From 325427c72382dbe8c2ce6ba7490959f8ff6b9e35 Mon Sep 17 00:00:00 2001
From: Arkadiusz Kondas <arkadiusz.kondas@gmail.com>
Date: Sat, 14 May 2016 21:30:13 +0200
Subject: [PATCH] update missing docs

---
 .../imputation-missing-values.md              | 44 +++++++++++
 .../preprocessing/normalization.md            | 58 ++++++++++++++
 docs/math/statistic.md                        | 79 ++++++++++++++++++-
 3 files changed, 178 insertions(+), 3 deletions(-)

diff --git a/docs/machine-learning/preprocessing/imputation-missing-values.md b/docs/machine-learning/preprocessing/imputation-missing-values.md
index db64d8d..186f424 100644
--- a/docs/machine-learning/preprocessing/imputation-missing-values.md
+++ b/docs/machine-learning/preprocessing/imputation-missing-values.md
@@ -1 +1,45 @@
 # Imputation missing values
+
+For various reasons, many real world datasets contain missing values, often encoded as blanks, NaNs or other placeholders.
+To solve this problem you can use the `Imputer` class.
+
+## Constructor Parameters
+
+* $missingValue (mixed) - this value will be replaced (default null)
+* $strategy (Strategy) - imputation strategy (read to use: MeanStrategy, MedianStrategy, MostFrequentStrategy)
+* $axis (int) - axis for strategy, Imputer::AXIS_COLUMN or Imputer::AXIS_ROW
+
+```
+$imputer = new Imputer(null, new MeanStrategy(), Imputer::AXIS_COLUMN);
+$imputer = new Imputer(null, new MedianStrategy(), Imputer::AXIS_ROW);
+```
+
+## Strategy
+
+* MeanStrategy - replace missing values using the mean along the axis
+* MedianStrategy - replace missing values using the median along the axis
+* MostFrequentStrategy - replace missing using the most frequent value along the axis
+
+## Example of use
+
+```
+$data = [
+    [1, null, 3, 4],
+    [4, 3, 2, 1],
+    [null, 6, 7, 8],
+    [8, 7, null, 5],
+];
+
+$imputer = new Imputer(null, new MeanStrategy(), Imputer::AXIS_COLUMN);
+$imputer->preprocess($data);
+
+/*
+$data = [
+    [1, 5.33, 3, 4],
+    [4, 3, 2, 1],
+    [4.33, 6, 7, 8],
+    [8, 7, 4, 5],
+];
+*/
+
+```
diff --git a/docs/machine-learning/preprocessing/normalization.md b/docs/machine-learning/preprocessing/normalization.md
index a0dbc80..61b1a8d 100644
--- a/docs/machine-learning/preprocessing/normalization.md
+++ b/docs/machine-learning/preprocessing/normalization.md
@@ -1 +1,59 @@
 # Normalization
+
+Normalization is the process of scaling individual samples to have unit norm.
+
+## L2 norm
+
+[http://mathworld.wolfram.com/L2-Norm.html](http://mathworld.wolfram.com/L2-Norm.html)
+
+Example:
+
+```
+use Phpml\Preprocessing\Normalizer;
+
+$samples = [
+    [1, -1, 2],
+    [2, 0, 0],
+    [0, 1, -1],
+];
+
+$normalizer = new Normalizer();
+$normalizer->preprocess($samples);
+
+/*
+$samples = [
+  [0.4, -0.4, 0.81],
+  [1.0, 0.0, 0.0],
+  [0.0, 0.7, -0.7],
+];
+*/
+
+```
+
+## L1 norm
+
+[http://mathworld.wolfram.com/L1-Norm.html](http://mathworld.wolfram.com/L1-Norm.html)
+
+Example:
+
+```
+use Phpml\Preprocessing\Normalizer;
+
+$samples = [
+    [1, -1, 2],
+    [2, 0, 0],
+    [0, 1, -1],
+];
+
+$normalizer = new Normalizer(Normalizer::NORM_L1);
+$normalizer->preprocess($samples);
+
+/*
+$samples = [
+   [0.25, -0.25, 0.5],
+   [1.0, 0.0, 0.0],
+   [0.0, 0.5, -0.5],
+];
+*/
+
+```
diff --git a/docs/math/statistic.md b/docs/math/statistic.md
index 89cc00e..626828e 100644
--- a/docs/math/statistic.md
+++ b/docs/math/statistic.md
@@ -1,7 +1,80 @@
 # Statistic
 
-### Correlation
+Selected statistical methods.
 
-### Mean
+## Correlation
 
-### Standard Deviation
+Correlation coefficients are used in statistics to measure how strong a relationship is between two variables. There are several types of correlation coefficient.
+
+### Pearson correlation
+ 
+Pearson’s correlation or Pearson correlation is a correlation coefficient commonly used in linear regression.
+
+Example:
+
+```
+use Phpml\Math\Statistic\Correlation;
+
+$x = [43, 21, 25, 42, 57, 59];
+$y = [99, 65, 79, 75, 87, 82];
+
+Correlation::pearson($x, $y);
+// return 0.549
+```
+
+## Mean
+
+### Arithmetic
+
+Example:
+
+```
+use Phpml\Math\Statistic\Mean;
+
+Mean::arithmetic([2, 5];
+// return 3.5
+
+Mean::arithmetic([0.5, 0.5, 1.5, 2.5, 3.5];
+// return 1.7
+```
+
+## Median
+
+Example:
+
+```
+use Phpml\Math\Statistic\Mean;
+
+Mean::median([5, 2, 6, 1, 3, 4]);
+// return 3.5
+
+Mean::median([5, 2, 6, 1, 3]);
+// return 3
+```
+
+## Mode
+
+Example:
+
+```
+use Phpml\Math\Statistic\Mean;
+
+Mean::mode([5, 2, 6, 1, 3, 4, 6, 6, 5]);
+// return 6
+```
+
+## Standard Deviation
+
+Example:
+
+```
+use Phpml\Math\Statistic\StandardDeviation;
+
+$population = [5, 6, 8, 9];
+StandardDeviation::population($population)
+// return 1.825
+
+$population = [7100, 15500, 4400, 4400, 5900, 4600, 8800, 2000, 2750, 2550,  960, 1025];
+StandardDeviation::population($population)
+// return 4079
+```