README.md in supervised_learning-0.0.1 vs README.md in supervised_learning-0.0.2

@@ -1,10 +1,10 @@
-# SupervisedLearning
+# Supervised Learning
 
 Supervised learning is the machine learning task of inferring a function from labeled training data. A supervised learning algorithm analyzes the training data and produces an inferred function, which can be used for mapping new examples.
 
-Credits for the underlying algorithms of the functions that make predictions go to [Andrew Ng](http://cs.stanford.edu/people/ang/) at Stanford University.
+Credits for some of the algorithms used go to [Andrew Ng](http://cs.stanford.edu/people/ang/) at Stanford University.
 
 ## Example
 
 One example is the prediction of house prices (output value) along two dimensions (features): the size of house in square meters and the number of bedrooms.
 
@@ -33,36 +33,58 @@
 
     $ gem install supervised_learning
 
 ## Usage
 
-1. Create a matrix of the training data.
+### 1. Create a matrix of the training data
 
-The **output value** (the type of value you want to predict) needs to be in the **last column**. The matrix has to have a) at least two columns (one feature and one output) and b) one row. The more data you feed it, the more accurate the prediction.
+The **output value** (the type of value you want to predict) needs to be in the **last column**. The matrix has to have a) at least two columns (one feature and one output) and b) at least one row. The more data you feed it, the more accurate the prediction.
 
-Consult the [Ruby API](http://www.ruby-doc.org/stdlib-2.1.2/libdoc/matrix/rdoc/Matrix.html) for information on how to build matrices for instances based on arrays of rows or columns.
+Consult the [Ruby API](http://www.ruby-doc.org/stdlib-2.1.2/libdoc/matrix/rdoc/Matrix.html) for information on how to build matrices. You can use both arrays of rows or columns to create a matrix.
 
 ```ruby
 require 'matrix'
 
 training_set = Matrix[ [2104, 3, 399900], [1600, 3, 329900], [3000, 4, 539900], [1940, 4, 239999] ]
 ```
 
-2. Instantiate an object with the training data.
+### 2. Instantiate an object with the training data
 
 ```ruby
+require 'supervised_learning' # if not automatically loaded
+
 program = SupervisedLearning::LinearRegression.new(training_set)
 ```
 
-3. Create a prediction in form of a matrix. 
+### 3. Create a prediction in form of a matrix
 
 This matrix has one row and the **columns follow the order of the training set**. It has one column less than the training set since the output value (the last column of the training set) is the value we want to predict.
 
 ```ruby
-# Predict the price of a house of 2000 square meters with 3 bedrooms
-prediction_set = Matrix[ [2000, 3] ]
+# Predict the price of a house of 2200 square meters with 3 bedrooms
+prediction_set = Matrix[ [2200, 3] ]
+
 program.predict(prediction_set)
-=> 
+=> 454115.66
+```
+
+### 4. Options
+
+The lower bound running time of the `#predict` method is cubic / Ω(n3). Hence, on very large datasets (more than 1,000 columns / features), the `#predict` method can be slow. If this happens, use the `#predict_advanced` method, which uses gradient descent (approximation) instead of normalization (direct calculation). Gradient descent can be a bit less accurate and also requires some optional parameters.
+
+The `#predict_advanced` method takes 4 parameters in the following order:
+
+1. The prediction_set, similar to the `#prediction` method discussed above
+2. The learning rate (how big of a "jump" each iteration makes). The smaller the learning rate, the less errors are to be expected. Unfortunately, a smaller learning rate requires more iterations (see below). Start at 0.001 and increase the parameter to 0.01, 0.1, 1, etc if the calculation is too slow.
+3. The number of iterations. The more iterations, the more accurate the result will but the slower the algorithm will run.
+4. Whether you want print out values to see at which point convergence happens.
+
+```ruby
+# Predict the price of a house of 2200 square meters with 3 bedrooms
+prediction_set = Matrix[ [2200, 3] ]
+
+program.predict_advanced(prediction_set, 0.01, 600, false)
+=> 443693.16
 ```
 
 ## Contributing
 
 1. Fork it ( https://github.com/[my-github-username]/supervised_learning/fork )