# pca's questions - English 1answer

2.352 pca questions.

### 9 Performing PCA with only a distance matrix

I want to cluster a massive dataset for which I have only the pairwise distances. I implemented a k-medoids algorithm, but it's taking too long to run so I would like to start by reducing the ...

### when do the principal components of PCA form a basis for the dataset?

Suppose I do a PCA on a data set and get $k$ principal components that explain 100% of the total variance of the data set. We can say any observation from the data set can be reconstructed by the ...

### The miracle of the Lanczos/conjugate gradient algorithm

Lanczos/Arnoldi/Rietz/CG-like algorithm share the same core strategy... In each, a little miracle appears, most of the Gram-Schmidt inner products are zeroes ! In others words, new direction need only ...

### Are eigenfaces same as eigenvectors?

I'm trying to understand the difference between eigenvectors and eigenfaces, are they different names for same concepts? I ask this because I got confused when I am trying to compute eigenvectors for ...

### Doubt regarding PCA

1 answers, 19 views pca dataset dimensionality-reduction
I have 5 different independent variables, lets name 1 to 5. The 3rd IV has 10 sub-variables under it and 4th IV has 11 sub-variables in it. Whereas other 3 IV's have just two sub-variables (...

I'm (very) new to PCA and confused about how to use the output of a PCA analysis to construct new variables that will be used as predictors in a regression analysis. I've looked at previous questions (...

### 4 Principal Component Analysis: whether a variable is significantly loaded on a principal component or not?

Often, a variable is considered to be significantly loaded on a PC if its loading value in the loading table is above a cut off value (suppose 0.4 or 0.5 in some published cases). Is there any ...

### Principal components: Can I interpret PCA as essentially a change of basis

I was hoping that someone could simply validate or correct my interpretation of Principal Components Analysis. There are a lot of questions on this site about Principal Components analysis--some ...

### PCA with oblimin rotation: should I interpret component matrix, pattern matrix or structure matrix?

1 answers, 1.056 views pca spss cronbachs-alpha factor-rotation
I conducted a principal component analysis (PCA) with direct oblimin factor rotation in SPSS. Because by that time I didn't know any better, I used the COMPONENT MATRIX for interpretation. I added ...

### 2 Should PCA be (always) done before Naive Bayes classification

According to Wikipedia page on Naive Bayes: .. Naive Bayes classifiers are a family of simple "probabilistic classifiers" based on applying Bayes' theorem with strong (naive) independence ...

### 13 PCA on high-dimensional text data before random forest classification?

Does it make sense to do PCA before carrying out a Random Forest Classification? I'm dealing with high dimensional text data, and I want to do feature reduction to help avoid the curse of ...

### 3 Why robust PCA results change with each run?

According to Filzmoser et al. 2009, the best way to conduct a principal component analysis for compositional data with outliers is: using a robust PCA method and using the isometric log ratio ...

### How to take the PCA components and perform a GLM with them alongside other data?

I have got a dataset that represents around 30 characteristics from a few hundred samples. Some of these characteristics could be condensed into 2 PCs as shown by a PCA. Now I would like to take these ...

### 1 Is it appropriate to run PCA on a subset of variables?

0 answers, 220 views regression pca
I was thinking about using PCA to deal with issues of multicollinearity on my dataset. I was wondering how appropriate it is to run PCA on only subsets of variables that seem to have issues of ...

### How Eigen faces can be used for image reconstruction? [closed]

I am reading the research paper “Eigen faces for Recognition”. https://www.cs.ucsb.edu/~mturk/Papers/jcn.pdf. In Figure 2, paper shows the seven Eigen faces having white and black spots on them. What ...

### What does it mean when PCA loadings are not reported? [on hold]

0 answers, 18 views r pca
I'm using the principal() from the R package psych. This is my call: ...

### Cumulative sum of pca explained variance greater than 1

1 answers, 23 views pca python
I am getting strange result. data_scaled = StandardScaler().fit_transform(dat_final) pca = PCA(.99) pca.fit(data_scaled) print(np.cumsum((pca.explained_variance_))) plt.plot(np.cumsum((pca....

