# What is Pca: Definition and 24 Discussions

The Pitcairn PCA-2 was an autogyro developed in the United States in the early 1930s. It was Harold F. Pitcairn's first autogyro design to sell in quantity. It had a conventional design for its day – an airplane-like fuselage with two open cockpits in tandem, and an engine mounted tractor-fashion in the nose. The lift by the four-blade main rotor was augmented by stubby, low-set monoplane wings that also carried the control surfaces. The wingtips featured considerable dihedral that acted as winglets for added stability.

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1. ### Lecture 5a - Pandemic Pedantics - Derivation of PCA and Kernel PCA

Here we talk about how we come to the formulas for PCA and Kernel PCA. We briefly introduce kernel functions, and talk about feature spaces. This builds on the introductory lecture for PCA and also that for Kernel PCA.
2. ### Lecture 5 - Science, Toys, and the PCA

We open this lecture with a discussion of how advancements in science and technology come from a consumer demand for better toys. We also give an introduction to Principle Component Analysis (PCA). We talk about how to arrange data, shift it, and the find the principle components of our dataset.
3. ### Lecture 2 - Understanding Everything from Data - The SVD

In this video I give an introduction to the singular value decomposition, one of the key tools to learning from data. The SVD allows us to assemble data into a matrix, and then to find the key or "principle" components of the data, which will allow us to represent the entire data set with only a few
4. ### A Has anybody programmed the mcKL expansion?

Hello everyone. I am trying to implement the mcKL expansion proposed in this article using Matlab and two vectors of correlated data of size 1000*50, meaning 50 realizations of two random processes measured 1000 times. As the article says, if two stochastic processes are correlated, one cannot...
5. ### Can PCA Be Used to Derive Equations of Motion?

Was wondering if PCA can be used to find equation of motions, like F = kx.
6. ### A PCA and Maximum Likelihood?

Hi, I am looking into a text on PCA obtained through path diagrams ( a diagram rep of the relationship between factors and the dependent and independent variables) and correlation matrices . There is a "reverse" exercise in which we are given a correlation matrix there is mention of the use of...
7. ### I Differences between the PCA function and Karhunen-Loève expansion

Hello everyone. I am currently using the pca function from MATLAB on a gaussian process. Matlab's pca offers three results. Coeff, Score and Latent. Latent are the eigenvalues of the covariance matrix, Coeff are the eigenvectors of said matrix and Score are the representation of the original...
8. ### Question about the PCA function

Greetings everyone. I have generated a gaussian random process composed of 500 realizations and 501 observations. The used random variables are gaussian normal. I have then applied the pca analysis to that process (Mathwork's help). However, if I plot the histograms of the coeffs I don't find...
9. ### MATLAB Problem with random variables in Matlab's PCA

Hello. I have designed a Gaussian kernel as: [X,Y] = meshgrid(0:0.002:1,0:0.002:1); Z=exp((-1)*abs(X-Y)); Now, I calculate PCA: [coeffG, scoreG, latentG, tsquaredG, explainedG, muG]=pca(Z, 'Centered',false); I can rebuid the original data propperly as defined in the dcumentation...
10. ### I Using PCA for variable reduction

In the textbook “Principal Component Analysis” Jolliffe (§9.2) suggests the following method for variable reduction: “When the variables fall into well-defined clusters, there will be one high-variance PC and, except in the case of 'single-variable' clusters, one or more low-variance PCs...
11. ### I Principal component analysis (PCA) coefficients

I am trying to use PCA to classify various spectra. I measured several samples to get an estimate of the population standard deviation (here I've shown only 7 measurements): I combined all these data into a matrix where each measurement corresponded to a column. I then used the pca(...)...
12. ### A Apliying PCA to two correlated stochastic processes

Hello everyone, I have two matrices of size 9*51, meaning that I have 51 measurements of a stochastic process measured at 9 times, being precise, it is wind speed in the direction X, I have the same data for the direction Y. I am aware that both stochastic processes are not independent, so I...
13. ### I Pca and eigenvalue interpretation

hello, i have a reasearch to analyse the movement of human walking using pca. i did it like this 1. i dibide the body into some part (thigh, foot, hand, etc) 2. i film it so i can track the x position of the parts 3. i get the x to t graph for every part 4. i make a matrix which column is the...
14. ### Java Eigenword embeddings and spectral learning; I'm a beginner....

Hi everyone, I am a mathematics undergraduate and I'm currently doing an internship at the informatics department of a university. I am well and truly out of my depth. My supervisor has assigned me tasks which include Java (a language I'm having to quickly pick up, having only used python/R)...
15. ### PCA principal component analysis standardized data

Why is better to use the standardized data using the correlation matrix than say converting data into just similar units. Like say I had data that measured car speeds measured in seconds for some data and the other data measured in minutes. Why would it be better just to measure the data using...
16. ### Is a Subset of the Eigenvector Matrix in PCA Equivalent to a Submanifold?

Hi all, Could anyone please clarify something for me. PCA of a data matrix X results in a lower dimensional representation Y through a linear projection to the lower dimensional domain, i.e Y=PX. Where rows of P are the eigenvectors of X. From a pure terminology point of view is it correct...
17. ### SVD, PCA, multi dimensional visualization

I just did some quick searches for open source multi dimensional data visualization, but can't find what I'm looking for. Before I spend time coding it up, I want to see if some one's done it already. The data will be points with multi (n>20) dimensional coordinates 1) I want to be...
18. ### MHB Combining PCA Models: Linear Algebra Help Needed

Hello, I am working with face recognition. I have two models from two separate datasets with the same number of dimensions. I wish to implement this method to combine PCA models. http://www.cs.cf.ac.uk/Dave/Papers/Pami-EIgenspace.pdf My linear algebra isn't great. So i am lost after step 1...
19. ### Is There a Linear Transformation to Map Data Set X to Y in PCA?

This question broadly relates to principle component analysis (PCA) Say you have some data vector X, and a linear transformation K that maps X to some new data vector Z: K*X → Z Now say you have another linear transformation P that maps Z to a new data vector Y: P*Z → Y is there...
20. ### Principal component analysis (PCA) with small number of observations

Dear all, I'd like to apply principal component analysis (PCA) to hyperspectral data (~1000 bands). The number of observations is 200. The estimated variance covarance matrix is singular because the number of observations is smaller than the number of variables. My questions are, Can I...
21. ### What is the difference between whitening and PCA?

Hi, all I am looking into whitening transformation. According to the definition and explanation of Wikipedia, whitening transformation is a decorrelating process and it can be done by eigenvalue decomposition (EVD). As far as I know, EVD is one of the solutions of principal component analysis...
22. ### Mean centering of the covariance matrix in PCA

Hi all, I thought I posted this last night but have received no notification of it being moved or can't find it the thread I have started list. I was wondering if you could help me understand how PCA, principal component analysis, works a little better. I have read often that it to get the...
23. ### Determining the Importance of Certain Data Types (PCA?)

Hello Forum, My first post... Im doing a project that extracts certain features from music files. These "feautures" will/may become the inputs to a neural network. I have 12 features in total which will correspond to a maximum of 12 inputs to the neural network. Essentially I will have 12...
24. ### PCA and variance on particular axis

Hi All: If given a set of 3D points data, it's very easy to calculate the covariance matrix and get the principle axises. And the eigenvalue will be the variance on the principle axis. I have a problem that if given a random direction, how do I calculate the variance of the data on the given...