Pulling the principal components out of a DimensionReducerFunction?How can I determine the importance of variables from Classify?Why is the classify function not giving the desired output?How to use Mathematica to train a network Using out of core classification?How to train a net for recognize the numberHow to train a network using out of core training when data have different length?FeatureSpacePlot freaks out with LatentSemanticAnalysis on wordsHow can I reproduce the result of DimensionReduction?How can I see the predictor function that Mathematica produces?Machine learning: How to fix part of the weight matrix?Ordinal subset in the set of classes

Does Dispel Magic work on Tiny Hut?

Is it possible to create a QR code using text?

Machine learning testing data

What does the same-ish mean?

Solving an equation with constraints

My ex-girlfriend uses my Apple ID to log in to her iPad. Do I have to give her my Apple ID password to reset it?

Processor speed limited at 0.4 Ghz

Am I breaking OOP practice with this architecture?

How can I deal with my CEO asking me to hire someone with a higher salary than me, a co-founder?

Can I hook these wires up to find the connection to a dead outlet?

How can saying a song's name be a copyright violation?

What is the fastest integer factorization to break RSA?

How could indestructible materials be used in power generation?

Getting extremely large arrows with tikzcd

Finitely generated matrix groups whose eigenvalues are all algebraic

How to Prove P(a) → ∀x(P(x) ∨ ¬(x = a)) using Natural Deduction

What is the opposite of "eschatology"?

Ambiguity in the definition of entropy

Is this draw by repetition?

Notepad++ delete until colon for every line with replace all

Was the Stack Exchange "Happy April Fools" page fitting with the '90's code?

Are British MPs missing the point, with these 'Indicative Votes'?

Different meanings of こわい

Using "tail" to follow a file without displaying the most recent lines



Pulling the principal components out of a DimensionReducerFunction?


How can I determine the importance of variables from Classify?Why is the classify function not giving the desired output?How to use Mathematica to train a network Using out of core classification?How to train a net for recognize the numberHow to train a network using out of core training when data have different length?FeatureSpacePlot freaks out with LatentSemanticAnalysis on wordsHow can I reproduce the result of DimensionReduction?How can I see the predictor function that Mathematica produces?Machine learning: How to fix part of the weight matrix?Ordinal subset in the set of classes













4












$begingroup$


Suppose I perform dimension reduction using PCA:



dr = DimensionReduction[1, 2, 3, 2, 3, 5, 3, 5, 8, 4, 5, 
 8.5, Method -> "PrincipalComponentsAnalysis"]


If I want to see the principal components themselves, in the original space, one thought is to use the "OriginalData" feature of the DimensionReducerFunction, on basis vectors in the new space:



In[8]:= dr[1.0, 0.0, "OriginalData"]
dr[0.0, 1.0, "OriginalData"]

Out[8]= 1.86006, 2.9998, 4.81724

Out[9]= 3.38701, 3.01026, 5.64163


Is this a reasonable thing to do, or am I misinterpreting how the "OriginalData" feature works? And is there a better way to pull out the principal components themselves? People often want to visualize these for various reasons.



(There are several other questions about how to solve a similar problem with the PrincipalComponents function; this is a question about a different function.)






machine-learning dimension-reduction







share|improve this question











$endgroup$
















    4












    $begingroup$


    Suppose I perform dimension reduction using PCA:



    dr = DimensionReduction[1, 2, 3, 2, 3, 5, 3, 5, 8, 4, 5, 
     8.5, Method -> "PrincipalComponentsAnalysis"]


    If I want to see the principal components themselves, in the original space, one thought is to use the "OriginalData" feature of the DimensionReducerFunction, on basis vectors in the new space:



    In[8]:= dr[1.0, 0.0, "OriginalData"]
    dr[0.0, 1.0, "OriginalData"]

    Out[8]= 1.86006, 2.9998, 4.81724

    Out[9]= 3.38701, 3.01026, 5.64163


    Is this a reasonable thing to do, or am I misinterpreting how the "OriginalData" feature works? And is there a better way to pull out the principal components themselves? People often want to visualize these for various reasons.



