Is it necessary to standardise data sets before performing PCA? My data sets are a combination of numerical and categorical data. The categorical data are inputted in a one-hot encoding manner. I would like to ask if it is necessary to standardise the data sets first here before performing PCA? If so, what would be a good way to standardise the data set?
Which variables should I transform, center, and/or standardize in my data for Principal Component Analysis? I have multiple datasets that I am attempting to use principal component analysis (PCA) on in order to infer the underlying structure of the data.  I'm attempting to predict growth increment of conifers (the response which apparently needed to be cube root transformed for my original linear models).  My predictor variables include: continuous (some log-transformed like size-related variables, some compositional, and some traditionally scaled); binary; ordinal; and nominal (of which I'm pretty sure I can order with respect to site productivity).  I'm mostly attempting to make inferences because some of my previous models from linear regression have not produced significant terms corresponding to categories like health or climate and I feel that they should have.  I've read in Joliffe (2002) that I might want to leave my compositional data uncentered.  Forgive my naiveté, but I'm wondering if I should also do this for my binary data.  It also seems that I might not want to scale these since they're already on a 0 - 1 scale but I'm not sure.  After only using my continuous predictors (including compositional variables), it appears that a size principal component makes up the largest portion of the variability and Joliffe also mentions that one might want to attempt a "double-centering" of the log-transformed data if this is the case.  I don't know if this is even possible since the log-transformed data only makes up a small portion of my datasets.  Finally, I should ask if having such a combination of data types will complicate analysis so much that it will make inferences unreliable.  I am currently using R for this analysis.  Thank you.
Option clash for package xcolor I'm writing a report, and have a rather large table in my appendix. I'd like to emphasize some specific values by coloring some single cells. I'm trying to do it with xcolor. But receiving the error:  ! LaTeX Error: Option clash for package xcolor. See the LaTeX manual or LaTeX Companion for explanation. Type H &lt;return&gt; for immediate help. ... l.17 The package xcolor has already been loaded with options: [] There has now been an attempt to load it with options [table]   My preamble looks as follows  \documentclass[a4paper,oneside,article]{memoir} \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} \usepackage[danish]{babel} \usepackage{lmodern} \usepackage{graphicx}     \graphicspath{{Figures/}} \usepackage{fullpage} \usepackage{modroman} \usepackage{float} \usepackage{caption} \usepackage[numbers]{natbib} \usepackage{url} \usepackage{pgfplots} \usepackage{mathtools} \usepackage[table]{xcolor}   And take out of my table  \begin{table}  \centering   \begin{tabular}{|c|c|c|}        \hline    \cellcolor{green!25}D &amp; x &amp; D/$L_0$ \\        \hline    65 &amp; 2600 &amp; 0,417\\        \hline    60 &amp; 2400 &amp; 0,385\\   \end{tabular}  \caption{Bestemmelse af bølgehøjde}  \label{tab:Q1} \end{table}   Read some other questions asking more or less the same. And the answer to them seems to be a "collision" between packages. I have no idea how to find the problem. So my question is:   Where is the "collision"? How on earth would I have found it without help ? Where can I get a clean ISO of a specific build of Windows 10? I need to repair my Windows 10 installation. Where can I get a clean ISO (with install.wim, no Install.ESD, so that I can run DISM against the WIM) of the specific Windows 10 build required for this?  In my case, I need the Anniversary update (Build 14393), Creators Update (Build 15063) or Fall Creators Update (Build 16299.15). Using media queries in Lightning component How to deal with hierarchical / nested data in machine learning A piecewise $C^1$ curve has Jordan measure zero. $\newcommand{\Reals}{\mathbb{R}}\gamma:[0,1]\to \Reals^2$ is an injective parametrization of a curve $\Gamma$, which is piecewise $C^1$ and the length of the curve is $L(\Gamma_k)&lt;\infty$.   1.1.: Show that for every $n\in N$ there is a decomposition $0=t_0&lt;t_1&lt; \dots &lt;t_n=1$ of $[0,1]$ so that $L(\Gamma_k) = \frac{L}{n}$ for $k=1,\dots ,n$ and $\Gamma_k=\operatorname{Im}(\gamma_k)$, $\gamma_k=\gamma|_{[t_{k-1},t_k]}$.   