# What is the method should I use to calculate similarity in a data set with outliers that must be included?

Information:

So I have a data set with 18 vectors with 167 components, each of with has a value with a range of $$[-2, 2]$$. I am trying to calculate the similarity between one arbitrary vector in this data set and another arbitrary vector in the data set, and so far I have tried using two methods: Spearman's Footrule Distance and Jaccard Similarity (by detecting if the values at position n in each vector was greater than zero; if yes, then it returns 1). Unfortunately, there are some outlier vectors in the data set (which must be included) in which a disproportionate amount of values are, say zero or less than zero, or larger than zero (in which case this outlier will be #1 in similarity in almost every case). In this situation, the value returned for the outliers by the methods I am using is far smaller than the values returned for the non-outliers, thus making the outliers the most dissimilar vector for each different vector tested.

What I need:

Is there either a specific type of similarity I can use or is there a way to adjust/normalize the data set so that this doesn't happen?

Context for the data:

Each vector is for a specific person, and the components are ratings of songs.

EDIT: Added comment: [The goal is] to see which people were similer. There are outliers that rated a large amount of songs as a -2 or a 2, for example, and are thus either very similar to all of them or dissimilar

• I don't understand. 18 people rated 167 songs, right? What is your aim? To see which people were similar? Which songs? Or what? And how are there outliers when the variable is -2 to 2 (sounds like a Likert type scale). Aug 16 '19 at 11:36
• @PeterFlom To see which people were similer. There are outliers that rated a large amount of songs as a -2 or a 2, for example, and are thus either very similar to all of them or dissimilar. Aug 16 '19 at 22:21