    (There are several other questions about how to solve a similar problem with the PrincipalComponents function; this is a question about a different function.)






    machine-learning dimension-reduction







    share|improve this question











    $endgroup$














      4












      4








      4


      2



      $begingroup$


      Suppose I perform dimension reduction using PCA:



      dr = DimensionReduction[1, 2, 3, 2, 3, 5, 3, 5, 8, 4, 5, 
       8.5, Method -> "PrincipalComponentsAnalysis"]


      If I want to see the principal components themselves, in the original space, one thought is to use the "OriginalData" feature of the DimensionReducerFunction, on basis vectors in the new space:



      In[8]:= dr[1.0, 0.0, "OriginalData"]
      dr[0.0, 1.0, "OriginalData"]

      Out[8]= 1.86006, 2.9998, 4.81724

      Out[9]= 3.38701, 3.01026, 5.64163


      Is this a reasonable thing to do, or am I misinterpreting how the "OriginalData" feature works? And is there a better way to pull out the principal components themselves? People often want to visualize these for various reasons.



      (There are several other questions about how to solve a similar problem with the PrincipalComponents function; this is a question about a different function.)






      machine-learning dimension-reduction







      share|improve this question











      $endgroup$




      Suppose I perform dimension reduction using PCA:



      dr = DimensionReduction[1, 2, 3, 2, 3, 5, 3, 5, 8, 4, 5, 
       8.5, Method -> "PrincipalComponentsAnalysis"]


      If I want to see the principal components themselves, in the original space, one thought is to use the "OriginalData" feature of the DimensionReducerFunction, on basis vectors in the new space:



      In[8]:= dr[1.0, 0.0, "OriginalData"]
      dr[0.0, 1.0, "OriginalData"]

      Out[8]= 1.86006, 2.9998, 4.81724

      Out[9]= 3.38701, 3.01026, 5.64163


      Is this a reasonable thing to do, or am I misinterpreting how the "OriginalData" feature works? And is there a better way to pull out the principal components themselves? People often want to visualize these for various reasons.



      (There are several other questions about how to solve a similar problem with the PrincipalComponents function; this is a question about a different function.)






      machine-learning dimension-reduction




      machine-learning dimension-reduction






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 2 days ago









      J. M. is slightly pensive♦

      98.9k10311467




      98.9k10311467










      asked 2 days ago









      Michael CurryMichael Curry

      786312




      786312




















          1 Answer
          1






          active

          oldest

          votes


















          6












          $begingroup$

          Here's your data:



          data = 1, 2, 3, 2, 3, 5, 3, 5, 8, 4, 5, 8.5;
          dr = DimensionReduction[data, Method -> "PrincipalComponentsAnalysis"];


          This is not exactly a top level solution, but we can pick apart the DimensionReducerFunction and see inside (try dr[[1]] to see many internal properties).



          Looking further, in there we have a matrix:



          Transpose[dr[[1, "Model", "Matrix"]]]



          -0.572383, -0.577502, -0.582125, 0.793367, -0.56945, -0.215163



          I think these are the components. We can try to verify:



          Transpose[Last[SingularValueDecomposition[Standardize[data], 2]]]



          -0.572383, -0.577502, -0.582125, 0.793367, -0.56945, -0.215163






          share|improve this answer











          $endgroup$








          • 2




            $begingroup$
            It doesn't look like you need the pre-multiplication by 2/Sqrt[3]; after all, any such rescaling would show itself in the singular values and not the orthogonal factors. The important thing is the shift, which Standardize[] of course does.
            $endgroup$
            – J. M. is slightly pensive♦
            2 days ago











          • $begingroup$
            Good catch, I've edited the post. I can't remember what I ran into that led me to such a conclusion.
            $endgroup$
            – Chip Hurst
            2 days ago












          Your Answer





          StackExchange.ifUsing("editor", function ()
          return StackExchange.using("mathjaxEditing", function ()
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          );
          );
          , "mathjax-editing");

          StackExchange.ready(function()
          var channelOptions =
          tags: "".split(" "),
          id: "387"
          ;
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function()
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled)
          StackExchange.using("snippets", function()
          createEditor();
          );

          else
          createEditor();

