I observe that in machine learning, scaling is done to make the numeric input fit within the range from -1 to +1. Why not a bigger range like -10 to -10? If smaller range is better, then why not -0.1 to +0.1? Why is this numeric range (-1 to +1) preferred? Is there a mathematical reason to choose this range?
I'm learning Neural Networks and I grasped the algebra behind them. I'm now interested in understanding how normalization and centering of the input data affect them. In my personal learning project (Regression with NN) I've transformed my input variables to a range between 0 and 1 using the following function:  normalize &lt;- function(x) {return((x - min(x))/ (max(x) - min(x)))}   The NN model fits well and has an acceptable out-of-sample prediction error.   However, I read in other  that scaling the inputs to have mean 0 and a variance of 1 is advised for NN. I don't fully understand:   how this transformation works better for NN against the min-max normalization between 0 and 1. how can I assess which transformation to apply in my data?
Get index of parent div from child divs Ramsey Number Inequality: $R(\underbrace{3,3,...,3,3}_{k+1}) \le (k+1)(R(\underbrace{3,3,...3}_k)-1)+2$ I want to prove that:  $$R(\underbrace{3,3,...,3,3}_{k+1}) \le (k+1)(R(\underbrace{3,3,...3}_k)-1)+2$$  where R is a Ramsey number. In the LHS, there are $k+1$ $3$'s, and in the RHS, there are $k$ $3's$. I really have no clue how to start this proof. Any help is appreciated! How to pick and differentiate a flat color? When I am using Color Picker in Photoshop or Illustrator I am unable to get a Flat color. What are the things or basic points that I should keep in mind so that I am able to judge a color whether it is flat or not. Although flat color can be picked form websites such as       e.t.c.    Picking a flat color is not my problem. I want to learn the skill needed to judge and differentiate a flat color from other. Do all flat  colors values follow a pattern ?(like specific hue and saturation). My specific question is with the ASUS M3N78-VM motherboard that my home server uses. I currently have 4x2GB installed for a total of 8GB but I was hoping to upgrade to say 16GB (4x4GB). The official specifications of that motherboard says it only supports up to 8GB but it was released back when only 2GB sticks were available. What, if any, would prevent it from working with 4GB sticks now that 4GB sticks are available?  My general question is with motherboards in general... what would prevent a motherboard from working with bigger sticks if its all just the same type (DDR2 for example and same speeds) of memory? Friendly way to make previous large calculation results reusable in a new session Counting overlapping polygons in GeoJSON to result in new set of polygons? Requires installation of untrusted packages? I tried installing VLC Player yesterday, and I got the Requires installation of untrusted packages error.  I searched for hours for a solution to this problem, and finally came upon a suggestion that said to change servers for downloading updates from.  I did this, and it gave me a 404 error when I clicked on "Check" in the Update Manager.  I tried switching my server back to the main one (and after that, several other ones), but I am now still getting a 404 error:   And the other error I get when downloading or updating:   Edit: Output of cat /etc/apt/sources.list:  deb-src http://us.archive.ubuntu.com/ubuntu/ precise main restricted #Added by software-properties  # See http://help.ubuntu.com/community/UpgradeNotes for how to upgrade to # newer versions of the distribution. deb http://us.archive.ubuntu.com/ubuntu/ precise main restricted multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise multiverse universe #Added by software-properties  ## Major bug fix updates produced after the final release of the ## distribution. deb http://us.archive.ubuntu.com/ubuntu/ precise-updates main restricted multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise-updates restricted main multiverse universe #Added by software-properties  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu ## team. Also, please note that software in universe WILL NOT receive any ## review or updates from the Ubuntu security team. deb http://us.archive.ubuntu.com/ubuntu/ precise universe deb http://us.archive.ubuntu.com/ubuntu/ precise-updates universe  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu  ## team, and may not be under a free licence. Please satisfy yourself as to  ## your rights to use the software. Also, please note that software in  ## multiverse WILL NOT receive any review or updates from the Ubuntu ## security team.  ## N.B. software from this repository may not have been tested as ## extensively as that contained in the main release, although it includes ## newer versions of some applications which may provide useful features. ## Also, please note that software in backports WILL NOT receive any review ## or updates from the Ubuntu security team. deb http://us.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse #Added by software-properties  deb http://us.archive.ubuntu.com/ubuntu/ precise-security main restricted multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise-security restricted main multiverse universe #Added by software-properties deb http://us.archive.ubuntu.com/ubuntu/ precise-security universe  ## Uncomment the following two lines to add software from Canonical's ## 'partner' repository. ## This software is not part of Ubuntu, but is offered by Canonical and the ## respective vendors as a service to Ubuntu users. deb http://archive.canonical.com/ubuntu precise partner deb-src http://archive.canonical.com/ubuntu precise partner  ## This software is not part of Ubuntu, but is offered by third-party ## developers who want to ship their latest software. I've tried different ways to install iTunes, but to no avail. I tried with Wine, but it didn't work. Is it possible to have iTunes on Ubuntu? General Information about Eigenvalues for an 3x3 symmetric matrix Apt-get stuck at 0% [Working] Why aren't search engines indexing my content? How can I remove the BOM from XmlTextWriter using C#? What is the best way to check whether a given object is of a given type? How about checking whether the object inherits from a given type?  Let's say I have an object o. How do I check whether it's a str? Any reason to have a strong user password? I recently decided to change my (very) strong user password to something trivial.  This was mostly to eliminate frustration with typing a long password each time I sudo or whatever.  My question is, is there any reason to have a strong user password? considering that most services which I run on my box do not use PAM for auth:   apache2 - uses .htpasswd for access   sshd - only private keys allowed   transmissiond - uses its own http auth   mpd - uses its own auth   samba - limited to LAN   Physical access to the box is out of the question. Can I use a Thunderbolt display for a macbook pro with a mini display port? The world I've been playing crashed recently and took the level.dat with it, so I've recreated it, however I have no idea what my seed used to be, and I really don't want to end up with another corrupted game world from exploring with the wrong seed.  How can I recover the seed which was used to generate my world? Problem understanding the logistic regression link function Gauss's Law with Moving Charges The reciprocal of many prime numbers p in base 10 have a set of repeating digits p-1. Why? I've noticed that the reciprocal of many prime numbers have a curious number of digits. For example. 1/7 has 6 repeating digits, 1/17 has 16 repeating digits, and 1/47 has 46. There's a rule here that makes this pattern, and I haven't quite figured it out. Does anyone have some insight on this?  There are a few other numbers that follow the pattern subversively. For example, 1/3 has two repeating digits: 33. 1/11 has ten repeating digits: 0909090909. The number 1/13 has a set of six that repeats twice, which makes a set that's 12 digits long.  For reference, here is a website that lists reciprocals of numbers 2 through 70, including non-primes.   The ones that break the rule are 1/2 and 1/5, but they seem to be a matched pair, where the 2 and 5 switch places in the equation 1/X = Y/10  What is the rule that makes this pattern? I'm very curious. How do I set my DNS when resolv.conf is being overwritten? Most of the info I see online says to edit /etc/resolv.conf, but any changes I make there just get overridden.  $ cat /etc/resolv.conf  # Dynamic resolv.conf(5) file for glibc resolver(3) generated by resolvconf(8) #     DO NOT EDIT THIS FILE BY HAND --  #     YOUR CHANGES WILL BE OVERWRITTEN nameserver 127.0.1.1   It seems that 127.0.1.1 is a local instance of dnsmasq. The dnsmasq docs say to edit /etc/resolv.conf. I tried putting custom nameservers in /etc/resolv.conf.d/base, but the changes didn't show up in /etc/resolv.conf after running sudo resolvconf -u.  FYI, I don't want to change DNS on a per-connection basis, I want to set default DNS settings to use for all connections when not otherwise specified.  UPDATE:  I answered this question myself:   I think it's the best solution since:   It works. It requires the least amount of changes and It still works in conjunction with dnsmasq's DNS cache, rather than bypassing it.