### 7 Very different results of principal component analysis in SPSS and Stata after rotation

3 answers, 6.145 views pca spss stata factor-analysis factor-rotation
For my PhD thesis I have to do a Principal Component Analysis (PCA). I didn't find it too difficult in Stata and was happy interpreting the results (I know there is a difference between factor and ...

### Is it correct to standardise (z-score) features within samples before PCA?

1 answers, 17 views pca standardization
Given a data set where we have different measured features in the same units for each subject. For example, numbers of different cell types (features) in a tumour (subject), where we have n tumours ...

### 2 how to optimize reduced rank regression with constant diagnoal constraint?

I am trying to optimize a panel regression $G=\beta G+e$. $G \in R^{N\times T}$. $\beta\in R^{N\times N}$ is unknown coefficient, constrained to $diag(\beta)=0$, and reduced rank $rank(\beta)\leq r$. ...

### PCA (or PLS-DA) on time series normalized to day 0 for each protein

I have a data set with about 1000 proteins (concentration levels) measured at 3 different time points for 10 different patients performing exercise. I would like to identify proteins that changes due ...

I’m using Stata 12.0, and I’ve downloaded the polychoricpca command written by Stas Kolenikov, which I wanted to use with data that includes a mix of categorical ...

### 8 How do children manage to pull their parents together in a PCA projection of a GWAS data set?

1 answers, 148 views pca python high-dimensional genetics gwas
Take 20 random points in a 10,000-dimensional space with each coordinate iid from $\mathcal N(0,1)$. Split them into 10 pairs ("couples") and add the average of each pair ("a child") to the dataset. ...

### 17 In genome-wide association studies, what are principal components?

1 answers, 17.940 views pca genetics gwas
In genome-wide association studies (GWAS): What are the principal components? Why are they used? How are they calculated? Can a genome-wide association study be done without using PCA?

### 1 What does it mean to apply k-means algorithm on transformed distance matrix?

1 answers, 26 views clustering pca k-means bioinformatics
I am reading a very good (recent) publication in clustering: Kiselev et al., 2017, SC3 - consensus clustering of single-cell RNA-Seq data (if you don't have access, see author PDF). The algorithm ...

### 4 Evaluating an autoencoder: possible approaches?

Literature suggests that Antoencoders can be effective in dimensionality reduction, like PCA. PCA can be evaluated based on the variance of each principal component generated. How to do the same for ...

### Does it make sense to use PCA right after GBM?

0 answers, 10 views pca boosting
My Problem: I'm trying to classify a data into two groups as A and B based on 25 observations (data point) and 100 features. I used the Gradient Boosting Machine (GBM) to find out which feature has ...

### 125 PCA on correlation or covariance?

7 answers, 95.840 views correlation pca covariance factor-analysis
What are the main differences between performing principal component analysis (PCA) on the correlation matrix and on the covariance matrix? Do they give the same results?

### Principal component analysis how to find important factors in spss

0 answers, 14 views pca spss factor-analysis
I did a survey to know the attitude of customers towards various elements of direct banking channels. I have performed Principal Component Analysis on a set of 70 items and generated five factors. I ...

### 6 Questions on PCA: when are PCs independent? why is PCA sensitive to scaling? why are PCs constrained to be orthogonal?

1 answers, 6.201 views pca dimensionality-reduction
I am trying to understand some descriptions of PCA (the first two are from Wikipedia), emphasis added: Principal components are guaranteed to be independent only if the data set is jointly normally ...

### Inferences from PCA plot

I have done a dimensionality reduction of binary labelled data (0,1 labels) from 300 features to 2 features. The plot looks like - What kind of inferences can I make from this plot? Can I infer - ...

### How PCA locates the origin (centre of data points) in the new space? [duplicate]

I am reading a document on PCA. I got some idea that PCA is a dimensionality reduction technique. It performs this tasks by shifting the data points in the new space. The centre of points in the old ...

### 1 Can I multiply samples' scores in PCA to project new data?

0 answers, 13 views r pca
I have m1 rows (samples) and n columns (variables) in matrix A, and m2 rows and n columns in matrix B (n>m1 and n>m2). Normally, I performed PCA on matrix A and got a low-dimensional representation of ...

