I'm working on a ranking problem where I want to measure the distance between a collection of query points (as a group) and each target point in my database. Each query point is part of the set of target points. I started with the Euclidean distance and cosine similarity by using the mean vector of the query points. However, the results were not satisfactory possibly because both of these measures don't take into account the variance and covariance of the query points. I stumbled across the  which seems to be exactly what I want to try: Measuring how many standard deviations a point is away from the mean of the subsample.  The problem is that I work in a 256-dimensional space while the number of query points is usually much lower than that. Therefore, I cannot calculate the Mahalanobis distance which relies on the covariance matrix. In order to calculate it, I need more observations n than dimensions p.  1) Is this assumption correct?  The past days I've been thinking about how I could still do "better" than the Euclidean distance without having enough data to calculate the Mahalanobis distance.  I thought about switching out the covariance matrix for the diagonal matrix of variances. As long as none of the variances is zero an inverse can be calculated.   2) Does this idea have a flaw?  Since the 256-dimensional vectors are the result of PCA over all target points, I could use n points to create a covariance matrix over the first n-1 dimensions and then fill the rest of the needed 256-dim covariance matrix with the diagonal of variances from before.  3) Would that make any sense?  4) Any other ideas that might help me to measure a more meaningful distance between a point and a subsample of points?  Please note: A very similar question has been asked  but I believe my problem is still different. There, OP wanted to measure pairwise distances between points given all points. I want to measure the distance between the distribution of a subsample to all other points. I believe, the reasoning of the accepted answer does not apply to my problem since the distribution of the subsample is likely to be different.
I have an issue which I could not solve, although I tried and I got some help on R forum.  I am trying to calculate Mahalanobis distances on a data.frame, where I have several hundreds of groups and several hundreds of variables. Whatever I do, I get the system is computationally singular: reciprocal condition number error.   It is clear that it is singular, but is there any way to get rid of it and run Mahalanobis? Should I forget solve this using another approach? If yes, then what else to use?  I have uploaded the data file to my :  It is a tab delimited txt file with no headers.  I was working with the R StatMatch Mahalanobis (also tried stats Mahalanobis) function. I have a deadline for this project (not a homework!), and I could always use this function, so I thought I will be able to keep the calculations short, but now I am lost.  Migrated .
For every $c\in [0;2]$ determine whether the sequence $\{a_n\}_{n\geq 1}$ which is defined as follows:  $a_1=c$, $a_{n+1}=1+\frac{(a_n-1)^2}{17}$ for $n\geq 1$  is monotonic for sufficiently large $n$, and determine whether its limit exits and if it exists, give its value.  I have no idea what to do with this problem. I was able to see that $a_{n+1}-a_n$ is a quadratic function and I also found ot that limit, if exists, is equal to either $1$ or $18$ (that's beacause if $a_n$ id convergent to $g$ then every subsequence is also convergent to $g$). So how to determine the limit for every $c\in [0;2]$? How do I make my textures show in cycles? I am admittedly new to Blender, and of course cycles. I am working on a scene and I have textures set to my objects that render with internal engine just fine. However, when I go into cycles, everything is greyish. I have two light sources that should be sufficient (I think), I just don't know what I'm doing wrong. This is a screenshot of the cycles result. Gollum had his life largely extended because he possessed the One Ring. He appeared to be an old, deformed, and twisted creature.  According to , he had the Ring for 478 years. His loss of the Ring and the events of The Lord of the Rings are separated by around 77 years.  Did the Ring continue to extend his life after he lost it? After parsing collada files I found out that we have to load two(or more) indices each pointing to say a vertex or normal etc. like this (&lt;p>3 0 2 0 0 0&lt;/p>)  Is there a way to load (and use)these indices to indices buffer(ELEMENT_ARRAY_BUFFER) like this (vnvnvn...) ; where v is vertex pointer, n is normal pointer from the above. with vertices loaded to VBO1 like (vvvv...) and in VBO2 like (nnnn...). So that we dont have to repeat the normals in VBO2.  VBO like (vnvnvn...) is also ok. (and not something like this ), I'm not trying to use multiple indices buffer. I'm trying to put all the given indices into one index buffer and use them alternately.  (If I wasnt clear i will try for more clarification.) Biblatex/biber fails with a strange error about missing recode_data.xml file Prove that the product of four consecutive positive integers plus one is a perfect square I need to prove the following, but I am not able to do it. This is not homework, nor something related to research, but rather something that came up in preparation for an exam.     If $n = 1 + m$, where $m$ is the product of four consecutive positive   integers, prove that $n$ is a perfect square.   