I would like to perform PCA on a dataset, however, not all of the data is in the same scale. Some variables are Height, Weight, Age, while others are Dribbles per Game, Shots per Game, Blocks per Game.  When I re-scale my data, can I use the standardizaiton method such that each newly transformed varaible has a mean of 0 and standard deviation of 1? So my process would be take each value, subtract the mean, divide by the standard deviation.   Also, I have read in some cases for variable like height or weight, it is better to take the log-normal transformation? Once you do that though, the scale is not helpful.  When I perfrom the PCA in R, I planned on using the covariance matrix to see how much of the data I explain with my 2 principal components.
What are the main differences between performing principal component analysis (PCA) on the correlation matrix and on the covariance matrix? Do they give the same results?
What does Use an Object cover? Create line heatmap with QGIS I have loaded my bike tours as .gpx files into QGIS.    It already looks quite nice but I was wondering if it might be possible to create something similar to the strava heatmap with tools of QGIS.     I have tried to generate points along the lines and use kernel density but it just does not look nice as a raster layer.  Any suggestions? Where can I find the status of the released versions of Ubuntu? 90s (or early 2000s) scifi (mini)series where a boy and old man chase a black guy in metal suit Why is the speed of light defined as $299792458$ $m/s$? Why did they choose that number and no other number?  Or phrased differently:  Why is a metre $1/299792458$ of the distance light travels in a sec in a vacuum? Find out which application listens to specific key bindings? Is there an application to know which key is bound by which process and therefore not usable in another application? How can I download an entire website? How can I download all pages from a website?  Any platform is fine. Proof by induction of summation inequality: $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\dots+\frac1{2^n}\ge 1+\frac{n}2$ If I run a randomForest model, I can then make predictions based on the model.  Is there a way to get a prediction interval of each of the predictions such that I know how "sure" the model is of its answer.  If this is possible is it simply based on the variability of the dependent variable for the whole model or will it have wider and narrower intervals depending on the particular decision tree that was followed for a particular prediction? Importance of normal distribution Why did the normal distribution become such a popular (important) distribution? I know one reason is because of CLT. Can you please give more reasons? Unitarily evolving a separable state into an entangled one Is it possible to set a global Blender preference so that all keyframed motion is linear by default? I've been working on some animations recently, and I've noticed that I'm having poor luck with certain things, namely the fact that I don't really use Blender's graph editor very well.  One of the major issues that I have is pretty widespread among 3D graphics programs; when I create an animated object, it defaults to using a curved graph instead of a linear graph, which means that the most movement is at the middle of the animation, and stuff just practically stops near the beginning or the end. While this helps with organic camera movements or such, it's also not what I usually want. Can I set animation curves to default to linear? Why should the "H" option not be used in floats? How do I transfer a Gmail account to a different Google account? In chapter 1, of Landau-Lifshitz Mechanics' book, Landau through isotropy and homogeneity of space and homogeneity of time proves that the Lagrangian must depend of magnitude of velocity of the particle.  This seemed fine. But he didn't give a reason as to why it must depend of $|v|^2$ and not on some $|v|^n$ where $n\neq2$. Books on cosmology I have finished Carroll's general relativity book, Spacetime and Geometry. I am specifically interested in cosmology, so is there any book which goes more in depth into cosmology? I prefer a mathematically rigorous book, which goes beyond the cosmology chapter in Carroll's book. The Big Bang and inflation theory should be dealt with in depth. When performing machine learning, the performance of the machine learning method is dependent on the original function $f$ that we are trying to learn (let's forget for a moment the non-deterministic error and focus on the properties of $f$).  I have a conceptual question. What would make a function easy to learn? For instance, a linear function can be easily learnt by linear methods such as linear regression and SVM. But in the general case, what would make a function easier to learn for decision trees or a neural network?   I believe feature engineering helps us move to a feature space in which the function we want to approximate is easier to represent. But what properties exactly are we trying to achieve for this function? What wand was used by Mr Graves at the time of Fantastic Beasts? We know that the movie Fantastic Beasts is set in 1926. From the movie, we learn that at this time, Dumbledore is a teacher at Hogwarts and Grindelwald is lose after escaping a previous arrest. In the movie we learn that      Mr Graves is in fact Grindelwald in disguise. Grindelwald is shown to be at least in his forties, maybe fifties so he should already be the owner of the wand since he stole it from Gregorovitch as a teen.   We know that Dumbledore won the wand from Grindelwald after defeating him in their historic duel. That duel is always described as being “the end of the dark wizard Grindelwald” so I’m assuming that it didn’t happen prior to the movie and that he didn’t escape after that duel, please correct me if you have cannon evidence stating the contrary.      In the movie, we see Graves’ wand a few time and it isn’t the (very recognizable) one used in DH as the Elder Wand. This could of course be a prop error but since David Yates was also the director on DH and a lot of the visuals are similar I’m assuming it wasn’t. Graves could of course be using another wand in the fear that someone could recognize it but he would still be the rightful master of the Elder Wand. At the end of the movie, Newt is the one that disarms Graves/Grindelwald.   In all logic, he should have been made the new owner of the wand, whether Grindelwald was actually using it or not. That would have made it impossible for Dumbledore to win it from Grindelwald later.  So my question is: What wand is that character using at that specific time? Is he already the owner of the Elder Wand?      And if so, why wasn’t Newt made the new owner of the wand? Theorem. Let $X$ and $Y$ be sets with $X$ nonempty. Then (P) there exists an injection $f:X\rightarrow Y$ if and only if (Q) there exists a surjection $g:Y\rightarrow X$.  For the P $\implies$ Q part, I know you can get a surjection $Y\to X$ by mapping $y$ to $x$ if $y=f(x)$ for some $x\in X$ and mapping $y$ to some arbitrary $\alpha\in X$ if $y\in Y\setminus f(X)$. But I don't know about the Q $\implies$ P part.  Could someone give an elementary proof of the theorem? Is verbatim copying several paragraphs of text with citation considered plagiarism? Is it plagiarism if I copy several paragraphs from another's source (let's say a CS paper) into my work and then footnote Source: ..., for example, as background information?