          );

          function createEditor()
          StackExchange.prepareEditor(
          heartbeatType: 'answer',
          autoActivateHeartbeat: false,
          convertImagesToLinks: false,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: null,
          bindNavPrevention: true,
          postfix: "",
          imageUploader:
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          ,
          onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          );



          );













          draft saved

          draft discarded


















          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f194324%2fpulling-the-principal-components-out-of-a-dimensionreducerfunction%23new-answer', 'question_page');

          );

          Post as a guest















          Required, but never shown

























          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          6












          $begingroup$

          Here's your data:



          data = 1, 2, 3, 2, 3, 5, 3, 5, 8, 4, 5, 8.5;
          dr = DimensionReduction[data, Method -> "PrincipalComponentsAnalysis"];


          This is not exactly a top level solution, but we can pick apart the DimensionReducerFunction and see inside (try dr[[1]] to see many internal properties).



          Looking further, in there we have a matrix:



          Transpose[dr[[1, "Model", "Matrix"]]]



          -0.572383, -0.577502, -0.582125, 0.793367, -0.56945, -0.215163



          I think these are the components. We can try to verify:



          Transpose[Last[SingularValueDecomposition[Standardize[data], 2]]]



          -0.572383, -0.577502, -0.582125, 0.793367, -0.56945, -0.215163






          share|improve this answer











          $endgroup$








          • 2




            $begingroup$
            It doesn't look like you need the pre-multiplication by 2/Sqrt[3]; after all, any such rescaling would show itself in the singular values and not the orthogonal factors. The important thing is the shift, which Standardize[] of course does.
            $endgroup$
            – J. M. is slightly pensive♦
            2 days ago











          • $begingroup$
            Good catch, I've edited the post. I can't remember what I ran into that led me to such a conclusion.
            $endgroup$
            – Chip Hurst
            2 days ago
















          6












          $begingroup$

          Here's your data:



          data = 1, 2, 3, 2, 3, 5, 3, 5, 8, 4, 5, 8.5;
          dr = DimensionReduction[data, Method -> "PrincipalComponentsAnalysis"];


          This is not exactly a top level solution, but we can pick apart the DimensionReducerFunction and see inside (try dr[[1]] to see many internal properties).



          Looking further, in there we have a matrix:



          Transpose[dr[[1, "Model", "Matrix"]]]



          -0.572383, -0.577502, -0.582125, 0.793367, -0.56945, -0.215163



          I think these are the components. We can try to verify:



          Transpose[Last[SingularValueDecomposition[Standardize[data], 2]]]



          -0.572383, -0.577502, -0.582125, 0.793367, -0.56945, -0.215163






          share|improve this answer











          $endgroup$








          • 2




            $begingroup$
            It doesn't look like you need the pre-multiplication by 2/Sqrt[3]; after all, any such rescaling would show itself in the singular values and not the orthogonal factors. The important thing is the shift, which Standardize[] of course does.
            $endgroup$
            – J. M. is slightly pensive♦
            2 days ago











          • $begingroup$
            Good catch, I've edited the post. I can't remember what I ran into that led me to such a conclusion.
            $endgroup$
            – Chip Hurst
            2 days ago














          6












          6








          6





          $begingroup$

          Here's your data:



          data = 1, 2, 3, 2, 3, 5, 3, 5, 8, 4, 5, 8.5;
          dr = DimensionReduction[data, Method -> "PrincipalComponentsAnalysis"];


          This is not exactly a top level solution, but we can pick apart the DimensionReducerFunction and see inside (try dr[[1]] to see many internal properties).



          Looking further, in there we have a matrix:



          Transpose[dr[[1, "Model", "Matrix"]]]



          -0.572383, -0.577502, -0.582125, 0.793367, -0.56945, -0.215163



          I think these are the components. We can try to verify:



          Transpose[Last[SingularValueDecomposition[Standardize[data], 2]]]



          -0.572383, -0.577502, -0.582125, 0.793367, -0.56945, -0.215163






          share|improve this answer











          $endgroup$



          Here's your data:



          data = 1, 2, 3, 2, 3, 5, 3, 5, 8, 4, 5, 8.5;
          dr = DimensionReduction[data, Method -> "PrincipalComponentsAnalysis"];


          This is not exactly a top level solution, but we can pick apart the DimensionReducerFunction and see inside (try dr[[1]] to see many internal properties).



