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I am new to machine learning and could understand the simple perceptron. I came to a formula while reading about perceptron.

$$ y = \sum_{k = 1}^{K}z_{k}(x)(\Theta _{0}^{(k)} + \sum_{j = 1}^{m}\Theta _{j}^{(k)}x_{j}) $$

where $$ z_{k}(x) \epsilon R^{+} $$

I could understand the inner block represents simple perceptron. and $$ z_{k}(x) $$ is a element from real number. What is exactly $$ z_{k}(x) $$ representing here. Could you give a hint ? Is it changing single layer perceptron to multi layer or other ?

Sanjay Shrestha
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  • where do you read this? – Siong Thye Goh Jun 14 '17 at 20:41
  • I would guess EITHER they mean $z_k$ instead of $z_k(x)$ OR $z_k:\mathbb{R}^n\rightarrow \mathbb{R}$ is a fixed function (i am assumimg you sum for $k=1,...,n$ since there is a typo in your upper sum limit) – Max Jun 14 '17 at 21:14
  • $z^{_{k}}(x)$denotes the degree of membership for an instance x to group k – Sanjay Shrestha Jun 15 '17 at 01:58
  • @SanjayShrestha $\sum_{k=1}^k$ is definitely a typo :-) if not by you, then by the authors of the paper. Can you link the paper? (or give the doi or whatever?) – Max Jun 15 '17 at 07:44
  • @Max My mistake, Was a typo from my side..Changed to bigger K :) – Sanjay Shrestha Jun 15 '17 at 08:10
  • @SanjayShrestha As Max suggested, you should link to the paper where this is written (or write in some more details), to help us understand the context. – user3658307 Jun 15 '17 at 15:04

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