Ambiguity in Perceptron loss function












3












$begingroup$



Bishop's Perceptron loss




On one hand, it is stated in equation 4.54 of Chris Bishop's book (pattern recognition and machine learning) that the loss function of perceptron algorithm is given by:



$${E_p}(mathbf{w}) = - sumlimits_{n in M} {{mathbf{w}^T}{phi _n}} {t_n}$$



where $M$ denotes the set of all misclassified data points.




Original Perceptron loss




On the other hand, The loss function used in the original perceptron paper written by Frank Rosenblatt is given by (wikipedia):



$${1 over s}sumlimits_{j = 1}^s {left| {{d_j} - {y_j}left( t right)} right|} $$
which when translated to the notation of Bishop's book is given by:



$${1 over N}sumlimits_{n = 1}^N {left| {{t_n} - {mathbf{w}^T}{phi _n}} right|} $$
where $N$ denotes the set of all data points.




My question




My question is that why Bishop's version of Perceptron loss is different from the original paper? Considering Bishop's book as a highly recognized book in machine learning field, can we call it Bishop's Perceptron?!




Scikit-learn's implementation




By the way, it seems that Scikit-learn uses Bishop's version of Perceptron loss (Scikit-learn documentation). It is apparent from the following formula and figure:



-np.minimum(xx, 0)


which for one sample reduces to:
$$ - min left( {0,{mathbf{w}^T}{phi _n}{t_n}} right)$$



enter image description here






machine-learning classification perceptron







share|improve this question











$endgroup$

















    3












    $begingroup$



    Bishop's Perceptron loss




    On one hand, it is stated in equation 4.54 of Chris Bishop's book (pattern recognition and machine learning) that the loss function of perceptron algorithm is given by:



    $${E_p}(mathbf{w}) = - sumlimits_{n in M} {{mathbf{w}^T}{phi _n}} {t_n}$$



    where $M$ denotes the set of all misclassified data points.




    Original Perceptron loss




    On the other hand, The loss function used in the original perceptron paper written by Frank Rosenblatt is given by (wikipedia):



    $${1 over s}sumlimits_{j = 1}^s {left| {{d_j} - {y_j}left( t right)} right|} $$
    which when translated to the notation of Bishop's book is given by:



    $${1 over N}sumlimits_{n = 1}^N {left| {{t_n} - {mathbf{w}^T}{phi _n}} right|} $$
    where $N$ denotes the set of all data points.




    My question




    My question is that why Bishop's version of Perceptron loss is different from the original paper? Considering Bishop's book as a highly recognized book in machine learning field, can we call it Bishop's Perceptron?!




    Scikit-learn's implementation




    By the way, it seems that Scikit-learn uses Bishop's version of Perceptron loss (Scikit-learn documentation). It is apparent from the following formula and figure:



    -np.minimum(xx, 0)


    which for one sample reduces to:
    $$ - min left( {0,{mathbf{w}^T}{phi _n}{t_n}} right)$$



    enter image description here






    machine-learning classification perceptron







    share|improve this question











    $endgroup$















      3












      3








      3





      $begingroup$



      Bishop's Perceptron loss




      On one hand, it is stated in equation 4.54 of Chris Bishop's book (pattern recognition and machine learning) that the loss function of perceptron algorithm is given by:



      $${E_p}(mathbf{w}) = - sumlimits_{n in M} {{mathbf{w}^T}{phi _n}} {t_n}$$



      where $M$ denotes the set of all misclassified data points.




      Original Perceptron loss




      On the other hand, The loss function used in the original perceptron paper written by Frank Rosenblatt is given by (wikipedia):



      $${1 over s}sumlimits_{j = 1}^s {left| {{d_j} - {y_j}left( t right)} right|} $$
      which when translated to the notation of Bishop's book is given by:



      $${1 over N}sumlimits_{n = 1}^N {left| {{t_n} - {mathbf{w}^T}{phi _n}} right|} $$
      where $N$ denotes the set of all data points.




