Could someone please explain me this reviewer comment:  asymmetric distribution could affect Principal Component Analysis results,  symmetry of distribution should be tested. Authors should also indicate if outliers were observed and consequently excluded because they could affect factors  My question: what does it mean asymmetry distribution could affect PCA? And also outliers, could they affect factors?
122498
I want to do principal component analysis (factor analysis) on SPSS based on 22 variables. However, some of my variables are very skewed (skewness calculated from SPSS ranges from 2&ndash;80!).   So here are my questions:   Should I keep the skewed variables like that or could I transform the variables on principal component analysis? If yes, how would I interpret factor scores?  What type of transformation should I do? log10 or ln? Originally, my KMO (Kaiser&ndash;Meyer&ndash;Olkin) is 0.413. Much literature recommends a minimum of 0.5. Can I still do factor analysis, or do I need to remove variables to raise my KMO to 0.5?
66142
After some searching, I find very little on the incorporation of observation weights/measurement errors into principal components analysis. What I do find tends to rely on iterative approaches to include weightings (e.g., ). My question is why is this approach necessary? Why can't we use the eigenvectors of the weighted covariance matrix?
24077
I have a dataset that has both continuous and categorical data. I am analyzing by using PCA and am wondering if it is fine to include the categorical variables as a part of the analysis. My understanding is that PCA can only be applied to continuous variables. Is that correct? If it cannot be used for categorical data, what alternatives exist for their analysis?
1306
In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues.   I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like a machine. But I didn't understand it. I didn't get the purpose of it. I didn't get the feel of it.        I strongly believe in the following quote:     You do not really understand something unless you can explain it to your grandmother. -- Albert Einstein   Well, I can't explain these concepts to a layman or grandma.   Why PCA, eigenvectors &amp; eigenvalues? What was the need for these concepts? How would you explain these to a layman?
23908
I have a problem with the normality of some data I have:  I've done a Kolmogorov test which says it isn't normal with p=.0000,  I don't understand: the skewness of my distribution =-.497, and the kurtosis =-0,024  Here is the plot of my distribution which looks very much normal ...  (I have three scores, and each one of this scores isn't normal with a significant p-value for the Kolmogorov test ... I really don't understand )
33215
I have a dataset with a large number of Yes/No responses. Can I use principal components (PCA) or any other data reduction analyses (such as factor analysis) for this type of data? Please advise how I go about doing this using SPSS.
75810
I did a principal component analysis, which resulted in 7 components that I am now using for a principal component regression on my independent variable.  However, I want to add 2 control variables, but these are not component scores, but "normal" variables (on a Likert scale, the same sort of variables my independent variables were).  Is that okay to do or do I have to make these into components as well? I have done the regression both with those two as variables and combined in a component and the results are practically the same.
32558
I have a dataset with 11 variables and PCA (orthogonal) was done to reduce the data. Deciding on the number of components to keep it was evident for me from my knowledge about the subject and the scree plot (see below) that two principal components (PCs) were enough to explain the data and the remaining components were only less informative.   Scree plot with parallel analysis:  observed eigenvalues (green) and simulated eigenvalues based on 100 simulations (red). Scree plot suggests 3 PCs, whereas parallel test suggests only the first two PCs.      As you can see only 48% of the variance could be captured by the first two PCs.    Plotting observations on the first plane made by the first 2 PCs revealed three different clusters using hierarchical agglomerative clustering (HAC) and K-means clustering. These  3 clusters turned out to be very relevant to the problem in question and were consistent with other findings as well. So except the fact that only 48% of variance was captured everything else was tremendously fine.      One of my two reviewers said: one cannot rely much on these findings as only 48% of variance could be explained and it is less than required.      Question Is there any required value of how much variance should be captured by PCA to be valid? Is it not dependent on the domain knowledge and methodology in use? Can anybody judge on the merit of the whole analysis just based on the mere value of the explained variance?    Notes     Data are 11 variables of genes measured by a very sensitive methodology in molecular biology called Real-Time Quantitative Polymerase Chain Reaction (RT-qPCR).   Analyses were done using R.   Answers from data analysts based on their personal experience working on real-life problems in the fields of microarray analysis, chemometrics, spectometric analyses or alike are much appreciated.   Please consider supporting you answer with references as much as possible.