          Looking further, in there we have a matrix:



          Transpose[dr[[1, "Model", "Matrix"]]]



          -0.572383, -0.577502, -0.582125, 0.793367, -0.56945, -0.215163



          I think these are the components. We can try to verify:



          Transpose[Last[SingularValueDecomposition[Standardize[data], 2]]]



          -0.572383, -0.577502, -0.582125, 0.793367, -0.56945, -0.215163







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited 2 days ago

























          answered 2 days ago









          Chip HurstChip Hurst

          23k15893




          23k15893







          • 2




            $begingroup$
            It doesn't look like you need the pre-multiplication by 2/Sqrt[3]; after all, any such rescaling would show itself in the singular values and not the orthogonal factors. The important thing is the shift, which Standardize[] of course does.
            $endgroup$
            – J. M. is slightly pensive♦
            2 days ago











          • $begingroup$
            Good catch, I've edited the post. I can't remember what I ran into that led me to such a conclusion.
            $endgroup$
            – Chip Hurst
            2 days ago













          • 2




            $begingroup$
            It doesn't look like you need the pre-multiplication by 2/Sqrt[3]; after all, any such rescaling would show itself in the singular values and not the orthogonal factors. The important thing is the shift, which Standardize[] of course does.
            $endgroup$
            – J. M. is slightly pensive♦
            2 days ago











          • $begingroup$
            Good catch, I've edited the post. I can't remember what I ran into that led me to such a conclusion.
            $endgroup$
            – Chip Hurst
            2 days ago








          2




          2




          $begingroup$
          It doesn't look like you need the pre-multiplication by 2/Sqrt[3]; after all, any such rescaling would show itself in the singular values and not the orthogonal factors. The important thing is the shift, which Standardize[] of course does.
          $endgroup$
          – J. M. is slightly pensive♦
          2 days ago





          $begingroup$
          It doesn't look like you need the pre-multiplication by 2/Sqrt[3]; after all, any such rescaling would show itself in the singular values and not the orthogonal factors. The important thing is the shift, which Standardize[] of course does.
          $endgroup$
          – J. M. is slightly pensive♦
          2 days ago













          $begingroup$
          Good catch, I've edited the post. I can't remember what I ran into that led me to such a conclusion.
          $endgroup$
          – Chip Hurst
          2 days ago





          $begingroup$
          Good catch, I've edited the post. I can't remember what I ran into that led me to such a conclusion.
          $endgroup$
          – Chip Hurst
          2 days ago


















          draft saved

          draft discarded
















































          Thanks for contributing an answer to Mathematica Stack Exchange!


          • Please be sure to answer the question. Provide details and share your research!

          But avoid …


          • Asking for help, clarification, or responding to other answers.

          • Making statements based on opinion; back them up with references or personal experience.

          Use MathJax to format equations. MathJax reference.


          To learn more, see our tips on writing great answers.




          draft saved


          draft discarded














          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f194324%2fpulling-the-principal-components-out-of-a-dimensionreducerfunction%23new-answer', 'question_page');

          );

          Post as a guest















          Required, but never shown





















































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown

































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown







          -

          Popular posts from this blog

          getting Checkpoint VPN SSL Network Extender working in the command lineHow to connect to CheckPoint VPN on Ubuntu 18.04LTS?Will the Linux ( red-hat ) Open VPNC Client connect to checkpoint or nortel VPN gateways?VPN client for linux machine + support checkpoint gatewayVPN SSL Network Extender in FirefoxLinux Checkpoint SNX tool configuration issuesCheck Point - Connect under Linux - snx + OTPSNX VPN Ububuntu 18.XXUsing Checkpoint VPN SSL Network Extender CLI with certificateVPN with network manager (nm-applet) is not workingWill the Linux ( red-hat ) Open VPNC Client connect to checkpoint or nortel VPN gateways?VPN client for linux machine + support checkpoint gatewayImport VPN config files to NetworkManager from command lineTrouble connecting to VPN using network-manager, while command line worksStart a VPN connection with PPTP protocol on command linestarting a docker service daemon breaks the vpn networkCan't connect to vpn with Network-managerVPN SSL Network Extender in FirefoxUsing Checkpoint VPN SSL Network Extender CLI with certificate