      My question




      My question is that why Bishop's version of Perceptron loss is different from the original paper? Considering Bishop's book as a highly recognized book in machine learning field, can we call it Bishop's Perceptron?!




      Scikit-learn's implementation




      By the way, it seems that Scikit-learn uses Bishop's version of Perceptron loss (Scikit-learn documentation). It is apparent from the following formula and figure:



      -np.minimum(xx, 0)


      which for one sample reduces to:
      $$ - min left( {0,{mathbf{w}^T}{phi _n}{t_n}} right)$$



      enter image description here






      machine-learning classification perceptron







      share|improve this question











      $endgroup$





      Bishop's Perceptron loss




      On one hand, it is stated in equation 4.54 of Chris Bishop's book (pattern recognition and machine learning) that the loss function of perceptron algorithm is given by:



      $${E_p}(mathbf{w}) = - sumlimits_{n in M} {{mathbf{w}^T}{phi _n}} {t_n}$$



      where $M$ denotes the set of all misclassified data points.




      Original Perceptron loss




      On the other hand, The loss function used in the original perceptron paper written by Frank Rosenblatt is given by (wikipedia):



      $${1 over s}sumlimits_{j = 1}^s {left| {{d_j} - {y_j}left( t right)} right|} $$
      which when translated to the notation of Bishop's book is given by:



      $${1 over N}sumlimits_{n = 1}^N {left| {{t_n} - {mathbf{w}^T}{phi _n}} right|} $$
      where $N$ denotes the set of all data points.




      My question




      My question is that why Bishop's version of Perceptron loss is different from the original paper? Considering Bishop's book as a highly recognized book in machine learning field, can we call it Bishop's Perceptron?!




      Scikit-learn's implementation




      By the way, it seems that Scikit-learn uses Bishop's version of Perceptron loss (Scikit-learn documentation). It is apparent from the following formula and figure:



      -np.minimum(xx, 0)


      which for one sample reduces to:
      $$ - min left( {0,{mathbf{w}^T}{phi _n}{t_n}} right)$$



      enter image description here






      machine-learning classification perceptron




      machine-learning classification perceptron






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 15 hours ago







      pythinker

















      asked yesterday









      pythinkerpythinker

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      8191213






















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          $begingroup$

          I managed to find the Bishop's version by unearthing! the Rosenblatt's 1962 Principles of neurodynamics, Page 110 book, so the Wikipedia's version must be the alternative one.







          It is worth noting that the book also has a chapter on error back-propagation (page 292), which resembles the Wikipedia version, but I think it is not exactly the same.










          share|improve this answer









          $endgroup$









          • 1




            $begingroup$
            Thanks a bunch for your detailed and demanding response. I’m really surprised by the amount of search you did in order to fix the issue.
            $endgroup$
            – pythinker
            6 hours ago










          • $begingroup$
            @pythinker My pleasure! I'm glad I could help. This detective stuff is fun ;)
            $endgroup$
            – Esmailian
            6 hours ago






          • 1




            $begingroup$
            I’m pleased to hear that you are interested in this type of questions. So I will try to pose more questions like this :)
            $endgroup$
            – pythinker
            6 hours ago












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          $begingroup$

          I managed to find the Bishop's version by unearthing! the Rosenblatt's 1962 Principles of neurodynamics, Page 110 book, so the Wikipedia's version must be the alternative one.







          It is worth noting that the book also has a chapter on error back-propagation (page 292), which resembles the Wikipedia version, but I think it is not exactly the same.










          share|improve this answer









          $endgroup$









          • 1




            $begingroup$
            Thanks a bunch for your detailed and demanding response. I’m really surprised by the amount of search you did in order to fix the issue.
            $endgroup$
            – pythinker
            6 hours ago










          • $begingroup$
            @pythinker My pleasure! I'm glad I could help. This detective stuff is fun ;)
            $endgroup$
            – Esmailian
            6 hours ago






          • 1




            $begingroup$
            I’m pleased to hear that you are interested in this type of questions. So I will try to pose more questions like this :)
            $endgroup$
            – pythinker
            6 hours ago
















          1












          $begingroup$

          I managed to find the Bishop's version by unearthing! the Rosenblatt's 1962 Principles of neurodynamics, Page 110 book, so the Wikipedia's version must be the alternative one.