Now since $m = p(p+1)(p+2)(p+3)$;     $p = 0, n = 1$ - Perfect Square      $p = 1, n = 25$ - Perfect Square      $p = 2, n = 121$ - Perfect Square   Is there any way to prove the above without induction? My approach was to expand $m = p(p+1)(p+2)(p+3)$ into a 4th degree equation, and then try proving that $n = m + 1$ is a perfect square, but I wasn't able to do it. Any idea if it is possible? What does the |= operator do in Java? How can I detect if my apple device supports Bluetooth Low Energy How to use the keyboard to drag and drop? Are any of the alien languages in Star Wars real Earth languages? Are any of the alien languages (other than English and binary) in Star Wars movies or TV shows real Earth languages? Why don't gksu/gksudo or launching a graphical application with sudo work with Wayland? I installed Ubuntu 17.10. Now I am having trouble with gksu:  $ gksu -dg synaptic No ask_pass set, using default! xauth: /tmp/libgksu-HgUjgQ/.Xauthority STARTUP_ID: gksu/synaptic/8760-0-alex-XPS-15-9530_TIME4974977 cmd[0]: /usr/bin/sudo cmd[1]: -H cmd[2]: -S cmd[3]: -p cmd[4]: GNOME_SUDO_PASS cmd[5]: -u cmd[6]: root cmd[7]: -- cmd[8]: synaptic buffer: -GNOME_SUDO_PASS- brute force GNOME_SUDO_PASS ended... Yeah, we're in... Unable to init server: Could not connect: Connection refused (synaptic:8767): Gtk-WARNING **: cannot open display: :1 xauth: /tmp/libgksu-HgUjgQ/.Xauthority xauth_env: (null) dir: /tmp/libgksu-HgUjgQ   If I don't use -g, the password dialog is disabled. So looks like a problem with creating a tty for root.  Any advice? "What kind of a person" vs. "what kind of person" Given a prime $p$ and number $a$, how do I find the smallest $n$ such that $n^a\equiv 1 \pmod p$? Is there a non trial-and-error method?  Edit: obviously removing $n=1$! Permission denied in 777 folder john@ubuntu01:~$ sudo ls -l /var/opt/gitlab/git-data/repositories/GL/www.git total 25068 drwxr-xr-x  2 git  git      4096 aug 14 19:58 branches -rw-r--r--  1 git  git        66 aug 14 19:58 config drwxrwxrwx  2 root root     4096 aug 15 14:56 custom_hooks -rw-r--r--  1 git  git        73 aug 14 19:58 description -rw-r--r--  1 git  git        23 aug 14 19:58 HEAD lrwxrwxrwx  1 git  git        47 aug 14 19:58 hooks -&gt; /opt/gitlab/embedded/service/gitlab-shell/hooks drwxr-xr-x  2 git  git      4096 aug 14 19:58 hooks.old.1471193907 -rw-r--r--  1 git  git      1329 aug 15 14:48 index drwxr-xr-x  2 git  git      4096 aug 15 13:58 info drwxr-xr-x 71 git  git      4096 aug 15 14:55 objects -rw-r--r--  1 git  git        98 aug 15 13:58 packed-refs -rw-r--r--  1 git  git  25618530 aug 15 14:03 post-receive.log drwxr-xr-x  5 git  git      4096 aug 14 20:31 refs john@ubuntu01:~$ ls -l /var/opt/gitlab/git-data/repositories/GL/www.git ls: cannot access '/var/opt/gitlab/git-data/repositories/GL/www.git': Permission denied   Here are ACLs  john@ubuntu01:~$ sudo lsattr /var/opt/gitlab/git-data/repositories/GL/www.git/custom_hooks -------------e-- /var/opt/gitlab/git-data/repositories/GL/www.git/custom_hooks/post-receive   I have never seen this before. No permission to LS even with 777? I need to share this folder for more convenient development. How can I solve it? Thank you.  EDITED: (here are your requests)  john@ubuntu01:~$ sudo ls -ld /var/opt/gitlab/git-data/repositories/GL/www.git drwxrwxrwx 8 git git 4096 aug 15 14:48 /var/opt/gitlab/git-data/repositories/GL/www.git john@ubuntu01:~$ sudo ls -ld /var/opt/gitlab/git-data/repositories/GL/www.git/custom_hooks drwxrwxrwx 2 root root 4096 aug 15 14:56 /var/opt/gitlab/git-data/repositories/GL/www.git/custom_hooks   EDITED MORE  sudo ls -ld /var/opt/gitlab/git-‌​data/repositories/GL/‌​www.git ls: cannot access '/var/opt/gitlab/git-‌​data/repositories/GL/‌​www.git': No such file or directory   hmmm... what is this? How to generate all permutations of a list? How do you generate all the permutations of a list in Python, independently of the type of elements in that list?  For example:  permutations([]) []  permutations([1]) [1]  permutations([1, 2]) [1, 2] [2, 1]  permutations([1, 2, 3]) [1, 2, 3] [1, 3, 2] [2, 1, 3] [2, 3, 1] [3, 1, 2] [3, 2, 1] Last seen not updating when using Android app This isn't directly related to the app, but probably more on the APIs it's using. The last seen on the profile page doesn't seem to reflect that I'm actively using the Android app, or taking actions. I was able to vote on items and the last seen property on the profile page said I was last seen 50 minutes ago, when I was using a computer.  I'm assuming it won't count as a visit for the Enthusiast and Fantic badges either. I don't want someone angrily posting on Meta swearing they used the app for a day, yet they lost the consecutive days and has to prove it by showing they voted for something (we're probably far from this situation since it's alpha...) I have a custom xmodmap file I use, including useful multi-language diacriticals, english quotes, dashes &amp;c. I want to use this map with kmscon, so I need to create a xkb configuration from it. Is there an automated method to do it? Or even a straightforward manual process, since I won't need to do this frequently? Is there a way to assign a value to a variable, that value which we get in terminal by writing any command?  Example command: sensors  From that we get CPU temperature. How can I assign this value to a temp_cpu variable? Use early 2009 20" iMac as external display for 2015 rMBP Weird $3^n$ in an identity to be combinatorially proved