you can try cosine similarity approach .   

I agree, cosine similarity approach gives good results with respect to other distances.

Many thanks!!! 

Another distance o similarity measure for nominal data (no binary data). I read that cosine similarity is applied for numeric data.

For each of the nominal variables, you could create a 1-of-K binary representation (where K is the number of values that the nominal variable can take).  Then, you can calculate the Hamming distance between these binary representations (note that for binary data Hamming and L1 distance will be equivalent).  This Hamming distance will be 2*(# nominal variables different).

Nominal variables do not have an implicit ordering, so be careful when you map the data to one that has an ordering - or you will be "creating" ordering that are not present! One measure that tells you the relatedness of two items is the so-called IS measure. We have recently published works on using this to compute correlation between two terms for missing value imputation. If you have two items a and b, the IS measure is given by P(a,b)/sqrt(P(a)*P(b)), where P stands for probability. a and b can be generalized to a list of items, so you could measure the relatedness of 2 lists of nominal values.

My suggestion: http://www.researchgate.net/publication/278403191_Numerical_Coding_of_Nominal_Data

Article Numerical Coding of Nominal Data

Not sure which one works best for you, but you can try:

1- Cosine distance (Angular)

2- Jaccard distance (Magnitude)

3- Fuzzy score (order kinda matters)

4- Hamming distance (the character sequences should have the same length)

5- Levenshtein Distance

6- JaroWinkler Distance

7- Any combination of the above!

Can I ask a question in the midst of these responses? Alireza Khodaei Chandra Prakash Belahcene Mebarka

Say I have the following data

id , gender , race , school, county, major

1, male, white, savannah, chatham, computer science

2, female, white, savannah, chatham, math

3, male, black, bismark, green, English

4, female, asian, macon, stattard, computer science.

Small data I realize, but how does one use cosine distance to compare say distance (object1, object3)?

I'm just trying to find an actual example, outside the high level theory. Also, when you say any combination, how does one combine say cosine with euclidian, or cosine with jaccard if say I wanted to use cosine for major, county, school, and race, but jaccard with gender since it is binary?

Thank you for your assistance.

Answering to Christopher Klecker :

> how does one use cosine distance to compare say distance (object1, object3)?

If you mean how practically use a cosine distance function, there are already libraries, at least in Java (e.g., org.apache.commons.text.similarity.*)

But if you wonder how conceptually it works, it actually measures the cosine between the n-element vectors that obj1 and obj3 define in an n dimensional space.

But remember, Cosine distance is not a metric as it does not satisfy the triangle inequality. It means you can't infer cosine distance between obj1 and obj3 by knowing cosDistance(obj1,obj2) and cosDistance(obj2,obj3)

> when you say any combination, how does one combine say cosine with euclidian, or cosine with jaccard if say I wanted to use cosine for major, county, school, and race, but jaccard with gender since it is binary?

I don't have one-solution-fits-all-problems sauce for that. You need to play with your dataset to see what turns out to be best.

One way would be measuring different features of your data with different distance. For example, if you have two objects that has a same euclidean distance from a reference point with respect to 'country' then you may want to measure 'race' distance with another method. Another way would be clustering objects based on a distance method and finding the distance between the clusters with another method.