Machine Learning for the Mathematically Inept*

• The Confusion Matrix

  A confusion matrix is a simple way to visually present the accuracy of a classification algorithm.

• The Curse Of Dimensionality

  High dimensional space is weird and counter intuitive, and the higher the number of dimensions the weirder it gets.

• The Cosine Rule and Dot Product

  This is a generalisation of Pythagoras’ theorem to apply to all triangles rather than just right angled ones. The cosine rule reduces to Pythagoras’ Theorem as well as providing the mathematical basis behind the usefulness of the dot product for establishing the extent to which two vectors are going in the same direction.

• Euclidean Distance

  Euclidean Distance is the ‘ordinary’ straight line distance between two points in Euclidean Space. It can be seen in action as the frustrating difference in distance between how far away something is (the straight line distance) and how far you have to go to get there (the rather disappointingly named distance travelled).

• K-NN

  k-Nearest Neighbours is probably the simplest of the classification techniques, it works by looping through the training dataset, checking each point to see how close it is to the sample you are trying to classify. Once it’s gone through all of them it returns a classification based on an arbitrary number of points (k) so if k is 1 it returns the class of the nearest point to the one you’re trying to classify, for values of k greater than 1 however it returns the class that the majority of the points belong to, so if you have two points from class a and one from class b it will assign the new point to class a.

*These are my notes from university, written up in order to consolidate my knowledge before my exams. I am the Mathematically Inept