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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MD, tICA and (random, stationary) processes
I am asking myself wether PCA and tICA mandatorily need:
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2) Random data as input, i.e. the values sampled per each feature need to have "no memory" of the other ones;
Indeed, I was ...
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Using PCA to check if parameters simulated from a hierarchical Bayesian model are close to real parameters
I have a hierarchical Bayesian model that learns a 5-parameter function for each of the N participants. The priors on each of the 5 parameters are parameterized by a scale parameter, so, it also ...
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Dimension reduction for multivariate functional target that varies in length
I have target features consisting of about 70 different discrete time-series and I want to use this data to learn a model. Now the data is of course very high-dimensional, as I can also use a very ...
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post processing in PCA and making sense of an example
The example is as follows:
A bunch of doctors were asked to score a list of desirable characteristics of sales representatives. The questions were like: "in-depth knowledge about his/her product&...
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Can principal components changed by a normalization method be used to construct original data shape with SVD
I'm planning to use an algorithm called Harmony, designed for data normalization, particularly in the context of single cell data analysis. Harmony operates by taking principal components (PCs) as ...
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Principal components analysis missing data SPSS
I have a large data set (27k) There are 63 variables of interest. I attempted PCA as a dimensionality reduction strategy. The items are scored on different metrics ranging from dichotomous variables ...
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Finding parameters which reveal clustering in t-SNE
These data are from SAMHSA, Mental Health Client-Level Data. I am trying to find the right parameters to obtain clustering as in this paper. Code here.
For now, I'm dropping columns which aren't ...
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Why does FPCA not use scaling as PCA?
Functional principal component analysis (FPCA), according to the original paper, does not use scaling before FPCA, as in PCA. Instead, it uses a covariance matrix to compute the eigen-components.
I ...
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Problem in PCA plot analysis
I have generated these two PCA plots on Galaxy using two different GEO datasets, as a part of RNA-Seq analysis. In both, each group has several clusters. Also in the Obese vs Control dataset, the PC1 ...
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FAVAR model, stationarity and Toda & Yamamoto
To overcome the problems of non-starionarity and cointegration between variables, Toda and Yamamoto (1995) suggested to estimate a VAR with a number of lags sufficient to avoid the problem of ...
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PCA and Gower's Distance
I have a dataset with nutrient information about different ingredients. There are a total of 70 nutrients (numeric features) and 3 categorical features for a total of around 550 ingredients. I am ...
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K-means clustering - weird PCA visualization
I performed PCA on 4 variables and are shown in this visualization:
At first look it doesn't look convincing and the some clusters seem weird.
The data was cleaned and standardized beforehand. Only ...
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PCA: Treating samples rather than variables as the dimensions to be reduced (will something similar to the transpose trick work?)
I have a matrix of data with approximately 200,000 samples and 30 variables. The variables have been standardized because their original units of measurement are arbitrary/irrelevant.
I am interested ...
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Is the assumption of a diagonal covariance matrix on the latent space in a variational autoencoder in any way restrictive?
The covariance matrix in an autoencoder is assumed to be diagonal. And, I see it mentioned in good places that this is a fairly restrictive assumption. To quote
However, in order to simplify the ...
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Why do I need Loadings when I can reconstruct data with eigenvectors in PCA?
I have read the responses to this question here, here and here, but I am still confused on the application of loadings and eigenvectors.
Principally this statement (from the first link),
It is ...
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Principal Component Analysis and Relation to the SVD of a matrix [duplicate]
We are learning about Principal Component analysis in our class, and I having trouble understanding how to compute the principal component given a matrix. For example, here is the matrix we were given....
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Performing PCA with results of multiple other PCAs? Is this legit, how do I interpret it?
I'm a biology researcher, working on a manuscript that involves folks from outside of my discipline. They are using PCA to create indices of demographic variables, to categorize geographic areas. For ...
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Feature selection using backward feature selection in scikit-learn and PCA
I have calculated the scores of all the columns in my dataframe, which has 312 columns and 650 rows, using PCA. I used the following code:
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What kind of data that I need to do my PCA?
So I have a not normal data (I did saphiro test and the result said it's not normal)
Then, I did data transform with log. So the data went normal.
Does the log data can work for my pca?
Or should I ...
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Exploratory Factor Analysis vs. PCA
There is a very nice and clear way to illustrate the geometry of PCA. Is there a similar, geometrical way to illustrate Exploratory Factor Analysis? For example, we have 3D data and we’re using 2 ...
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Are squared loadings and squared distances the same in Principal Component Analysis?
I read online that:
Eigenvalue: Represents the variance explained by the principal component. It equals both the sum of squared loadings for that component and the sum of squared projections of data ...
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Is it okay to report zero eigen values for some PC components if the first few components are greater than one?
I have a dataset which collected household responses over 3 years. It is unbalanced since not all households participated during the three surveys. I run multilevel PCA in stata to account for within ...
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How Do Global Translation and Rotation Relate to the First Six Principal Components in PCA of Molecular Data?
I'm working with Principal Component Analysis (PCA) on molecular data, specifically focusing on the Cartesian coordinates of atoms within molecules. My goal is to preprocess this data for a machine ...
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Can we use Variable loadings from Multi Factor Analysis to define the variable importance
I wanted to know more in-depth about drawing the relationship between variable loadings that we get from Multi-Factor Analysis to variable importance. In other words, for what purposes can we use ...
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Is the FPCA just a PCA on coefficients?
Is functional principal-components analysis (FPCA) on basis representations just a PCA on the component coefficients? The following seems to indicate that yes, it is:
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If I do a PCA on centered only variables (of the same unit), does it mean that the principal components created expresses themselves with that unit?
