proximity measure

similarity

numerical measure of the degree to which two objects are alike

dissimilarity

another alternative or opposite measure of the degree to which objects are different

proximity

both dissimilarity and similarity are also termed as _, ranges from zero to come finite or infinite value

distance

synonym or special case for dissimilarity; estimate similarity between two objects defined with interval-scaled attributes

similarity measure

higher when objects are more alike

dissimilarity measure

lower when objects are more alike, minimum dissimilarity is often 0 and upper limit varies

binary

for nominal variables, measures are _, indicating whether two values are equal or not

1

similarity value is _ if the two objects contains the same attribute value

0

similarity value is _ implies objects are not at all similar

proximity calculation for nominal data

symmetric binary coefficient

asymmetric binary or jaccard coefficient

minkowski disatnce

generalization of euclidean and manhattan distance, identity condition, order is not important, triangle inequality

triangle inequality

the least distance between objects x and z is always less than or equal to the sum of the distance between objects x and y, and between y and z

manhattan distance

sum of the absolute value of the difference between x and y, also known as taxicals metric, city-block metric

hamming distance

special instance of manhattan distance when values are either 0 or 1 (binary vectors)

euclidean distance

square root of the sum of the squared difference of x and y

chebychev distance

maximum absolute value between the differences of x and y

numerical data normalization

ordinal data normalization

cosine similarity

essentially a measure of the (_ of the) angle between x and y

similar vectors

angle close to 0, cosine close to 1

orthogonal vectors

angle close to 90, cosine close to 0

opposite vectors

angle close to 180, cosine close to -1