Principal component analysis is a technique to decompose an array of numerical data into a set of orthogonal vectors (uncorrelated linear combinations of the variables) called principal components. The first few principal components often suffice to grasp nearly all the multivariate variability of ...

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31 views

Loadings vs eigenvectors in PCA: when to use one or another?

In principal component analysis (PCA), we get eigenvectors (unit vectors) and eigenvalues. Now, let us define loadings as $$\text{Loadings} = \text{Eigenvectors} \cdot \sqrt{\text{Eigenvalues}}.$$ I ...
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18 views

Why is feature normalization important in PCA? [duplicate]

If feature normalization is not performed, does the algorithm give incorrect results or is it it inefficient or both?
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1answer
49 views

Rotation in PCA and Factor Analysis

I want to know what elements are (varimax-)rotated when I rotate after PCA and after Factor Analysis. Let’s assume a standardized data vector $X$ of dimension $N \times q$. In PCA, I have the ...
0
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1answer
17 views

Do the values in the second factor from a principal component analysis have to have different signs?

I am computing the principle component matrix of a financial database and to obtain the second factor I extrapolate the second vector. So far, it's easy, but I wonder, do the signs of the second ...
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1answer
49 views

Relation between variance of eigenvalues and the effectiveness of PCA on the data

If the covariance matrix has eigenvalues $$\lambda_1 \ge \lambda_2 \ldots \ge \lambda_d > 0,$$ why is the variance of the eigenvalues, $$\sigma^2=\frac{1}{d}\sum_{i=1}^d (\lambda_i-\bar ...
2
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1answer
44 views

Factor analysis to remove noise

I would like to perform factor analysis/PCA to remove potential hidden latent variables from methylation data that would be due to noise/measurement error and batch effects. However, the variable i ...
0
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0answers
30 views

How to account for repeated measurements and unequal sample sizes in RDA

I have a question going in the same direction as this one: Restricted Permutations However, I have a dataset of multiple Locations from which I have samples of sometimes 5 sometimes only 3 years. Not ...
2
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1answer
41 views

Why is the weight vector in PLS constrained to be of unit length?

In the SIMPLS formulation of partial least squares (PLS) regression, the weights are constrained to have length of 1, $$r_a^Tr_a = 1,$$ where $a$ represents a latent component (from $1$ to $A$). This ...
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1answer
31 views

Interpretation of interaction between a PC and a continuous predictor on a logical response

I'm using lme4 in R to test the effect of various continuous explanatory variables, some of which I've corrected for their collinearity using PCA, on a logical response variable. My optimal model ...
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0answers
23 views

PCA - more than 2 principal components for >80% variance

I have analyzed some datasets using prcomp and some of my data is nice and amenable to PCA. But the summary of one set is showing that at least 6 components are needed to cover 80% of the variance. ...
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20 views

Help with interpreting PCA loadings

I know that there are already a few questions on PCA loadings on this site, however after reading them I still have some problems in understanding the interpretation. I have 22 days of data and I did ...
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0answers
25 views

How to use the weights from principal component analysis (PCA) to build an composite indicator

I'm working on the construction of a composite index based on five sub-indicators. The method I used is Principal Components Analysis (PCA). I visited Jeromy Anglim's blog post calculating composite ...
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0answers
18 views

PCA using prcomp and princomp in R [duplicate]

I have been trying to do Principal Component Analysis (PCA) via R. The data set is available at https://www.dropbox.com/s/s3jstl8pu1e1xcp/Cars.csv?dl=0 I tried to do PCA via 2 different methods - ...
3
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2answers
51 views

What is the relation between singular correlation matrix and PCA?

Can anyone kindly give me some information about the statement (last sentence) at the end of below definition. What does it mean by "It can be used when a correlation matrix is singular"? This quote ...
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0answers
26 views

Why PCA gives vector as output for 294*40 matrix in matlab [closed]

I am new to stats and matlab too. I referred tutorial to use pca in matlab I have 294*40 matrix named pcaInput and I write ...
4
votes
2answers
72 views

Is dimensionality reduction almost always useful for classification?

