I have too many environmental variables to use in a multiple regression analysis. If I use all the variables the models are just too complex. The use of the PCA axes in the regression analysis was impossible to interpret (since there wasn't a clear correlation with environmental variables), so we chose to select a limited number of variables, namely those that had the higher explanation in PCA.  A PCA was used for each set of environmental variables, namely the variables related with the structure of the stream, the evolving vegetation, the climatic, the physical-chemical characteristics of the water from summer period and from winter period, separately. The PCA was performed using the correlation matrix option, using the software PC-ORD, v. 4.21 (McCune &amp; Mefford 1999).  For each set of variables, only the variables with coordinates higher than 0.20, for the two first axes, of the PCA, were selected to be used in multiple regression analysis.  I could not find literature that confirms that it's OK to do this, but I think it is not wrong.
I'm new to feature selection and I was wondering how you would use PCA to perform feature selection. Does PCA compute a relative score for each input variable that you can use to filter out noninformative input variables? Basically, I want to be able to order the original features in the data by variance or amount of information contained.
Nature of the quantum degeneracy pressure Why are symmetric positive definite (SPD) matrices so important? I know the definition of symmetric positive definite (SPD) matrix, but want to understand more.   Why are they so important, intuitively?  Here is what I know. What else?   For a given data, Co-variance matrix is SPD. Co-variance matrix is a important metric, see this  for intuitive explanation. The quadratic form $\frac 1 2 x^\top Ax-b^\top x +c$ is convex, if $A$ is SPD. Convexity is a nice property for a function that can make sure the local solution is global solution. For Convex problems, there are many good algorithms to solve, but not for non-covex problems. When $A$ is SPD, the optimization solution for the quadratic form $$\text{minimize}~~~ \frac 1 2 x^\top Ax-b^\top x +c$$ and the solution for linear system $$Ax=b$$ are the same. So we can run conversions between two classical problems. This is important because it enables us to use tricks discovered in one domain in the another. For example, we can use the conjugate gradient method to solve a linear system.  There are many good algorithms (fast, numerical stable) that work better for an SPD matrix, such as Cholesky decomposition.   EDIT: I am not trying ask the identities for SPD matrix, but the intuition behind the property to show the importance. For example, as mentioned by @Matthew Drury, if a matrix is SPD, Eigenvalues are all positive real numbers, but why all positive matters. @Matthew Drury had a great answer to flow and that is what I was looking for. The other day I was looking at Stack Overflow on my Android phone. All is made very nice and all, but I could not find the Review button/link. Is it being implemented, did I miss it, or it is not available? Why are hand-built wheels considered to be better than machine-built wheels? Why are hand-built wheels considered to be better than machine-built wheels? I would think that a machine-built wheel would be better and cheaper, since machines generally do a more precise job than humans. Remap Keys in Linux I'd like to switch my Ctrl and Alt keys under Linux (to make it more Mac-like).  How do I do this?  If it helps, I'm running Ubuntu 9.04. INT vs Unique-Identifier for ID field in database How can we do pagination in datagridview in winform Batch script to resize height of all layers to same height but keeping their original aspect ratio I have hundreds of product image layers and I am trying to resize them all to the same height (ignoring the width) and retaining their individual aspect ratio's.  Is there a script available that does this? Or a feature I am unaware of?  Thanks! Narrow-phase collision detection algorithms The more I use Stack Exchange, the more it is getting a knowledge-base for me. All questions, that I need for later reference I mark as favorite. Now I need to store these pages locally on my laptop. It is really time-consuming:  I could use Ctrl+S on each favorite question page  on Linux: there could be a solution with wget -N -r -l 1 &quot;https://stackoverflow.com/users/1069083/rubo77?tab=favorites&quot;  this will download all favorite questions but it creates no correct index.html Another approach would be to use the  to automatically follow into all your Stack Exchange-accounts. But that would have to be somehow limited to only favorites links on your  in each stack. cross-platform: You would need a firefox-plugin that downloads links recursively but only within the favorite-area of the  in your stack  Additionally, I would like to  and Equivalence between least squares and MLE in Gaussian model I am new to Machine Learning, and am trying to learn it on my own. Recently I was reading through  and had a basic question.   Slide 13 says that "Least Square Estimate is same as Maximum Likelihood Estimate under a Gaussian model". It seems like it is something simple, but I am unable to see this. Can someone please explain what is going on here? I am interested in seeing the Math.   I will later try to see the probabilistic viewpoint of Ridge and Lasso regression also, so if there are any suggestions that will help me, that will be much appreciated also. I've got two arrays of the same size.  I'd like to merge the two so the values of one are the key indexes of the new array, and the values of the new array are the values of the other.  Right now I'm just looping through the arrays and creating the new array manually, but I have a feeling there is a much more elegant way to go about this.  I don't see any array functions for this purpose, but maybe I missed something?  Is there a simple way to this along these lines?  $mapped_array = mapkeys($array_with_keys, $array_with_values); What is a good general document size for web page mockups and prototypes? I do mockups and prototypes of sites and designs all the time, but I've always wondered if there is a standard size or width I should be using. Generally I'll make my document either 1024, 1200, or 2560px wide, depending on what I'm doing.  So what do you think? What is a good or standard size for this? I am trying to make folder that everyone can view and can't copy,modify.    For all answers.I thinking about specially ms office files. I tried following methods  Software  - copy protect    - anti copy    This method can't protect save as and upload  MS office macro    Users can enable,disable macros.  MS office restriction    This is best choice but can't protect from file uploading.   Almost I found the solution. Way is combination of MS office restriction and restrict access from browsers using firewall or antivirus. But I don't exact how to do this. Make "compact view" as a default directory view instead of "icon view" How can I make "compact view" the default for all directory views in File Manager, instead of "icon view" ? What's the difference between using black and white mode in-camera, and converting in post? For black and white photography, will there be any quality difference between using the built-in black and white mode, or shooting in color initially and then removing the color later using Photoshop (or similar application)?  I have a high-end compact camera, the . In many machine learning applications, the so called data augmentation methods have allowed building better models. For example, assume a training set of $100$ images of cats and dogs. By rotating, mirroring, adjusting contrast, etc. it is possible to generate additional images from the original ones.  In the case of images, the data augmentation is relatively straightforward. However, suppose (for example) that one has a training set of $100$ samples and few hundred continuous variables that represent different things. The data augmentation does not anymore seem so intuitive. What could be done in such case? Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a differentiable function such that $f(0) = 0$ and $f'(x) = [f(x)]^{2}$, $\forall x \in \mathbb{R}$. Show that $f(x) = 0$,  $\forall x \in \mathbb{R} $.  I first (unsuccessfully) tried using the Mean Value Theorem, but this is in the Integrals chapter so the solution probably involves them. Can't really see where integrals come in here though.  What I've got so far:   (i) Since $f$ is differentiable, thus it is continuous and, hence,  integrable. Therefore $f^2$ is also integrable and as $f'=f^2$, $f'$ is too.   (ii) $f' \geq 0$, $\forall x \in \mathbb{R}$ When I run this command :  apt install libkf5*   I get the following error :  Unable to locate package libkf5*    I'm sure that the packages whose names start with libkf5 exist (tab-completion says so) . So the problem is not about the absence of those packages.(Note the asterisk at the end of that error message , the wildcard's not working at all) I use apt v.1.9. Thanks in advance. How do I create tools with multiple properties?