Pca Definition and 24 Threads

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.

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.

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

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...

Was wondering if PCA can be used to find equation of motions, like F = kx.

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...

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...

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...

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...

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...

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(...)...

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...

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...

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)...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...