Is singular value decomposition almost always useful in practice for enhancing the predicative power of a trained classification model? E.x. A dataset for classification has 20,000 features. Run SVD ...
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0answers
27 views

Eigenvectors of a Wishart matrix

I have been trying to find a good source (or clarifications) to help me understand this point. I am very new to random matrix theory so any pointers will be appreciated. Here is what I think I have ...
0
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0answers
40 views

Principal Component Score scaling issue

I am trying to replicate PCA results from an external report, being a paid report I cant see exactly how the numbers are being calculated but I do have a good high level understanding. After a lot of ...
0
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0answers
23 views

can I use PCA and PAF on Kendall's and Spearman's correlation matrix?

I have a dataset of 77 items, ranked by 17 people, with many ties (actually: Q-sorted under a forced quasi-normal distribution ...
0
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0answers
16 views

What is the heuristic to decide number of components for LDA dimensionality reduction?

In the PCA case, I prefer to plot the variance and choose number of components regarding that plot's breaking point. In the LDA (linear disriminant analysis) case, what can be used for such an ...
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0answers
19 views

Q-Methodology: which correlation coefficient to use: Pearson vs Spearman vs Kendall

Please note: This question pertains to Q Methodology, a research method used to study people's subjectivity. Q embodies ontological and epistemological assumptions that sometimes differ markedly ...
1
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2answers
47 views

Kernel PCA and classification

I need to perform kernel PCA on the colon-­‐cancer dataset and then I need to plot number of principal components vs classification accuracy with PCA data. For the first part I am ...
4
votes
2answers
114 views

Goodness of fit chi-square test for a number of PCA components

I have been trying to carry out Principal Component Analysis (PCA) in R using the function psych::principal. However the returned $p$-value has been very low in ...
4
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1answer
29 views

Zero-centering the testing set after PCA on the training set

I have a training set of data on which I do principal components analysis (PCA) and save the loadings/eigenvectors/coefficient matrix. I want to use the eigenvectors to transform my testing data into ...
0
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0answers
19 views

How to determine which variables need to be trimmed in PCA or Factor analysis?

Background: I'm working with log returns for about 400 tech stocks. I want to use PCA to reduce these into principal components (Internet companies, software developers, circuit board manufacturers, ...
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4answers
170 views

How can top $k$ principal components retain the predictive power on a dependent variable?

Suppose I am running a regression $Y \sim X$. Why by selecting top $k$ principle components of $X$, does the model retain its predictive power on $Y$? I understand that from ...
2
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1answer
48 views

Nonlinear total least squares / Deming regression in R

I've been using nls() to fit a custom model to my data, but I don't like how the model is fitting and I would like to use an approach that minimizes residuals in ...
4
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1answer
106 views

PCA and Correspondence analysis in their relation to Biplot

Biplot is often used to display results of principal component analysis (and of related techniques). It is a dual or overlay scatterplot showing component loadings and component scores simultaneously. ...
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17 views

Can we use Principal component analysis for identifying important Independent variables (X's) [duplicate]

I have read principal component analysis is mainly used for variable reduction. I have the concept that we are converting the variables in to new principal components using orthogonal transformation ...
0
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0answers
11 views

Help with PCA and linear optimization

I am trying to use PCA (as implemented in scikits-learn) to reduce the dimensionality of a linear optimization problem (where I have vector contraints). Essentially I'm trying to solve a system: ...
4
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1answer
84 views

Null distribution of subspaces similarity, or what is the distribution of $\mathrm{tr}(AA'BB')$?

What is the distribution of $\mathrm{tr}(AA'BB')$ where $A$ and $B$ are two random matrices of $d \times k$ size with orthonormal columns? Maybe the expected value is easier to compute? A fallback ...
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0answers
24 views

Using PCA to find most 'similar' points to a given observation (mixed data)

I am trying to find the most 'similar' points to each other in a dataset of mixed data. I understand that if these were all numeric variables on the same scale, one could simply use Euclidean Distance ...
0
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0answers
16 views

Using PCA and MANOVA to assess similarity of twins

the general answer to my question has been provided before ( Test if paired data are more similar than non-paired data ), but I'm very much out of my depth and would like to know if my implementation ...
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2answers
39 views

How to find which variables are related to a given variable? Can one use PCA?