57446
For a given data matrix $A$ (with variables in columns and data points in rows), it seems like $A^TA$ plays an important role in statistics. For example, it is an important part of the analytical solution of ordinary least squares. Or, for PCA, its eigenvectors are the principal components of the data.  I understand how to calculate $A^TA$, but I was wondering if there's an intuitive interpretation of what this matrix represents, which leads to its important role?
15959
Equivalently, about variance?  I realize it measures the spread of a distribution, but many other metrics could do the same (e.g., the average absolute deviation). What is its deeper significance? Does it have    a particular geometric interpretation (in the sense, e.g., that the mean is the balancing point of a distribution)?  any other intuitive interpretation that differentiates it from other possible measures of spread?   What's so special about it that makes it act as a normalizing factor in all sorts of situations (for example, convert covariance to correlation)?
67663
Can anything be stated about the distribution of the digits of Pi, i.e., if I were to sample n digits of Pi, can anything be said about the probability to observe certain digits, or is there any reason to assume that they would not be evenly distributed? This is purely a curiosity question.
78311
What are principal component scores (PC scores, PCA scores)?
95815
a very naive question for some of you. I have a population of 80000 data points. Some points in the population are many SD away from the rest of the population and they could be easily identified and visualized assigning them a p-value. I know that excluding those values, the population follow a nice normal distribution. What I ask you today is whether you can suggest me an approach to assigning a pvalue to each data point in the population where the null hypothesis is that the data contribute to the normality.
105346
I've come across a scenario where I have 10 signals/person for 10 people (so 100 samples) containing 14000 data points (dimensions) that I need to pass to a classifier. I would like to reduce the dimensionality of this data and PCA seems to be the way to do so. However, I've only been able to find examples of PCA where the number of samples is greater than the number of dimensions. I'm using a PCA application that finds the PCs using SVD. When I pass it my 100x14000 dataset there are 101 PCs returned so the vast majority of dimensions are obviously ignored. The program indicates the first 6 PCs contain 90% of the variance.   Is it a reasonable assumption that these 101 PCs contain essentially all the variance and the remaining dimensions are neglectable?  One of the papers I've read claims that, using a similar (though slightly lower quality) dataset than my own, they were able to reduce 4500 dimensions down to 80 retaining 96% of the original information. The paper hand-waves over the details of the PCA technique used, only 3100 samples were available, and I have reason to believe less samples than that were used to actually perform PCA (to remove bias from the classification phase).   Am I missing something or is this really the way that PCA is used with high dimensionality-low sample size dataset? Any feedback would be greatly appreciated.
91033
I have a sample of 250 units. The distribution is asymmetric.  I want to test a hypothesis that the median of the population is different from 3.5, so I think a one-sample test would be appropriate. I know that the Wilcoxon rank test is not appropriate because the distribution is not symmetric. Is a sign test appropriate to use? If it is not can anyone recommend any other test?
76066
As far as I understand,  principal components are obtained by rotating the coordinate axes to align them with the directions of maximum variance.   Nevertheless, I keep reading about "unrotated principal components" and my statistics software (SAS) gives me varimax-rotated principal components as well as the unrotated ones. Here I am confused: when we compute principal components, the axes are already rotated; so why is there another rotation needed? And what does "unrotated principal component"  mean?
3300
I know that in a regression situation, if you have a set of highly correlated variables this is usually "bad" because of the instability in the estimated coefficients (variance goes toward infinity as determinant goes towards zero).  My question is whether this "badness" persists in a PCA situation.  Do the coefficients/loadings/weights/eigenvectors for any particular PC become unstable/arbitrary/non-unique as the covariance matrix becomes singular?  I am particularly interested in the case where only the first principal component is retained, and all others are dismissed as "noise" or "something else" or "unimportant".  I don't think that it does, because you will just be left with a few principal components which have zero, or close to zero variance.  Easy to see this isn't the case in the simple extreme case with 2 variables - suppose they are perfectly correlated.  Then the first PC will be the exact linear relationship, and the second PC will be perpindicular to the first PC, with all PC values equal to zero for all observations (i.e. zero variance).  Wondering if its more general.