1.2.: Show that you can cover $\Gamma$ with a system of spheres of radius $\frac{L}{n}$.   1.3.: Use 1.2. and 1.3. to show that $\Gamma$ has Jordan measure zero.   I wasn't there when they discussed when a function has Jordan measure zero  and how those things correlate with this exercise so if someone could give me some hints that would be great. How can a single slit diffraction produce an interference pattern? How can a light passed though a single slit produce a similar interference pattern to the double-slit experiment? How does the diffracted wave produce the points of cancellation and reinforcement, if there is only one wave? How can I port forward with iptables? Power Series proofs $$\alpha(x) =\sum_{j=0}^\infty \frac{x^{3j}}{(3j)!}$$  $$\beta(x) = \sum_{j=0}^\infty \frac{x^{3j+2}}{(3j+2)!}$$  $$\gamma(x) = \sum_{j=0}^\infty \frac{x^{3j+1}}{(3j+1)!}$$  Show that $\alpha(x+y) = \alpha(x)α(y) + \beta(x)\gamma(y) + \beta(y)\gamma(x)$ for every $x, y \in\mathbb R$.  Show that $\alpha(x)^3 + \beta(x)^3 + \gamma(x)^3 − 3\alpha(x)\beta(x)\gamma(x) = 1$ for every $x\in\mathbb R$.  My work:  Ive noticed that $$\sinh(x)=\sum_{j=0}^\infty \frac{x^{2j+1}}{(2j+1)!}$$ and $$\cosh(x)=\sum_{j=0}^\infty \frac{x^{2j}}{(2j)!}$$ Can hyperbolic trig identies be used to solve these and if so how? Idea behind proof that $\frac{21n+4}{14n+3}$ is irreducible for all $n$ I have a proof of $\frac{21n+4}{14n+3}$ being an irreducible fraction for any positive integer $n$. The proof starts with the following: Indeed, from the equality: $$2(21n+4)-3(14n+3)=-1$$ and so on..But how does this equality follow from the fraction? For realism should I use the maximum number of Subsurf levels? I was wondering if I always need to use the maximum value of the options from the elements of "Add Modifier". For example, do I need to use the view 6 in Subdivision surface? I know it depends of what we are trying to achieve, but we all want the same. Make something look the most believable. So do you always use the maximum value Blender offers? Blender 2.8 contains a number of HDRi's in it by default for the LookDev. I'd like to know how to use them in final renders (EEVEE or Cycles), because quite frankly they appear fantastic. I'm in Belgium (french part) and I cannot find the proper keyboard layout in Settings > Region and Languages > Input Sources.  the closest I found is the french (AZERTY) one but for the symbols such as ! and _ it's not the same keys...  what can I do to solve it ?  Thank you. Is it possible to find the origin of a virus? Is there any method with which you can determine the origin for a given piece of malware in Windows?  One of my PCs was recently infected with the  password stealing trojan. Is there any way to tell from what source this virus was downloaded from? I upgraded my Mega Ring and have been looking for Mega Stones, and I found . However, the Mega Stone isn't in the place it's supposed to be, and I'm sure the location is right. Why isn't my Mega Stone here? What is the definition of textbook or "raw" RSA?  What are some of the properties of textbook RSA?  How does it differ from other schemes based on RSA? I have cobbled together a command to return the process ID of a running daemon:  ps aux | grep daemon_name | awk "{ print \$2 }"   It works perfectly and returns the PID, but it also returns a second PID which is presumably the process I'm running now. Is there a way I can exclude my command from the list of returned PIDs?  I've tested it a few times and it appears my command is always the second PID in the list, but I don't want to grab just the first PID in case it's inaccurate. latex : Exclude draftwatermark from specific pages I am using draftwatermark package. Is there any option to exclude watermark from some specific pages? Say no watermark from pg 3-4. I can not use xwatermark package. It conflicts with the geometry package of my document.  MWE:  \documentclass[12pt,a4paper]{exam} \usepackage{draftwatermark}  \usepackage{lipsum}   \SetWatermarkAngle{45}  \SetWatermarkLightness{.8}  \SetWatermarkFontSize{10cm}  \SetWatermarkScale{5}  \SetWatermarkText{\tt{12345}}  \begin{document}  \lipsum[1-20]  \end{document} Making image positioned on textbox clickable in case of ipad (Creating HTML5 Search input type for iOS) How come if $\ i\ $ not of the following form, then $12i + 5$ must be prime? Can anyone help me with a solution? Write down the assumptions in a form of clauses and give a resolution proof that the proposition                               $$\Big((p \rightarrow q) \land ( q \rightarrow r) \land p \Big) \rightarrow r$$  is a tautology.