### 194 What are the differences between Factor Analysis and Principal Component Analysis?

13 answers, 194.093 views pca factor-analysis
It seems that a number of the statistical packages that I use wrap these two concepts together. However, I'm wondering if there are different assumptions or data 'formalities' that must be true to use ...

### 33 How does Factor Analysis explain the covariance while PCA explains the variance?

2 answers, 11.844 views pca factor-analysis geometry
Here is a quote from Bishop's "Pattern Recognition and Machine Learning" book, section 12.2.4 "Factor analysis": According to the highlighted part, factor analysis captures the covariance between ...

### 1 High proportion of zero values and PCA

My aim is to perform PCA since I have 76 variables in my dataset. Problem is that most of my variables are highly skewed as you can see in the histogram below. These variables are proportions ...

### Visual Representation of Eigen Faces(i.e Eigen Vector s)

0 answers, 8 views machine-learning pca
I am studying about eigen faces. I have some confusion in understanding the concepts. Initially we have a 255*255 2d array but then we create 1d vectors i.e N^2 * 1 vector. We can do this for M images....

### What is the relation between the number of components in PCA vs. overall number of components?

1 answers, 20 views machine-learning pca
For example, if I have a 64-dimension problem, and 80% of the variance lies within just 12 components. Is there some mathematical relationship that says something about the number of components that ...

### 1 Can the Eigen faces be negative?

I have checked several sites and found that eigen faces are Eigen Vectors. PCA transforms the faces into a new space such that the hyper plane is in the direction of maximum variance. I have attached ...

### 9 Principal Component Analysis and Regression in Python

4 answers, 28.791 views pca python scikit-learn
I'm trying to figure out how to reproduce in Python some work that I've done in SAS. Using this dataset, where multicollinearity is a problem, I would like to perform principal component analysis in ...

### 1 How do I get the density of a region in a vector space?

I have a simple problem, which I think must have an easy solution. I have a vector space say with a 1000 dimensions for each vector. Now, I have a large number of sample vectors from this vector ...

### 1 PCA's eigenvector with low variance, why people think they are 'noise'?

0 answers, 21 views pca factor-analysis stationarity
When we do a textbook PCA decomposition, get a series of eigenvalue $\lambda$ and eigenvector $v$ that fulfill: $Av= \lambda v$ we can sort these eigenvalues (together with the corresponding eigen ...

### 1 principal component analysis with missing data

2 answers, 508 views clustering pca multivariate-analysis
for a prospective study of parameters affecting student's success in graduate school I am looking at a population of about 1500 med students. I have performed a cluster analysis (using Gower's ...

### FAVAR using PCA

0 answers, 15 views pca factor-analysis var
I am doing a FAVAR analysis with 2 steps PCA method. I am confused a bit about the second step. When I get the PCs, how should then I estimate VAR? Just including PCs as other variables and simply ...

### residualized covariance matrix from pca/eigenvalue decomposition

I understand that given N dimensional data you can use PCA to construct an N dimensional orthonormal basis that explains 100% of the variance of the original data. However, you can also construct ...

### Compositional data tranformation and clustering

0 answers, 23 views clustering pca compositional-data
I am working with datasets that consists of mixed type purchase data for a whole year of 2017. My aim is to use PCA/FA for dimension reduction since I have many variables in this dataset and then do ...

### 1 Is PCA a continuous function of the data?

Suppose that my data are such that a PCA gives a unique solution for the first principal component up to scaling (e.g. my data do not all lie on a circle, or some such weirdness). Is it the case that ...

### 3 Best way to analyse percentage data

I have percentage data and would like to see if these different variables have an affect on certain factors; i.e., I have different habitats of an area e.g., improved grassland: 40%, arable: 15%, ...

### Kendall regression on a criterion based on principal components

0 answers, 11 views regression pca
I am reading a paper and the data passed to a data.frame in R. On R: X[60x14] = matrix of predictors (without the dependent) R_xx: Correlation Matrix. evalues and vectors of R_xx Then the author say:...

### -2 Example for Principal Component Analysis

1 answers, 29 views pca dimensionality-reduction
Where principal component analysis can potentially be used ? some examples with some explanation would be great