          Image
          If human space travel is limited by the G force vulnerability, is there a way to counter G forces? Did Shadowfax go to Valinor? Do I have a twin with permutated remainders? Blender 2.8 I can't see vertices, edges or faces in edit mode 1960's book about a plague that kills all white people How can I make my BBEG immortal short of making them a Lich or Vampire? Alternative to sending password over mail? Is it inappropriate for a student to attend their mentor's dissertation defense? Why is Collection not simply treated as Collection<?> Took a trip to a parallel universe, need help deciphering Assassin's bullet with mercury Why is it a bad idea to hire a hitman to eliminate most corrupt politicians? I Accidentally Deleted a Stock Terminal Theme Is there a hemisphere-neutral way of specifying a season? What about the virus in 12 Monkeys? Why can't we play rap on piano? Arrow those variables! Today is the Center Modeling an IP Ad...
          Read more

          Cannot Extend partition with GParted The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern) 2019 Community Moderator Election ResultsCan't increase partition size with GParted?GParted doesn't recognize the unallocated space after my current partitionWhat is the best way to add unallocated space located before to Ubuntu 12.04 partition with GParted live?I can't figure out how to extend my Arch home partition into free spaceGparted Linux Mint 18.1 issueTrying to extend but swap partition is showing as Unknown in Gparted, shows proper from fdiskRearrange partitions in gparted to extend a partitionUnable to extend partition even though unallocated space is next to it using GPartedAllocate free space to root partitiongparted: how to merge unallocated space with a partition

          Image
          Make it rain characters Keeping a retro style to sci-fi spaceships? How to split my screen on my Macbook Air? How can I define good in a religion that claims no moral authority? does high air pressure throw off wheel balance? Scientific Reports - Significant Figures Relations between two reciprocal partial derivatives? How to delete random line from file using Unix command? How did passengers keep warm on sail ships? How are presidential pardons supposed to be used? Are my PIs rude or am I just being too sensitive? He got a vote 80% that of Emmanuel Macron’s Change bounding box of math glyphs in LuaTeX Match Roman Numerals Was credit for the black hole image misattributed? How to pronounce 1ターン? how can a perfect fourth interval be considered either consonant or dissonant? Working through the single responsibility principle (SRP) in Python when calls are expensive High Q peak in frequency response means what in time domain? ...
          Read more

          Marilyn Monroe Ny fiainany manokana | Jereo koa | Meny fitetezanafanitarana azy.

          Image
          OlonaBiôgrafiaVangovangoMpilalaoMpilalao amin'ny horonantsaryMpamoaka horonantsaryTeraka tamin'ny taona 1926Maty tamin'ny taona 1962 EtazoniaLos Angeles fanitarana azy . Marilyn Monroe Avy amin'i Wikipedia Sauter à la navigation Sauter à la recherche Marilyn Monroe Ankapobeny Anarana Marilyn Monroe Teraka 1 Jiona 1926 Maty 5 Aogositra 1962 Fiaviana sy ny andraikitra Firenena Etazonia Asa : mpilalao mpilalao amin'ny horonantsary mpamoaka horonantsary Fiainana manokana Marilyn Monroe dia mpilalao, mpilalao amin'ny horonantsary, mpamoaka horonantsary mizaka ny zom-pirenen'i Etazonia teraka ny 1 Jiona 1926 tao Los Angeles ary maty ny 5 Aogositra 1962 Ny fiainany manokana | Ny vadiny dia James Dougherty, Joe DiMaggio, Arthur Miller. Jereo koa | Biôgrafia Rohy ivelany | Ao amin'i Freebase: [1] Mbola ambangovangony ity lahatsoratra ity ary tokony hofenoina . Azonao atao ny mandray anjara eto amin'ny Wikipedia amin...
          Read more