This question might look very trivial, but PCA is still nebulous to me.
If I have a set of individuals described by 10 variables: $A, B, C, D, E, F, G, H, I, J$, all quantitative and having the same ...
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Input-Output Correlations using PCA
I want to understand the correlation between a set of $\color{red}{\textrm{inputs}}$ and a set of $\color{blue}{\textrm{outputs}}$ deriving from numerical simulations, and possibly reduce dimensions ...
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How to compute the correlations of extra features with respect to the principal components
I have a dataset with 4 features and n observations. I have done a Principal Components Analysis using only 3 features. Now I need to find the correlation between the extra feature and the principal ...
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Nonlinear PCA vs Encoder in Autoencoders
I see that encoders have the benefit over PCA that they can transform both linear and non-linear data. However, isn't non-linear PCA designed to work with non-linear data? So, why do we still prefer ...
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Imaginary numbers in PCA output
Using PCA manually on correlation matrix, I'm getting imaginary numbers in both eigenvalues and eigenvectors. Is this expected behavior?
I understand that when interpreting a matrix as a linear ...
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Error function of Functional Principal Component Regression is itself a curve. Why?
I have data indexed from 0 to 54. Using 6 principal components that explains 99% variation of data I was not expecting the error function to exhibit such a clear shape? By error function from ...
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Differences Between Independent Components from ICA Directly on Samples vs. Mixing Matrix from ICA on Features After PCA Dimensionality Reduction
My understanding is that for Independent Component Analysis (ICA), it is recommended to have more samples than features to avoid underdetermination which might cause convergence or stability issues. ...
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How to create social participation index using STATA?
In order to construct the Social Participation Variable (SPV) for older adults, the study employs a comprehensive set of questions designed to capture the diverse spectrum of social activities in ...
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Independent Component Analysis (ICA): Why rotate whitened data by principal components instead of right singular vectors?
I have a data matrix $ X $ that is $n \times m$, where $n$ is the number of features and $m$ is the number of samples and $ n < m$. Let the Singular Value Decomposition (SVD) of $X$ be $$ X = U \...
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Interpreting PCA Output
I have 40 columns (variables); my PCA output (from Minitab) says PC1-PC14 account for 75% of my variation. How do I pick/determine which of the (original) variables in each PC column are most ...
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Normalize age frequency data for PCA
I am working on a project to forecast house ownership rates. One dataset I have consists of number of people of each age from 1-99 per geographic area code. For example, 20 people aged 1, 59 people ...
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How much is the data energy loss in PCA?
Recently in a slide in about PCA (Principal Component Analysis) I saw a question: "How much is the data energy loss in PCA?&...
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Principal Component Analysis (PCA) the constant sum constraint [closed]
I have data that sums to 100 % +/- 5%, and I was reading that data that sums to 100% should be altered before doing PCA. A method that I found others have done is to use the centered log-ratio (clr) ...
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Interpreting eigenvalues of non-normalized covariance matrix of physical system
Cross-posted from physics stackexchange
Summary: Eigenvalues of a "non-normalized" covariance matrix of time-series measurements from a linear system have units of Action (energy * time). ...
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Determining an efficient index on sample sets
Context: I have an ever-growing data set of samples. (It consists of around $500$ samples currently.) Each sample in this set is an $m \times 3$ matrix where the $m$ rows represent $m$ different ...
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Interpretation of PCA principal components
As a result of a PCA analysis with some initial correlated variables $X_1,..,X_k$ we often do a plot of the loadings to intepret the principal components:
PLOT 1: Plot of the loadings:
We call $v^i,i=...
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Generating Composite Index by PCA for a Single Country with Many Variables
I am doing a course project where I am trying to generate an index to measure the overall level of prosperity of a single country - such as the United States. What I hope is that this index could be ...
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What is the appropriate normalization for finding correlations between Poisson distributions? [closed]
I am interested in using this algorithm, glm-pca, to find a lower dimensional embedding in time series data, specifically neuronal spiking data, which is Poisson distributed. I have looked at some ...
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Calculating the Orthogonal Distance to Kernel PCA subspace (with a new data)
I am studying Kernel PCA methods and now I'm trying to calculate orthogonal distances (OD) on the feature space. What I've found is, you can calculate ODs with a kernel trick if you are interested in ...
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PCA, dot product, column space
Let's assume a data matrix $X_{n\times p}$. The idea of PCA is to find the projection $Xv$ that has the maximum variance. When thinking about column space $C(X)$ then $Xv$ is obviously a linear ...
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Independent features but PCA improves classifiers accuracy significantly. Why?
that's my first question on here :)
I am working with the kNN classifier on datasets from the multivariate normal distribution. I have to groups coming from ...
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Performing PCA on count data with many true 0´s [duplicate]
I have a dataset with behavioural observations that are split into different types within each category.
For example one category would be: "Boldness". Within "Boldness" 7 ...
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Difference between Principal Component as closest linear surface and regression line as best linear approximation in two-dimensions
I am currently working on a presentation on PCA as part of a seminar programme and one slide is about giving an interpretation on the first constructed Principal Component on an arbitrary two-...
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Multiple linear regression with possibly non-independent explanatory variables
For a given household for which I have many years of historical data,
I want to predict the home gas consumption (heating) with a few variables among:
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Principal Component Regression with a Generalized Linear MIXED EFFECTS Model
According to the wiki page on Principal Component Regression, it is possible to transform the beta values obtained from doing regression with PCA data into beta values for the original features. This ...