations of the input variables.
6
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Accepted
PCA on train and test datasets: do I need to merge them?
Jolliffe's Principal Component Analysis is a standard and great reference on PCA; I would strongly recommend it. …
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8
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Why is the eigenvector in PCA taken to be unit norm?
It is not true that they "should be of unit length"; PCA works fine without using unit vectors given your data $x$ as long as you use a fixed arbitrary length $l$. …
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19
votes
PCA iteratively finds directions of greatest variance; but how to find a whole subspace with...
. :)
(Once more, Peter Flom's answer is the correct answer in terms of principal components, I am huge fan of PCA don't get me wrong, just it is not always the optimal solution. …
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2
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How is the principal component applied on to the data?
Note that I used the work-flow of calculating PCA using the covariance matrix. … The thread here, contains an excellent answer on how SVD relates to PCA. …
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2
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How to perform dimensionality reduction with PCA in R
Practically with PCA you are using the projections of the PCs (the "scores") as surrogate data for your original sample. … PCA just gives you a linearly independent sub-sample of your data that is the optimal under an RSS reconstruction criterion. …
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3
votes
Accepted
Projecting a new entry onto the two largest eigenvectors of a PCA model
If you want the eigenvectors that are the same as the ones returned by PCA you are looking to use $V^*$. … Please see the post by the user @amoeba found here regarding the relation between SVD and PCA. I believe it will aid your understanding a lot. …
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9
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Accepted
Normalizing all the variarbles vs. using scale=TRUE option in prcomp in R
Having said that, when applying PCA in general it is a good idea to scale your variables. Otherwise the magnitude to certain variables dominates the associations between the variables in the sample. … Unless all your variables are recorded in the same scale and/or the difference in variable magnitudes are of interest I would suggest you normalise your data prior to PCA. …
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1
vote
Accepted
Sample projected onto principal component
Projection means that we use the axis proposed by the principal component to map the data to this new space. Mathematically this is usually called a vector projection.
Principal component (PC) is the …
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1
vote
Why is sum of squares equal to eigenvalue in PCA?
Because that eigenvalue $\lambda_i$ is the variance of a zero-centred variable $\xi_i$, $\xi_i$ being the principal component score for the $i$ eigen-component. By definition the variance of a variabl …
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13
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Accepted
Is there any required amount of variance captured by PCA in order to do later analyses?
Regarding your particular questions:
Is there any required value of how much variance should be captured by PCA to be valid?
No, there is not (to my best of knowledge). … Try to see if your results agree with PCA findings from other studies.
Can anybody judge on the merit of the whole analysis just based on the mere value of the explained variance? …
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13
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Choosing number of principal components to retain
As matter of personal preference, I like Minka's approach on this Automatic choice of dimensionality for PCA which based on a probabilistic interpretation of PCA but then again, you get into the game of …
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11
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Accepted
PCA model selection using AIC (or BIC)
The works of Minka (Automatic choice of dimensionality for PCA, 2000) and of Tipping & Bishop (Probabilistic Principal Component Analysis) regarding a probabilistic view of PCA might provide you with the …
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105
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Are there cases where PCA is more suitable than t-SNE?
PCA is deterministic; $t$-SNE is not. … In fairness, PCA does not deal with them either but numerous extensions of PCA for incomplete data (eg. probabilistic PCA) are out there and are almost standard modelling routines. …
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3
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Accepted
Why is the amount of Eigenvalue of the first Principal component much higher than the rest o...
Finally, on the "is my data (not) suitable for PCA" side-question: All data is suitable for PCA; it is a question what we do with the PCA results and whether they are suitable/insightful for our respective …
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3
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What is the meaning of the variable "scores" in MATLAB's PCA?
In terms of PCA, SVD contains only the left singular vectors, $U$ (the eigenvectors of the covariance matrix of $X$) and the singular values S (the square root of the eigenvalues of the covariance matrix … A side-comment: When I started reading on PCA I first try to get the covariance derivation right and then moved to the SVD. …
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