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How to optimize the order of elements based on similarity coefficients?
How do you detect Credit card type based on number?Fastest sort of fixed length 6 int arrayClosest Pair of Points AlgorithmMap Tiling AlgorithmImage Processing: Algorithm Improvement for 'Coca-Cola Can' RecognitionGiven an even number of vertices, how to find an optimum set of pairs based on proximity?Finding the best cosine similarity in a set of vectorsHow to pair socks from a pile efficiently?Find row and column number of eight neighbors conditionally in MatlabHow to select k nodes in a fully connected graph with max separation between any pair of nodes?
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I have to reorder a sequence of elements based on the similarity between each other (expressed by a coefficient) so that each element is the most similar possible to each of its neighbors. I have to find an algorithm rather than a code.
Example with 10 elements and similarity coefficients calculated for each pair of the elements below :
The excel file can be find here : https://1drv.ms/x/s!AtmZN4-kjgrPms99fqgaDwAS_F4uYw
What I have tried :
- Find a pair with the highest coefficient. In the example : 0.98 for T3 (left-end) and T5 (right-end)
- Find maximum coefficient between the left-end and the remaining elements
- Find maximum coefficient between the right-end and the remaining elements
- Take the maximum between 2. and 3.
- If maximum is 2. add on the left the element corresponding to the maximum coefficient for the left-end. Else, add on the right the element corresponding to the maximum coefficient for the right-end
- Repeat points 2 - 6 until no elements left.
Here is the result :
The result isn't bad. One of the disadvantages I see is that 0.99>0.98 is considered in the same way as 0.99>0.01.
The second option I thought about was maximizing the sum of coefficients between all neighbors, but don't really know where to start from. Especially if there are significantly more than 10 elements. More, it could result in a more "flat" order where while having better similarities overall some extremely similar elements could be placed far from each other.
Being really new to this kind of problems I am pretty sure this should be a rather standard issue with existing solutions. Could you please point to those?
Thank you!
algorithm grouping heuristics
asked Mar 25 at 23:18
NoazertyNoazerty
131 silver badge3 bronze badges
add a comment |
I have to reorder a sequence of elements based on the similarity between each other (expressed by a coefficient) so that each element is the most similar possible to each of its neighbors. I have to find an algorithm rather than a code.
Example with 10 elements and similarity coefficients calculated for each pair of the elements below :
The excel file can be find here : https://1drv.ms/x/s!AtmZN4-kjgrPms99fqgaDwAS_F4uYw
What I have tried :
- Find a pair with the highest coefficient. In the example : 0.98 for T3 (left-end) and T5 (right-end)
- Find maximum coefficient between the left-end and the remaining elements
- Find maximum coefficient between the right-end and the remaining elements
- Take the maximum between 2. and 3.
- If maximum is 2. add on the left the element corresponding to the maximum coefficient for the left-end. Else, add on the right the element corresponding to the maximum coefficient for the right-end
- Repeat points 2 - 6 until no elements left.
Here is the result :
The result isn't bad. One of the disadvantages I see is that 0.99>0.98 is considered in the same way as 0.99>0.01.
The second option I thought about was maximizing the sum of coefficients between all neighbors, but don't really know where to start from. Especially if there are significantly more than 10 elements. More, it could result in a more "flat" order where while having better similarities overall some extremely similar elements could be placed far from each other.
Being really new to this kind of problems I am pretty sure this should be a rather standard issue with existing solutions. Could you please point to those?
Thank you!
algorithm grouping heuristics
asked Mar 25 at 23:18
NoazertyNoazerty
131 silver badge3 bronze badges
add a comment |
I have to reorder a sequence of elements based on the similarity between each other (expressed by a coefficient) so that each element is the most similar possible to each of its neighbors. I have to find an algorithm rather than a code.
Example with 10 elements and similarity coefficients calculated for each pair of the elements below :
The excel file can be find here : https://1drv.ms/x/s!AtmZN4-kjgrPms99fqgaDwAS_F4uYw
What I have tried :
- Find a pair with the highest coefficient. In the example : 0.98 for T3 (left-end) and T5 (right-end)
- Find maximum coefficient between the left-end and the remaining elements
- Find maximum coefficient between the right-end and the remaining elements
- Take the maximum between 2. and 3.
- If maximum is 2. add on the left the element corresponding to the maximum coefficient for the left-end. Else, add on the right the element corresponding to the maximum coefficient for the right-end
- Repeat points 2 - 6 until no elements left.
