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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 ...

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Evaluating the distribution of a continuous variable in a two dimensional space

I have performed a Principal Component Analysis on a set of hydrological indices. Those hydrological indices are derived from the discharge of some rivers (e.g. how long the river needs to get back to ...
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WEKA: splitting training and testing data and using PCA feature transformation and clustering for Neural Network training

I'm working on an assignment that requires me to split some data into a training and testing set, learn a Principal Component Analysis feature transformation on the training set and project it onto ...
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Analytic approach for multi-sensor data

We have sensor data (temperature, pressure) for about 80 sensors and am wanting to be able to recognise when a component 'failure' is occurring to shut down in advance. Predicting the next failure ...
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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 ...
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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 ...
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Doubt regarding PCA

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 (...
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21 views

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 ...
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18 views

What does it mean when PCA loadings are not reported? [closed]

I'm using the principal() from the R package psych. This is my call: ...
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24 views

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

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

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

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

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

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 ...
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69 views

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 ...
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68 views

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 ...
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38 views

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

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

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 ...
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41 views

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

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

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

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 ...
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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 ...
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FAVAR using PCA

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 ...
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23 views

Compositional data tranformation and clustering

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

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:...
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Example for Principal Component Analysis

Where principal component analysis can potentially be used ? some examples with some explanation would be great
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27 views

What does ICA return?

I am confused with ICA. With PCA I understood that it always gives the components with maximum variance. What does ICA return? Does it return components with maximum independence? How to find best ...
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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 ...
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How to perform leave one out validation on multivariate step-wise regression using PCA scores?

I am trying to create a multivariate regression model to predict Y using the scores from principle components analysis (PCA) done on some imaging data X which is composed of coordinates in 2-D space (...
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PCA- creating a model with values obtained

Hoping somebody can help me. I cannot find an example that 'finishes' a problem. I run a proc princomp in SAS. I have hundreds of variables but used four for the purpose of an example. I ...
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How to perform PCA in the cross-validation/test set? [duplicate]

I was using PCA in my whole dataset (and after split to training, cross-validation and test), but after some researchs I found out that is wrong way to do. Then I have few questions: -Are there some ...
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What is the last component of PCA returned by scikit-learn when $n<p$?

Related to this question: Maximum number of principal components in PCA. Is sklearn wrong? If n_samples < n_features, PCA should only returns ...
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Best method for analysing survey data

I have a data set of 10 categorigal variables and one quantitative variable describing the population plus 1 score or measure from 10 seperate experts. Variables 1 to 5 describe a customer profile e....
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What to conclude for the data-set when the variance for principal components is too low or too high?

I am working on analysing and visualizing a dataset having 12 features and came across PCA. I reduced the dataset to 2 principal components which together explain a variance of 18%. I was able to plot ...
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Create a score/rank using the columns in the data set

I have a date set which consists of variables like : Cookies used Locations Product Utilization rate Page visited etc, and so on. Using these columns I want to create a scoring algorithm which ...
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Do you standardize the data before PCA whitening?

I have a data set ranged in different scales as well as some variables are sparse, for example, ...
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98 views

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 ...
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33 views

Finding correlation between 2 predictors and a response

I've created a dataset, where the response, y, is related to the predictors X1, X2, by the formula: y = 2X1 + 5X2. If we look at correlating y with X1, and then y with X2, we get the following: And ...
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How to perform PCA in R, where the eigenvector of the first PC is a constant [closed]

I have the data on 10 variables and I want to perform PCA, forcing the first eigenvector to be a constant, i.e., $q_1 = \frac{1}{\sqrt{10}} \mathbf{1}$, where $\mathbf{1}$ is a vector of ones. I tried ...
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Does non-Gaussian probabilistic PCA give orthogonal basis?

Probabilistic PCA - Gaussian: In their Probabilistic PCA model, Tipping and Bishop assume the following model $$ \boldsymbol{x} \sim \mathcal{N}(0, \mathbf{I})\\ \mathbf{t} | \boldsymbol{x} \sim \...
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Principal Component Analysis, should I interpret the component matrix or the component score?

I am doing a Principal Component Analysis on some demographic data. I have extracted four principal components and I hope to find out how each component is characterized by the original variables. I ...
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principle component analysis: help with interpretation

I'm teaching PCA to myself for some environmental data analysis. I understand the intuitive and geometric definition, but I'm not quite sure what exactly it's telling me. What exactly do the ...
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R: Is there a method similar to PCA that incorperates dependence

Background We currently applied PCA to a set of variables, and noticed that our dataset actually contains two "motifs". To explain, let say we have the variables ...
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How to recover the original coefficients in principal components regression?

Let $y$ be a response variable of size $n\times1$, and $X$ be a covariates matrix of dimension $n\times p$, being $p>n$. Since $p>n$, I cannot directly solve the linear model $\tilde{y}=X\tilde{\...