add Math functions, add Fit method for LinearRegression

Author: kortirso

lib/learn_kit/math.ex

@@ -65,10 +65,7 @@ defmodule LearnKit.Math do
 
   def variance(list, list_mean) when is_list(list) do
     list
-    |> Enum.map(fn x ->
-      list_mean - x
-      |> :math.pow(2)
-    end)
+    |> Enum.map(fn x -> pow(list_mean - x, 2) end)
     |> mean
   end
 
@@ -132,4 +129,84 @@ defmodule LearnKit.Math do
     others = Enum.map(rows, fn(x) -> tl(x) end)
     [firsts | swap_rows_cols(others)]
   end
+
+  @doc """
+  Division for 2 elements
+
+  ## Examples
+
+      iex> LearnKit.Math.division(10, 2)
+      5
+
+  """
+  @spec division(number, number) :: number
+
+  def division(x, y) when y != 0 do
+    x / y
+  end
+
+  @doc """
+  Pow number
+
+  ## Examples
+
+      iex> LearnKit.Math.pow(10, 2)
+      100
+
+  """
+  @spec pow(number, number) :: number
+
+  def pow(x, y) do
+    :math.pow(x, y)
+  end
+
+  @doc """
+  Calculate the covariance of two lists
+
+  ## Examples
+
+      iex> LearnKit.Math.covariance([1, 2, 3], [14, 17, 25])
+      5.5
+
+  """
+  @spec covariance(list,list) :: number
+
+  def covariance(x, y) when length(x) == length(y) do
+    mean_x = mean(x)
+    mean_y = mean(y)
+    size = length(x)
+
+    Enum.zip(x, y)
+    |> Enum.map(fn {xi, yi} -> (xi - mean_x) * (yi - mean_y) end)
+    |> Enum.sum
+    |> division(size - 1)
+  end
+
+  @doc """
+  Correlation of two lists
+
+  ## Examples
+
+      iex> LearnKit.Math.correlation([1, 2, 3], [14, 17, 25])
+      0.9672471299049061
+
+  """
+  @spec correlation(list, list) :: number
+
+  def correlation(x, y) when length(x) == length(y) do
+    mean_x = mean(x)
+    mean_y = mean(y)
+
+    divider = Enum.zip(x, y)
+            |> Enum.map(fn {xi, yi} -> (xi - mean_x) * (yi - mean_y) end)
+            |> Enum.sum
+    denom_x = x
+              |> Enum.map(fn xi -> pow(xi - mean_x, 2) end)
+              |> Enum.sum
+    denom_y = y
+              |> Enum.map(fn yi -> pow(yi - mean_y, 2) end)
+              |> Enum.sum
+
+    divider / :math.sqrt(denom_x * denom_y)
+  end
 end

lib/learn_kit/regression/linear.ex

@@ -3,44 +3,71 @@ defmodule LearnKit.Regression.Linear do
   Module for Linear Regression algorithm
   """
 
-  defstruct factors: [], results: []
+  defstruct factors: [], results: [], coefficients: []
 
   alias LearnKit.Regression.Linear
 
+  use Linear.Fit
+
   @type factors :: [number]
   @type results :: [number]
+  @type coefficients :: [number]
 
   @doc """
-  Creates classificator with empty data_set
+  Creates predictor with empty data_set
 
   ## Examples
 
-      iex> classificator = LearnKit.Regression.Linear.new
-      %LearnKit.Regression.Linear{factors: [], results: []}
+      iex> predictor = LearnKit.Regression.Linear.new
+      %LearnKit.Regression.Linear{factors: [], results: [], coefficients: []}
 
   """
-  @spec new() :: %LearnKit.Regression.Linear{factors: [], results: []}
+  @spec new() :: %LearnKit.Regression.Linear{factors: [], results: [], coefficients: []}
 
   def new do
     Linear.new([], [])
   end
 
   @doc """
-  Creates classificator with data_set
+  Creates predictor with data_set
 
   ## Parameters
 
-    - data_set: Keyword list with labels and features in tuples
+    - factors: Array of predictor variables
+    - results: Array of criterion variables
 
   ## Examples
 
-      iex> classificator = LearnKit.Regression.Linear.new([1, 2, 3, 4], [2, 3, 4, 5])
-      %LearnKit.Regression.Linear{factors: [1, 2, 3, 4], results: [2, 3, 4, 5]}
+      iex> predictor = LearnKit.Regression.Linear.new([1, 2, 3, 4], [2, 3, 4, 5])
+      %LearnKit.Regression.Linear{factors: [1, 2, 3, 4], results: [2, 3, 4, 5], coefficients: []}
 
   """
-  @spec new(factors, results) :: %LearnKit.Regression.Linear{factors: factors, results: results}
+  @spec new(factors, results) :: %LearnKit.Regression.Linear{factors: factors, results: results, coefficients: []}
 
   def new(factors, results) do
     %Linear{factors: factors, results: results}
   end
+
+  @doc """
+  Fit train data
+
+  ## Parameters
+
+    - predictor: %LearnKit.Regression.Linear{}
+
+  ## Examples
+
+      iex> predictor |> LearnKit.Regression.Linear.fit
+      %LearnKit.Regression.Linear{
+        coefficients: [1.0, 1.0],
+        factors: [1, 2, 3, 4],
+        results: [2, 3, 4, 5]
+      }
+
+  """
+  @spec fit(%LearnKit.Regression.Linear{factors: factors, results: results}) :: %LearnKit.Regression.Linear{factors: factors, results: results, coefficients: coefficients}
+
+  def fit(%Linear{factors: factors, results: results}) do
+    %Linear{factors: factors, results: results, coefficients: fit_data(factors, results)}
+  end
 end

lib/learn_kit/regression/linear/fit.ex

@@ -0,0 +1,17 @@
+defmodule LearnKit.Regression.Linear.Fit do
+  @moduledoc """
+  Module for fit functions
+  """
+
+  alias LearnKit.Math
+
+  defmacro __using__(_opts) do
+    quote do
+      defp fit_data(factors, results) do
+        beta = Math.correlation(factors, results) * Math.standard_deviation(results) / Math.standard_deviation(factors)
+        alpha = Math.mean(results) - beta * Math.mean(factors)
+        [alpha, beta]
+      end
+    end
+  end
+end