I am having trouble understanding how one-class SVMs work. They were introduced in a paper by Scholkopf and others (and can be found ).  One-class SVMs perform "novelty detection", where a point is classified as either normal or abnormal, but you can only train your model on normal points.  In the paper linked above, the authors use SVMs for novelty detection by separating the training examples from the origin in feature space. They further claim that for certain values of parameters (specifically, their parameter $\nu$) their method is equivalent to a thresholded  if the kernel function integrates to 1 over $\mathbb{R}$. Mathematically, this makes sense (equations 5 and 6 in the paper reduce to Parzen Windows for large values of $\nu$), however I am having trouble understanding this intuitively.  So here is my question: As I see it, separating points from the origin in feature space will necessarily mean that there exists some $n$-dimensional ball centered at the origin with radius $r$ such that for all points outside of this ball, they will be classified as normal. Wouldn't this lead to a large portion of $\mathbb{R}^n$ being classified as normal? However, their paper claims that the solution has small volume.
I was using , implemented in scikit-learn, for my research work. But I have no good understanding of this.   Can anyone please give a simple, good explanation of one class SVM?
Mathematical expression to form a vector from diagonal elements I would like to know is there any way to express mathematically (using matrices multiplication, addition, etc.) a vector which is formed from the diagonal elements of a matrix. For example, I have a matrix called $\mathbf{M}$ and I want to create a vector  $\mathbf{v}$ such that $\mathbf{v}= \text{diagonal elements of } \mathbf{M} $  Any matrix algebra or operation do that ? Thank you. When we implement the Always Encrypted feature in SQL Server 2016, do the .mdf files, .ldf files and .bak files get encrypted as well?  I would like to know if the data/log/backup files gets encrypted or not. Multiple entry visa to UK (sponsored visitor) Add markdown support for hidden-until-you-click text (aka spoilers) Add "paragraphs" to Markdown help Like balpha once , a &lt;br&gt; line break (newline) should be used in very few cases, and surely is not the same as a new &lt;p&gt; paragraph. Still  only explains line breaks, not paragraphs:      Some sites  an additional &quot;New paragraphs only occur when there is a blank line. A single carriage does not create a new paragraph.&quot;, but I feel that's not very clear*, and the emphasis is still on line breaks while it should be on paragraphs:      So: As a minimum, please add (rephrase) a note about the blank line, and maybe use &quot;Only when really needed [...] force&quot;:  Paragraphs and line breaks Simply use a blank line between two paragraphs to start a new &lt;p&gt; paragraph. Only when really needed, end a line with two spaces to force a &lt;br/&gt; line break: How do I love thee?__     Let me count the ways   I'd even prefer an explicit example, simply as I think &lt;p&gt; should be favoured over &lt;br&gt; in most situations:  Paragraphs and line breaks Simply use a blank line to start a new &lt;p&gt; paragraph: First sentence in the first paragraph. Another sentence. And a third. Maybe making this multiple consecutive lines of text, but still one paragraph.  The second paragraph.  Only when really needed, end a line with two spaces to force a &lt;br/&gt; line break: How do I love thee?__     Let me count the ways   Alternatively, slightly change the existing &quot;Linebreaks&quot;† part, and above that add a standalone section, :  Paragraphs A paragraph is simply one or more consecutive lines of text, separated by one or more blank lines: A blank line is any line that looks like a blank line. A line containing nothing but spaces or tabs is considered blank.  Normal paragraphs should not be indented with spaces or tabs.  Line breaks Only when really needed, end a line with two spaces to force a &lt;br/&gt; line break: How do I love thee?__     Let me count the ways   And: maybe even add a section &quot;Paragraphs&quot; to the inline post help on top of the editor? I'm not sure which help tab should then be shown  though.  * Also note how not all sites highlight the two spaces with a different background color. † Yes, I think &quot;line break&quot; likes a space too... Determine whether a number is prime How do I determine if a number is prime?  I'm writing a program where a user inputs any integer and from that the program determines whether the number is prime, but how do I go about that? Can somebody give me an example of a graph on eight vertices that has a pair of pseudosimilar vertices? Or, is it not possible? If it is not possible, please do not give me a proof, as I would like to figure out how to prove it myself.     Definition: vertices $u$ and $v$ in a graph $X$ are similar if there is an automorphism of $X$ that maps $u$ to $v$. If $u$ and $v$ are similar, then the vertex-deleted subgraphs $X-u$ and $X-v$ are isomorphic. If $X-u$ and $X-v$ are isomorphic but $u$ and $v$ are not similar, we say that they are pseudosimilar. losing ligatures when switching font series or color in the middle of a word Why don't we double the final consonant in the word cooking SO here is the rule I find about doubling consonant     if a word ends with a short vowel sound plus a consonant, and the stress is on the last syllable, then the final consonant is doubled if you add an ending that starts with a vowel.    I find this rule to be much more powerful than the one I learned at school, aka:V+C, But the rule doesn't seem to apply to cooking, which is not doubled. Is this a contradiction of the rule I quoted above? (I am not so sure about the short vowel but, but simple Google tells me that ʊ in cooking is indeed a short vowel. )  Also, if cooking is indeed an exception to this rule, are there any other similar exceptions that I should be aware of? Anime with a boy hiring a creature from a stone, meets a man named Dante and starts a journey to collect crystals After trying (and failing) to install better ATI drivers in 11.10, I've somehow lost my grub menu at boot time.  The screen does change to the familiar purple colour, but instead of a list of boot options it's just blank solid colour, and then disappears quickly and boots into the default entry normally.    How can I get the bootloader back?  I've tried sudo update-grub and also various different combinations of resolutions and colour depths in startupmanager application with no success (640x480, 1024x768, 1600x1200, 16 bits, 8 bits, 10 second delay, 7 second delay, 2 second delay...)   edit:   I have already tried holding down Shift during bootup and it does not seem to change the behaviour.  I get the message "GRUB Loading" in the terminal, but then the place where the grub menu normally appears I get a solid blank magenta screen for a while.  Here are the contents of /etc/default/grub  # If you change this file, run 'update-grub' afterwards to update # /boot/grub/grub.cfg. # For full documentation of the options in this file, see: #   info -f grub -n 'Simple configuration'  GRUB_DEFAULT=0 GRUB_HIDDEN_TIMEOUT=0 GRUB_HIDDEN_TIMEOUT_QUIET=true GRUB_TIMEOUT=10 GRUB_DISTRIBUTOR=`lsb_release -i -s 2&gt; /dev/null || echo Debian` GRUB_CMDLINE_LINUX_DEFAULT="quiet splash" GRUB_CMDLINE_LINUX=" vga=798 splash"  # Uncomment to enable BadRAM filtering, modify to suit your needs # This works with Linux (no patch required) and with any kernel that obtains # the memory map information from GRUB (GNU Mach, kernel of FreeBSD ...) #GRUB_BADRAM="0x01234567,0xfefefefe,0x89abcdef,0xefefefef"  # Uncomment to disable graphical terminal (grub-pc only) #GRUB_TERMINAL=console  # The resolution used on graphical terminal # note that you can use only modes which your graphic card supports via VBE # you can see them in real GRUB with the command `vbeinfo' #GRUB_GFXMODE=640x480  # Uncomment if you don't want GRUB to pass "root=UUID=xxx" parameter to Linux #GRUB_DISABLE_LINUX_UUID=true  # Uncomment to disable generation of recovery mode menu entries #GRUB_DISABLE_RECOVERY="true"  # Uncomment to get a beep at grub start #GRUB_INIT_TUNE="480 440 1" I am asked to solve $$u_x+u_y=1$$ If is was homogeneous i.e., $u_x+u_y$ the answer would be $u(x,y)=f(y-x)$ where $f$ is an arbitrary function. I have found the