Questions tagged [pca]

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.

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Why is there an inconsistency between PLS projections and energy statistic output?

On R, I use the mixOmics package to run a repeated measures ("multilevel") Partial Least Squares analysis. I'm able to plot the 2-dimensional PLS projections such ...
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PCA - imperfect reconstruction using maximum number of components [on hold]

I'm struggling with PCA on a theoretical level. I have a dataset of 500 vectors, in 256 dimensions. I then applied Principal Component Analysis to the data set multiple times, for ...
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De-standardizing covariance matrices after applying PCA?

If I decide to use PCA to estimate a high-dimensional asset portfolio covariance matrix using reduced dimensions, I can use the following procedure to transform the low-dimensional matrix back to the ...
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What does PC1 mean in prcomp output?

I'm having trouble trying to understand the output of the prcomp function from package stats in ...
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Weighting in Likert Scale results

I have referred to similar questions on this topic, but the problem presented then was not quite in line with my research, so I have created a new question. My research is the following: I have ...
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Finding PCA-like directions in feature space that maximise sensitivity to a target variable

I have a fairly large space of feature variables in which I want to build a predictor for a target variable. My input dataset for training the predictor are sampled from the space using a mix of log ...
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Is there a extension of PCA for when input variables have a repeating or nested structure?

Is there an analysis technique similar to principal component analysis, but which respects the repeated/tiled nature of the input factors? An illustrative (but somewhat contrived) example might be in ...
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K means clustering on principle components with low explained variance ratios?

Say I have a situation where I do PCA with three components on a data set and the summed explained variance ratios of the three components is relatively low, say less than 0.5. If I were to then do k ...
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Is the first principal component is the one with the largest eigenvalue and how to convert it to explained variance?

In PCA, after we calculate the eigenvalues of each variable, we need to get the explained variance, I read an article which suggests: ...
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Explaining MDS space

I have a set of dummy variables (~300) indicating a particular feature, and rows which represent an individual. I plot this data after using nMDS to visualize which individuals are more similar to ...
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Why does the intercept of Principal Component Regression differ from the orginal regression?

I am comparing two regressions: $y= \beta_0+ \beta_1 x_1 + \beta_2 x_2 + \epsilon $ and $ y = \gamma_0 + \gamma_1 PC_1 + \gamma_2 PC_2 +\eta $. The regressors in the second regression, $PC_1, ...
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Comparing two subsets of data for same observations

I have a data set with 50 test subject and 500 features. The features can be divided into two subsets: profile data of the test subject (pass/fail, age, education, IQ,...) and scoring on the test(...
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How to combine PCA scores? [duplicate]

I was wondering if anyone knew how to combine the different PCA scores. In my dataset I have 3 PCs that explain more than 10% of the variation of shape of a bone and each one explains different ...
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Is it meaningful to reduce dimension from 300 to 100 by PCA?

as I have only learned PCA for a short while, some problems occured when I faced practice. I am willing to accept solution or advice for the following content and great many thanks for anyone's kindly ...
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mathematics behind autoencoders

Someone knows of an article that explains in detail the mathematics behind the auto-encoders. All the articles I find show the typical diagrams ...
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Including binary data during pca [closed]

I'm doing some PCA on scaled features but where I also have some binary variables. When I include the binary features they seem to really impact the PCA and I'm concerned that they will also ...
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Cluster quality internal validity after PCA

Last week I asked: Compare clusters quality (internal validity) after and before dimensionality reduction by PCA I've been trying to calculate internal validity for clusters after PCA using the iris ...
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Matrix representation of PCA

In both Wikipedia and this medium post, I see the succinct principle components decomposition of X represented as $$T=XW$$ However, it seems to me that it should be $T = WX$ instead, if according ...
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Kernel PCA: Find most important variables for each PC

To find the most important variable for each Principal Component is easy with PCA: With data->X and variables->variable_names ...
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Why is there a reconstruction loss in PCA with orthonormal eigenvectors?

I've already read How to reverse PCA and reconstruct original variables from several principal components? and I understand conceptually and visually why there has to be a reconstruction loss. ...
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Why does a PCA component have negative values when all inputs are strictly positive?

Let's say I have X1, X2, X3, and X4. All four variables are strictly positive (no values below zero). The variables are on different scales. I do a PCA on the four variables' correlation matrix and ...
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Compare clusters quality (internal validity) after and before dimensionality reduction by PCA

I've asked this question a few days ago Evaluating HCPC clusters using cluster.stats from fpc library because I was trying to evaluate the quality of my clusters after I did dimensionality reduction ...
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Find most representative variable using PCA in Matlab

I have a dataset with 400 variables and have to find the most representative variable by using PCA in Matlab. I normalized the data X and used: ...
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Principle Component Analysis on categorical predictors [duplicate]

I tried running prcomp() on my training set, which contains some categorical/factor predictors (as well as a binary response), and was given an error saying my data needs to be numeric. Can PCA not be ...
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PCA: Iteratively reducing dimensions

ist there a difference between Iteratively removing one dimension with the least variance by computing pca and repeating this process until the data has k dimensions less... Compared to calculating ...
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Latent Semantic Indexing coordinates vs PCA scores

For PCA: Let $X$ be a mean-centered matrix having as columns observations and as rows features. Via SVD, we have $X = U \Sigma V^\top$. Then PCA scores are $U^\top X = \Sigma V^\top$. For LSA/LSI: ...
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How to get an intuition to draw the eigenvectors for PCA? [duplicate]

For exam preperation I want to know how to get an intuition to draw in the eigenvectors corresponding to the smallest and largest eigenvalue. Student friends say "just get the direction of the largest ...
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Multicollinearity in logistic regression: how to estimate proper model?