          It is worth noting that the book also has a chapter on error back-propagation (page 292), which resembles the Wikipedia version, but I think it is not exactly the same.










          share|improve this answer









          $endgroup$









          • 1




            $begingroup$
            Thanks a bunch for your detailed and demanding response. I’m really surprised by the amount of search you did in order to fix the issue.
            $endgroup$
            – pythinker
            6 hours ago










          • $begingroup$
            @pythinker My pleasure! I'm glad I could help. This detective stuff is fun ;)
            $endgroup$
            – Esmailian
            6 hours ago






          • 1




            $begingroup$
            I’m pleased to hear that you are interested in this type of questions. So I will try to pose more questions like this :)
            $endgroup$
            – pythinker
            6 hours ago














          1












          1








          1





          $begingroup$

          I managed to find the Bishop's version by unearthing! the Rosenblatt's 1962 Principles of neurodynamics, Page 110 book, so the Wikipedia's version must be the alternative one.







          It is worth noting that the book also has a chapter on error back-propagation (page 292), which resembles the Wikipedia version, but I think it is not exactly the same.










          share|improve this answer









          $endgroup$



          I managed to find the Bishop's version by unearthing! the Rosenblatt's 1962 Principles of neurodynamics, Page 110 book, so the Wikipedia's version must be the alternative one.







          It is worth noting that the book also has a chapter on error back-propagation (page 292), which resembles the Wikipedia version, but I think it is not exactly the same.











          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 7 hours ago









          EsmailianEsmailian

          3,181320




          3,181320








          • 1




            $begingroup$
            Thanks a bunch for your detailed and demanding response. I’m really surprised by the amount of search you did in order to fix the issue.
            $endgroup$
            – pythinker
            6 hours ago










          • $begingroup$
            @pythinker My pleasure! I'm glad I could help. This detective stuff is fun ;)
            $endgroup$
            – Esmailian
            6 hours ago






          • 1




            $begingroup$
            I’m pleased to hear that you are interested in this type of questions. So I will try to pose more questions like this :)
            $endgroup$
            – pythinker
            6 hours ago














          • 1




            $begingroup$
            Thanks a bunch for your detailed and demanding response. I’m really surprised by the amount of search you did in order to fix the issue.
            $endgroup$
            – pythinker
            6 hours ago










          • $begingroup$
            @pythinker My pleasure! I'm glad I could help. This detective stuff is fun ;)
            $endgroup$
            – Esmailian
            6 hours ago






          • 1




            $begingroup$
            I’m pleased to hear that you are interested in this type of questions. So I will try to pose more questions like this :)
            $endgroup$
            – pythinker
            6 hours ago








          1




          1




          $begingroup$
          Thanks a bunch for your detailed and demanding response. I’m really surprised by the amount of search you did in order to fix the issue.
          $endgroup$
          – pythinker
          6 hours ago




          $begingroup$
          Thanks a bunch for your detailed and demanding response. I’m really surprised by the amount of search you did in order to fix the issue.
          $endgroup$
          – pythinker
          6 hours ago












          $begingroup$
          @pythinker My pleasure! I'm glad I could help. This detective stuff is fun ;)
          $endgroup$
          – Esmailian
          6 hours ago




          $begingroup$
          @pythinker My pleasure! I'm glad I could help. This detective stuff is fun ;)
          $endgroup$
          – Esmailian
          6 hours ago




          1




          1




          $begingroup$
          I’m pleased to hear that you are interested in this type of questions. So I will try to pose more questions like this :)
          $endgroup$
          – pythinker
          6 hours ago




          $begingroup$
          I’m pleased to hear that you are interested in this type of questions. So I will try to pose more questions like this :)
          $endgroup$
          – pythinker
          6 hours ago


















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