following set of solutions: $$u(x,y)=\lambda x +(1-\lambda)y$$ where $\lambda$ is an arbitrary constant(real or imaginary). I just have no idea what method other then trial and error would have lead me here. Any ideas? Thanks! In discussing , I noted that while the statement:     Any vector space has a basis   is equivalent to the axiom of choice, I wondered if the statement that:     Any vector space either has a finite basis or an infinite set of linear independent vectors   was weaker than the axiom of choice. It feels weaker - it feels like you can inductively define a countably infinite set of linearly independent vectors without full choice, but I'm not sure if that is possible with ZF alone, or requires all of the Axiom of Choice, or is weaker but requires some form of choice. String concatenation: concat() vs "+" operator Assuming String a and b:  a += b a = a.concat(b)   Under the hood, are they the same thing?  Here is concat decompiled as reference. I'd like to be able to decompile the + operator as well to see what that does.  public String concat(String s) {      int i = s.length();     if (i == 0) {         return this;     }     else {         char ac[] = new char[count + i];         getChars(0, count, ac, 0);         s.getChars(0, i, ac, count);         return new String(0, count + i, ac);     } } Getting MAC Address I need a cross platform method of determining the MAC address of a computer at run time.  For windows the 'wmi' module can be used and the only method under Linux I could find was to run ifconfig and run a regex across its output.  I don't like using a package that only works on one OS, and parsing the output of another program doesn't seem very elegant not to mention error prone.   Does anyone know a cross platform method (windows and linux) method to get the MAC address?    If not, does anyone know any more elegant methods then those I listed above? Correct formula for LED current-limiting resistor? I'm trying to work out what value resistor to use in a LED circuit. The equation I'd use to do this is:  $$ R = \frac{V_{cc} - V_f}{I_f} $$  Seems logical, and makes complete sense. The answers to the question  confirm this too.  I have the following LEDs:   \$ V_f = 3.3V \$ \$ I_{f_{typ}} = 20mA \$   Using a 5V power supply:   \$ V_{cc} = 5V \$   Plugging these into the above equation gives:  $$ \begin{eqnarray} R &amp; = &amp; \frac{V_{cc} - V_f}{I_f} \\   &amp; = &amp; \frac{5V - 3.3V}{20mA} \\   &amp; = &amp; 85\Omega \end{eqnarray} $$  All good so far.  However, if I use the calculator at , that gives me 100&Omega;. If I use the ElectroDroid app on my phone, that gives me 85&Omega;.  So, I assume that the linear1 calculator is using a different method of calculating this resistor value; is there some better way of doing this? Basically, I acidentally spawned too many ArmorStands due to a wrong code writing , resulting in the game crashing, and wanted to know how to delete those armorstands from the World save folder. They hava names and I belive they also have a scoreboard set, if that helps.   I have already tried to open the world but it crashes, I tried to open a server (Since it worked the last time I tried it) and killing it all from the console but, different from the last time, it crashed before killing them and now I just tried MCedit but it crashes as well. In the decimal system: $...-3, -2, -1, 0, 1, 2, 3...$ In the binary system: $...-11, -10, -1, 0, 1, 10, 11...$ In the unary system: $-111, -11, -1, \text{ ??? }, 1, 11, 111...$   I was only able to find a related question but none with an answer so far: Why is my Canon 300D not switching on despite changing both batteries and the CF card? How to conduct an Accent Sensitive search in MySql I have a MySQL table with utf8 general ci collation. In the table, I can see two entries:  abad abád  I am using a query that looks like this:  SELECT *  FROM `words` WHERE `word` = 'abád'   The query result gives both words:  abad abád  Is there a way to indicate that I only want MySQL to find the accented word? I want the query to only return    abád    I have also tried this query:  SELECT *  FROM `words` WHERE BINARY `word` = 'abád'   It gives me no results. Thank you for the help.