I have a table which contains about 80 variables. I will give one variable as input and as output I want to have all the variables that are related to the input variable. Example: I have hospital ...
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0answers
21 views

Forecasting with use of PCA variables as independent and one ternary dependent variable in R

I'm having trouble in taking a direction of my research project. I have independent variables that are commonly used as economic indicators and I want to include variables/indicators that are not ...
3
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1answer
49 views

Understanding cluster plot and component variability

I have run k-means clustering. I have also plotted the results using the following code in R: ...
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0answers
22 views

Best approach to solve this time series classification problem

Hi I have a large data set that contains many time series signals which are labeled to classes, the time series signals look as in the following picture: The time series contain 2000 time samples, ...
1
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1answer
68 views

Principal component analysis for questionnaire data - is it allowed to combine repeated measures into one data set?

My participants evaluated 8 different situations via questionnaire items and I now want to conduct a principal component analysis (PCA) on the questionnaire items to extract the underlying factors. My ...
5
votes
1answer
95 views

Positioning the arrows on a PCA biplot

I am looking to implement a biplot for principal component analysis (PCA) in JavaScript. My question is, how do I determine the coordinates of the arrows from the $U,V,D$ output of the singular vector ...
0
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0answers
18 views

PCA on Wine data with only one binary data(white/red wine) and other quantitative data

I am working on wine data with the following format: ...
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0answers
16 views

Variable not correlating with other variables - reason for deletion in PCA?

When I run PCA on a set of variables, I notice that there is one variable that has very low correlations with the other variables and also most of the correlations are not statistically significant. ...
0
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0answers
20 views

Problematic variables and number of factors in PCA

I have a problem with two variables in PCA. I obtain a certain number of factors (lets say n factors), but on the last factor I obtain only one variable (I will call it X) that loads high on that ...
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0answers
47 views

How to destandardize PCA scores in R

I ran PCA in R using the principal() function in the "psych" package. Suppose my dataset is called "data" (118 rows and 8 columns). The 8 variables are answers from a questionnaire, with a scale that ...
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votes
1answer
35 views

Map PCA eigenvalues to the columns of the data matrix

I am unsure if this questions is valid mathematically speaking, but I am wondering if it is possible to map the eigenvalues that prcomp returns to the original ...
2
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0answers
42 views

Intuition behind random matrices

I am looking for an intuition for random matrices. Say, Gaussian or Binary squares matrices to begin with. I am considering three possible viewpoints: As a $n$ random points in $\mathbb{R}^n$. As a ...
3
votes
2answers
204 views

Does a correlation matrix of two variables always have the same eigenvectors?

I wanted to conduct a total least squares regression on two variables. My statistical programme does not provide TLS, but TLS luckily equals Principal Component Analysis, as far as I know. Since all ...
0
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1answer
32 views

Standardizing sample factor scores: population or standard deviation

Please note: This question pertains to Q Methodology, a research method used to study people's subjectivity. Q embodies ontological and epistemological assumptions that sometimes differ markedly from ...
1
vote
0answers
14 views

What is this “PCA-based re-ordering” for a correlation heatmap / correlogram? [duplicate]

The R function corrgram (in the corrgram package) offers several options for re-ordering the correlation matrix. One of them is ...
0
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0answers
37 views

How to use minor component analysis to forecast time series?

I would like to forecast a time series based on minor eigenvalues of the autocorrelation matrix. But I seem to be doing something wrong. I have the following steps implemented in MATLAB, but the ...
0
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2answers
44 views

Which variables to keep in my analysis based on loadings from PCA? [duplicate]

Could someone please explain me how I should decide which variables to keep in my analysis based on loadings from PCA. The output is: ...