quick look at machine learning had included the fact that reptile eggs have amnios, we could devise rule that separates reptiles from fish unfortunatelyin most practical applications of machine learning it is not possible to construct feature vectors that allow for perfect discrimination does this mean that we should give up because all of the available features are mere noiseno in this case the features scales and cold-blooded are necessary conditions for being reptilebut not sufficient conditions the rule has scales and is cold-blooded will not yield any false negativesi any animal classified as non-reptile will indeed not be reptile howeverit will yield some false positivesi some of the animals classified as reptiles will not be reptiles distance metrics in figure we described animals using four binary features and one integer feature suppose we want to use these features to evaluate the similarity of two animalse to askis boa constrictor more similar to rattlesnake or to dart frog? the first step in doing this kind of comparison is converting the features for each animal into sequence of numbers if we say true and false we get the following feature vectorsrattlesnake[ , , , , boa constrictor[ , , , , dart frog[ , , , , there are many different ways to compare the similarity of vectors of numbers the most commonly used metrics for comparing equal-length vectors are based on the minkowski distance!"!"! ! !"#$%&'! ! !!the parameter defines the kinds of paths that can be followed in traversing the distance between the vectors ! and ! this can be mostly easily visualized if the vectors are of length twoand represent cartesian coordinates consider the picture on the left is the circle in the bottom left corner closer to the cross or to the starit depends if we can travel in straight linethe cross is closer the pythagorean theorem tells us that the cross is the square root of units from the circleabout unitswhereas we can amnios are protective outer layers that allow eggs to be laid on land rather than in the water this question is not quite as silly as it sounds naturalist and toxicologist (or someone looking to enhance the effectiveness of blow dartmight give different answers to this question