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neural-networkperceptronbias-neuron

Clarification on bias of a perceptron


Isn't it true that if a bias is not present, a line passing through origin should be able to linearly separate the two data sets??

But the most popular answer in this -->> question says

y                             
^                              
|  - + \\  +                   
| -    +\\ +   +               
| - -    \\ +                  
| -  -  + \\  +                
---------------------> x       
    stuck like this            

I am confused about it. Do you mean the origins in figure above are somewhere in middle of x-axis and y-axis? Can somebody please help me and clarify this?


Solution

  • Alright, so perhaps the original ASCII graph was not 100% accurate! Let me try to depict this again:

                y                                    y
                ^                                    ^
       - + \\   | +                       -\\+       | +
     -     +\\  | +   +                 -   \\ +     | +   +
     - -     \\ |  +                    - -  \\      |  +
     -  -   + \\|    +                  -  -  \\+    |    +
    ------------------------> x        ---------------------------> x
        - -     |\\    +                   - - \\    |      +
     -   -    + | \\ +                  -   -   \\ + |    +
      -    - -  |  \\  + +               -    - -\\  |      + +
     -- -    -  |  +\\     ++           -- -    - \\ |  +       ++
    
         stuck like this                  needs to get like this
              y = ax                            y = ax + b
         (w0*x + w1*y = 0)               (w0*x + w1*y + w2*1 = 0)