If the answer is no, could someone give a simple counterexample? Thank you!
It is a common practice to apply PCA (principal component analysis) before a clustering algorithm (such as k-means). It is believed that it improves the clustering results in practice (noise reduction).   However I am interested in a comparative and in-depth study of the relationship between PCA and k-means. For example, Chris Ding and Xiaofeng He, 2004,  showed that "principal components are the continuous solutions to the discrete cluster membership indicators for K-means clustering". However, I have hard time understanding this paper, and Wikipedia actually .  Also, the results of the two methods are somewhat different in the sense that PCA helps to reduce the number of "features" while preserving the variance, whereas clustering reduces the number of "data-points" by summarizing several points by their expectations/means (in the case of k-means). So if the dataset consists in $N$ points with $T$ features each, PCA aims at compressing the $T$ features whereas clustering aims at compressing the $N$ data-points.  I am looking for a layman explanation of the relations between these two techniques + some more technical papers relating the two techniques.
Possible to specify the GUID when adding a List to a SPListCollection? I found  which goes over how to add a list, but it doesn't seem possible to specify a GUID if you use this method.  Is there any way to create a list and specify the GUID?  I am trying to recreate several lists on a different server and if they do not have the same GUIDs other functionality may break. Keyboard shortcut/command for opening a new nautilus window and raise it What is the shortcut for opening a new window (opening folders). for that I have to go to folder options and right click and then need to click on open new window.  or I have to make focus on the folder icon or open a folder then press  Ctrl+N  for opening a new window is there any direct command spcific to open a new window in ubuntu. Wikipedia introduces the vector product for two vectors $\vec a$ and  $\vec b$ as $$ \vec a \times\vec b=(\| \vec a\| \|\vec b\|\sin\Theta)\vec n $$ It then mentions that $\vec n$ is the vector normal to the plane made by $\vec a$ and  $\vec b$, implying that $\vec a$ and  $\vec b$ are 3D vectors. Wikipedia mentions something about a 7D cross product, but I'm not going to pretend I understand that.  My idea, which remains unconfirmed with any source, is that a cross product can be thought of a vector which is orthogonal to all vectors which you are crossing.  If, and that's a big IF, this is right over all dimensions, we know that for a set of $n-1$ $n$-dimensional vectors, there exists a vector which is orthogonal to all of them.  The magnitude would have something to do with the area/volume/hypervolume/etc. made by the vectors we are crossing.  Am I right to guess that this multidimensional aspect of cross vectors exists or is that last part utter rubbish? How do you auto resize cells in Excel? Why is my camera metering indoor scenes as darker than I expect, forcing me to use a high ISO? I am shooting in natural light, with my subject facing a full floor-to-ceiling south facing window. You would think my meter would allow ISO between 200-400 in bright light, but I was lucky to get it to 640, with f/3.2 and 1/60 (manual mode).  I've read other places that people say put your ISO down to 100 for indoor shots for greatest clarity (especially sharp eyes) — but don't know how I can with subjects potentially moving. Is there a setting in my camera (Canon 5D Mark III) I am missing, or something that might be making my meter need more light? I have read the Rules of a competition. The text of the Rules include a sentence as follows:     As per stated in the Rules the entrants will be notified by May 30th 2010.   Does the sentence above mean that May 30th is included in the term of notification or not? Text gets stretched or disappears when scrolling When scrolling in the Stack Exchange Android app, the text gets stretched vertically, code disappears, and sometimes the entire post content disappears.  This doesn't make the app completely useless, but it's pretty close.   Motorola Razr MAXX, Android 4.0.4. How to find the URLs accessed by iOS Apps? As far as I can tell, it's something like this:  damage reduction = armor / (armor + 100)   Is this accurate? Do I need a visa to visit the UK with my EU partner? I am not from EU. I have Spanish partner and we live in Spain and, because of our official relationship, I have a Spanish family resident permit. We are going to travel to the UK together for tourism. I am confused whether I need an EEA family permit or not.  I will not live there and I'm going to travel with my partner. I was told that I don't need a visa, that showing our civil union document will be sufficent. Is this correct, or do I need a visa to enter the UK?    Thank you so much for your answer. Let me give you more detail.  I hold Turkish citizenship.  My resident card exactly says that Residence Card of a Family Member of a Union Citizen " tarjeta de familiar de la union.   my case is like For example, a non-EEA spouse of a German national living in Germany will usually hold a residence permit issued under German domestic law. Therefore, a United Kingdom EEA family permit is required for travel and entry to the UK , therefore I should consider that I need to EEA Family Permit even if for touristic trip with my partner. "Nikki's and Alice's X" vs. "Nikki and Alice's X" Which option is grammatical?        There will be readings from Nikki Giovanni’s and Alice Walker’s writings.   There will be readings from Nikki Giovanni and Alice Walker's writings.      Saying it out loud the latter sounds right, but looking at it the former looks better. At work we were discussing this as my boss has never heard of normalization. In Linear Algebra, Normalization seems to refer to the dividing of a vector by its length. And in statistics, Standardization seems to refer to the subtraction of a mean then dividing by its SD. But they seem interchangeable with other possibilities as well.   When creating some kind of universal score, that makes up $2$ different metrics, which have different means and different SD's, would you Normalize, Standardize, or something else? One person told me it's just a matter of taking each metric and dividing them by their SD, individually. Then summing the two. And that will result in a universal score that can be used to judge both metrics.  