Ss ts

Rolf Reeves
Oct 30, 2023
4 min read

How to convert TS-SS result to similarity measure between 0 - 1?

I'm currently developing a question plugin for some LMS that auto grade the answer based on the similarity between the answer and answer key with cosine similarity. But lately, I found that there is a better algorithm that promised to be more accurate called TS-SS. But, the result of the calculation 0 - infinity. Being not a machine learning guy, I was assuming that the result maybe a distance, just like Euclidean Distance, but I'm not sure. It can be a geometry or something, because the algorithm is calculating the triangle and sector, so I'm assuming that it is a geometric similarity or something, I'm not sure though. So I have some example in my note, and then I tried to convert it with what people suggest, S = 1 / (1 + D) , but the result was not what I'm looking for. With cosine similarity I got 0.77, but with TS-SS plus equation before, I got 0.4. And then I found this SO answer that uses S = 1 / (1.1 ** D) . When I tried the equation, sure enough it gave me 'relevant' result, 0.81. That is not far from cosine similarity, and in my opinion the result is better suited for auto grading than 0.77 one based on the answer key. But unfortunately, I don't know where that equation come from, and I tried to google it but no luck, so that is why I'm asking this question. How to convert the TS-SS result to similarity measure the right way? Is the S = 1 / (1.1 ** D) enough or. Edit: When calculating TS-SS, it is actually using cosine similarity calculation as well. So, if the cosine similarity is 1, then the TS-SS will be 0. But, if the cosine similarity is 0, the TS-SS is not infinty. So, I think it is reasonable to compare the result between the two to know what conversion formula will be used

TS-SS Cosine Similarity 38.19 0 7.065 0.45 3.001 0.66 1.455 0.77 0.857 0.81 0.006 0.80 0 1 another random comparison from multiple answer key 36.89 0 9.818 0.42 7.581 0.45 3.910 0.63 2.278 0.77 2.935 0.75 1.329 0.81 0.494 0.84 0.053 0.75 0.011 0.80 0.003 0.98 0 1 comparison from the same answer key 38.11 0.71 4.293 0.33 1.448 0 1.203 0.17 0.527 0.62

That result didn't 'come from' somewhere you can simply research. As I said in the comments of that other quest, it comes from being familiar with algebra, and fitting an equation to the characteristics needed. I managed to give that OP (original poster) an equation to fit, because they gave clear characteristics of the desired equation.

If you want comparable help, then you need to specify what you want, with qualitative properties for us to know the general shape of the function, and enough quantitative properties to provide useful coefficients for the class of equation. 'Relevant', 'not far', and 'better suited' are okay for general discussion, but we need a clearer description of what you do want, rather than only vague comparisons.

@prune basically, what I want is to convert the TS-SS result to similarity measure between 0 - 1, and I don't know what formula that suited most for my particular problem, which is comparing two documents, answer key and answer response. Is that clear enough? qualitative properties for us to know the general shape of the function, and enough quantitative properties to provide useful coefficients for the class of equation I'm sorry, I don't understand this part. Can you simplify it more? Thanks

A typical similarity will map D=0 to S=1, and D=infinity to S=0. However, to craft you a function, we need some ideas of the values in between. If the distance is 1 instead of 0, about how far should the similarity fall away from 1? How about 10, 100, . ? What does that curve look like? How fast and how far does it drop from 1 toward 0?

Qualitative properties are a general description of shape: the qualities of the curve. For instance, 'the function has to be concave up/right, with a smooth slope.' Quantitative properties are those you can measure. For instance, 'In general, increasing the distance by 10x should cut the similarity roughly in half.'

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Python, Java implementation of TS-SS called from 'A Hybrid Geometric Approach for Measuring Similarity Level Among Documents and Document Clustering'

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taki0112/Vector_Similarity

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