I have a data set with highly correlated predictors (CIC-IDS 2017: data set about traffic on computer network). Some predictors have even correlation 1, rest of them are very highly or quite highly ...
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Suggestion for a statistical test

I hope this is the right forum for chemometrics related questions well. Imagine that we have a list of tabulated molecular properties for 40 different molecules such as A) dipole moments B) water ...
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Cross validation score for PCA

I've recently seen an example (Python with scikit learn), where sklearn.decomposition.PCA was passed to cross_val_score as ...
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Evaluating HCPC clusters using cluster.stats from fpc library

I'm trying to get quality measures for example silhouette from HCPC clusters I can get avg.silwidth from the k-means algorithm, using cluster.stats from fpc library : ...
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How to transform test data in Functional Principal Component Analysis in R

I am doing a functional principal component analysis on time series data, and when I finished the FPCA on train data and extracted the PCs. Next, I need to project the test data onto the PCs, here I ...
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Do I really need PCA or scaling in this case?

My dataset have 141 variables, all are numeric. To do clustering based on them, it seems that PCA is required to reduce dimensionality. The var plot shows that variance among these variables are ...
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How to make a scree plot out of SVD data to validate PCA

After doing a singular value decomposition (SVD) of a data set, I'm left with three matrices: 1. An orthogonal Left Singular Vector (U) 2. diagonal matrix with elements in descending order (S) 3. ...
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PCA biplot vs separate score+loading plots

In the context of PCA, is there any reason why the scores and loadings are put into a single plot, the biplot? Do they interact somehow or it is just a preference of just 1 plot over 2 plots?
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eigen value decomposition of co-variance a series generated by factor model

Let's assume $N\times T$ series $Y_t$ is generated by the following equation. $$ Y_t = \begin{bmatrix}A_x & A_m\end{bmatrix}\begin{bmatrix}x_t \\ m_t \end{bmatrix}$$ Where $A_x$ and $A_m$ are $N\...
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Index construction using PCA

If one wants to construct an index using PCA, can he use loadings of the first leading component as weights? For instance, if there are 6 different variables: debt, export, import, FDI, remittances ...
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Can cross validation be applied to threshold based outlier detection model?

I have a threshold based outlier detection model. I apply PCA then calculate the distance from the centre of the features, and use the MSE to differentiate if the datapoint is a outlier. However, I ...
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Differences between matlab's PCA and theoretical Karhunen-Loève expansion

Matlab's pca offers coeff and score as results. Coeff represent the eigenvectors of the covariance matrix of the process in question, while score is the representation of the data in the components ...
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Measuring mutual dependencies between variables. The most fundamental relation

One has a simple dataset of 3 independent variables, e.g., x, y, z. Now: y and z are logically connected (this is known a priori) and indeed a nice & tight correlation (small scatter) between ...
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Orthogonal principal component of submatrix

Consider a data matrix $M_{n ~ x ~Features}$ and its top two principal components ($PC_1$ and $PC_2$). For any of submatrix $S_{n ~x ~F}$, where $F \subset Features$ (i.e. S contains all samples but a ...
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How to measure changes in condition indices over time

I am trying to understand how adding data, one observation at a time, affects the condition indices of a model. A similar question is how adding individual observations affects the principal ...
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Finding the variables that explain a label through LDA and PCA

I have a dataset of about 200 continuous variables with an also continuous target variable. I want to find those predictors that explain target values that are below 50. To do that I create an ...
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Test Error on various types of Regression

I'm testing a dataset for various types of regression, comparing test error for each one to the Mean Prediction Error, that I found at the beginning. Unfortunately I don't have any experience in this ...
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Comparison of explaned variances in PCA

I computed a PCA and am interestet in the explained variance of the first unrotated component. The same procedure was used in a previous study. Question: How do I test whether the two explaned ...
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Why transpose feature vector of eigenvectors during PCA?

As I understand matrix vector multiplication, a matrix linearly transforms a vector because the columns of the matrix represent the basis vectors of the coordinate system to which the vector is being ...
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PCA that includes residuals scores AND the original regressed variable?

I have several variables that I included in a PCA: body length, mass, and development stage. We often calculate a variable we call 'condition'm which is the residuals of mass ~ (body length)^3. ...
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Problem regarding visualizing high dimensional data using PCA

I have 10000 samples, each of which has 100 features. To visualize this high dimensional sample, I use 2 component PCA. Here is a the result: Here, results are colored based on a target value for ...
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feature selection using PCA

is there any way to use PCA for feature selection?! I know what is pca and it is used for dimension reduction. if you can say no or give me some sources if answer is yes, I would be greatly appreciate ...
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Need PCA or other dimensionality reduction with mixed type variables, before doing clustering

I have a fairly large dataset of 171 mixed variables (104 dichotomous/qualitative, and 67 continuous). My goal is to build a typology of agricultural systems. I originally used a PCA to reduce the ...