For instance, say you had the number of people who take the subway to work (in NYC) and the number of people who drove to work (in NYC).   $$\text{Train} \longrightarrow x$$ $$\text{Car} \longrightarrow y$$  If you wanted to create a universal score to quickly report traffic fluctuations, you can't just add $\text{mean}(x)$ and $\text{mean}(y)$ because there will be a LOT more people who ride the train. There's 8 million people living in NYC, plus tourists. That's millions of people taking the train everyday verse hundreds of thousands of people in cars. So they need to be transformed to a similar scale in order to be compared.  If $\text{mean}(x) = 8,000,000$  and $\text{mean}(y) = 800,000$  Would you normalize $x$ &amp; $y$ then sum? Would you standardize $x$ &amp; $y$ then sum? Or would you divide each by their respective SD then sum?  In order to get to a number that when fluctuates, represents total traffic fluctuations.  Any article or chapters of books for reference would be much appreciated. THANKS!  Also here's another example of what I'm trying to do.   Imagine you're a college dean, and you're discussing admission requirements. You may want students with at least a certain GPA and a certain test score. It'd be nice if they were both on the same scale because then you could just add the two together and say, "anyone with at least a 7.0 can get admitted." That way, if a prospective student has a 4.0 GPA, they could get as low as a 3.0 test score and still get admitted.  Inversely, if someone had a 3.0 GPA, they could still get admitted with a 4.0 test score.  But it's not like that. The ACT is on a 36 point scale and most GPA's are on 4.0 (some are 4.3, yes annoying). Since I can't just add an ACT and GPA to get some kind of universal score, how can I transform them so they can be added, thus creating a universal admission score.  And then as a Dean, I could just automatically accept anyone with a score above a certain threshold.  Or even automatically accept everyone whose score is within the top 95%.... those sorts of things.  Would that be normalization? standardization? or just dividing each by their SD then summing? How to Select Columns in Editors (Atom,Notepad++, Kate, VIM, Sublime, Textpad,etc) and IDEs (NetBeans, IntelliJ IDEA, Eclipse, Visual Studio, etc) Why are accepted answers not included in the tag badge calculation? For the 400 votes tag badge, does it take into consideration answers marked as the accepted answer?  The description indicates it does not.  I would think an accepted answer would be worth more, or at least the same amount, towards getting a tag badge than just a simple upvote?  Lots of users mark answers as accepted and do not bother giving an upvote since the 15 points is like and upvote and a tip.  So it's possible for a user to have 400 accepted answers with no upvotes and not get a badge where a user with 400 answers (which could be right or wrong) with a single upvote and no accepted answers ever would get the badge.  Just seems a little odd or does accounting for accepted answers make the badge calculation too complicated / slow?  Edit: Questions you ask and submit an answer to shouldn't be counted towards the total for accepted answers.  Edit: It just seems to me that the most important thing in the system is an accepted answer yet there are no badges for achieving more than one accepted answer.  If up votes were more important, and therefore far more worthy of a badge, then why do the top voted answers not appear above the accepted answer?  When it come to badges, accepted answers are second class citizens as compared to a possibly random upvote.   I have seen many upvotes on completely wrong answers but rarely do I see an accepted answer that was completely wrong. Can I have multiple primary keys in a single table? Can I have multiple primary keys in a single table? Alternative version of the Final Value theorem for Laplace Transform Filling cells with sequential numbers in an Excel (2003) macro I need to fill an excel column with a sequential series, in this case from -500 to 1000.  I've got a macro to do it, but it takes a lot of lines for something that seems like it should be a single function [something like FillRange(A2:A1502, -500, 1000, 1)].  But if that function exists, I can't find it.  Is the following as simple and elegant as it gets?  'Draw X axis scale Cells(1, 1).Value = "mV" Cells(2, 1).Value = -500 Cells(3, 1).Value = -499 Cells(4, 1).Value = -498  Dim selection1 As Range, selection2 As Range  Set selection1 = Sheet1.Range("A2:A4") Set selection2 = Sheet1.Range("A2:A1502")  selection1.AutoFill Destination:=selection2 It's clear on how to delete conversations in iMessage one by one. Does anyone know how I can delete multiple or all conversations all at once? Thanks. Any Info on Generalized Binomial and Exponential Series? I was reading Concrete Mathematics by Knuth et al. and on p. 200, it references the generalized binomial series $\mathcal B_t(z)$ and the generalized exponential series $\mathcal E_t(z)$, defined as $$\mathcal B_t(z)=\sum_{k\ge0}(tk)^{\underline{k-1}}\frac{z^k}{k!}\quad\text{and}\quad\mathcal E_t(z)=\sum_{k\ge0}(tk+1)^{k-1}\frac{z^k}{k!},$$ where $x^{\underline k}$ denotes the falling factorial. I was interested in the generalized binomial series because it satisfied the identity $$\frac{\mathcal B_t(z)^r}{1-t+t\mathcal B_t(z)^{-1}}=\sum_{k\ge0}\binom{tk+r}{k}z^k.$$ I've been trying to find a way to compute the sum $\sum_{n\le k\le m}\binom{tk+r}{k}$, so this seemed related. It seems that $\mathcal E_1(z)$ is also somewhat related to the Lambert $W$ function, though I might be wrong. Searching them up online didn't seem to get anywhere, and I just want to find more sources where I can learn about these functions. If anyone can find some resources, I'd appreciate it! Intuition behind using complementary CDF to compute expectation for nonnegative random variables I've read the proof for why $\int_0^\infty P(X &gt;x)dx=E[X]$ for nonnegative random variables (located ) and understand its mechanics, but I'm having trouble understanding the intuition behind this formula or why it should be the case at all. Does anyone have any insight on this? I bet I'm missing something obvious.