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authorTimothy Hunter <timhunter@databricks.com>2015-12-08 18:40:21 -0800
committerJoseph K. Bradley <joseph@databricks.com>2015-12-08 18:40:21 -0800
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[SPARK-8517][ML][DOC] Reorganizes the spark.ml user guide
This PR moves pieces of the spark.ml user guide to reflect suggestions in SPARK-8517. It does not introduce new content, as requested. <img width="192" alt="screen shot 2015-12-08 at 11 36 00 am" src="https://cloud.githubusercontent.com/assets/7594753/11666166/e82b84f2-9d9f-11e5-8904-e215424d8444.png"> Author: Timothy Hunter <timhunter@databricks.com> Closes #10207 from thunterdb/spark-8517.
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----
-layout: global
-title: Multilayer perceptron classifier - ML
-displayTitle: <a href="ml-guide.html">ML</a> - Multilayer perceptron classifier
----
-
-
-`\[
-\newcommand{\R}{\mathbb{R}}
-\newcommand{\E}{\mathbb{E}}
-\newcommand{\x}{\mathbf{x}}
-\newcommand{\y}{\mathbf{y}}
-\newcommand{\wv}{\mathbf{w}}
-\newcommand{\av}{\mathbf{\alpha}}
-\newcommand{\bv}{\mathbf{b}}
-\newcommand{\N}{\mathbb{N}}
-\newcommand{\id}{\mathbf{I}}
-\newcommand{\ind}{\mathbf{1}}
-\newcommand{\0}{\mathbf{0}}
-\newcommand{\unit}{\mathbf{e}}
-\newcommand{\one}{\mathbf{1}}
-\newcommand{\zero}{\mathbf{0}}
-\]`
-
-
-Multilayer perceptron classifier (MLPC) is a classifier based on the [feedforward artificial neural network](https://en.wikipedia.org/wiki/Feedforward_neural_network).
-MLPC consists of multiple layers of nodes.
-Each layer is fully connected to the next layer in the network. Nodes in the input layer represent the input data. All other nodes maps inputs to the outputs
-by performing linear combination of the inputs with the node's weights `$\wv$` and bias `$\bv$` and applying an activation function.
-It can be written in matrix form for MLPC with `$K+1$` layers as follows:
-`\[
-\mathrm{y}(\x) = \mathrm{f_K}(...\mathrm{f_2}(\wv_2^T\mathrm{f_1}(\wv_1^T \x+b_1)+b_2)...+b_K)
-\]`
-Nodes in intermediate layers use sigmoid (logistic) function:
-`\[
-\mathrm{f}(z_i) = \frac{1}{1 + e^{-z_i}}
-\]`
-Nodes in the output layer use softmax function:
-`\[
-\mathrm{f}(z_i) = \frac{e^{z_i}}{\sum_{k=1}^N e^{z_k}}
-\]`
-The number of nodes `$N$` in the output layer corresponds to the number of classes.
-
-MLPC employes backpropagation for learning the model. We use logistic loss function for optimization and L-BFGS as optimization routine.
-
-**Examples**
-
-<div class="codetabs">
-
-<div data-lang="scala" markdown="1">
-{% include_example scala/org/apache/spark/examples/ml/MultilayerPerceptronClassifierExample.scala %}
-</div>
-
-<div data-lang="java" markdown="1">
-{% include_example java/org/apache/spark/examples/ml/JavaMultilayerPerceptronClassifierExample.java %}
-</div>
-
-<div data-lang="python" markdown="1">
-{% include_example python/ml/multilayer_perceptron_classification.py %}
-</div>
-
-</div>