Here is the result :
The result isn't bad. One of the disadvantages I see is that 0.99>0.98 is considered in the same way as 0.99>0.01.
The second option I thought about was maximizing the sum of coefficients between all neighbors, but don't really know where to start from. Especially if there are significantly more than 10 elements. More, it could result in a more "flat" order where while having better similarities overall some extremely similar elements could be placed far from each other.
Being really new to this kind of problems I am pretty sure this should be a rather standard issue with existing solutions. Could you please point to those?
Thank you!
algorithm grouping heuristics
asked Mar 25 at 23:18
NoazertyNoazerty
131 silver badge3 bronze badges
I have to reorder a sequence of elements based on the similarity between each other (expressed by a coefficient) so that each element is the most similar possible to each of its neighbors. I have to find an algorithm rather than a code.
Example with 10 elements and similarity coefficients calculated for each pair of the elements below :
The excel file can be find here : https://1drv.ms/x/s!AtmZN4-kjgrPms99fqgaDwAS_F4uYw
What I have tried :
- Find a pair with the highest coefficient. In the example : 0.98 for T3 (left-end) and T5 (right-end)
- Find maximum coefficient between the left-end and the remaining elements
- Find maximum coefficient between the right-end and the remaining elements
- Take the maximum between 2. and 3.
- If maximum is 2. add on the left the element corresponding to the maximum coefficient for the left-end. Else, add on the right the element corresponding to the maximum coefficient for the right-end
- Repeat points 2 - 6 until no elements left.
Here is the result :
The result isn't bad. One of the disadvantages I see is that 0.99>0.98 is considered in the same way as 0.99>0.01.
The second option I thought about was maximizing the sum of coefficients between all neighbors, but don't really know where to start from. Especially if there are significantly more than 10 elements. More, it could result in a more "flat" order where while having better similarities overall some extremely similar elements could be placed far from each other.
Being really new to this kind of problems I am pretty sure this should be a rather standard issue with existing solutions. Could you please point to those?
Thank you!
algorithm grouping heuristics
algorithm grouping heuristics
asked Mar 25 at 23:18
NoazertyNoazerty
131 silver badge3 bronze badges
asked Mar 25 at 23:18
NoazertyNoazerty
131 silver badge3 bronze badges
asked Mar 25 at 23:18
NoazertyNoazerty
131 silver badge3 bronze badges
asked Mar 25 at 23:18
NoazertyNoazerty
131 silver badge3 bronze badges
asked Mar 25 at 23:18
NoazertyNoazerty
131 silver badge3 bronze badges
131 silver badge3 bronze badges
add a comment |
add a comment |
1 Answer
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After researching I have found that my problem can be seen as the "Travelling Salesman Problem" (TSP). More here : https://en.wikipedia.org/wiki/Travelling_salesman_problem
To apply it you can see "elements" in my example as "cities" in TSP and (1-Similarity coefficient) as "distances".
answered Mar 30 at 23:27
NoazertyNoazerty
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add a comment |
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1 Answer
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1 Answer
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active
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active
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After researching I have found that my problem can be seen as the "Travelling Salesman Problem" (TSP). More here : https://en.wikipedia.org/wiki/Travelling_salesman_problem
To apply it you can see "elements" in my example as "cities" in TSP and (1-Similarity coefficient) as "distances".
answered Mar 30 at 23:27
NoazertyNoazerty
131 silver badge3 bronze badges
add a comment |
After researching I have found that my problem can be seen as the "Travelling Salesman Problem" (TSP). More here : https://en.wikipedia.org/wiki/Travelling_salesman_problem
To apply it you can see "elements" in my example as "cities" in TSP and (1-Similarity coefficient) as "distances".
answered Mar 30 at 23:27
NoazertyNoazerty
131 silver badge3 bronze badges
add a comment |
After researching I have found that my problem can be seen as the "Travelling Salesman Problem" (TSP). More here : https://en.wikipedia.org/wiki/Travelling_salesman_problem
To apply it you can see "elements" in my example as "cities" in TSP and (1-Similarity coefficient) as "distances".
answered Mar 30 at 23:27
NoazertyNoazerty
131 silver badge3 bronze badges
After researching I have found that my problem can be seen as the "Travelling Salesman Problem" (TSP). More here : https://en.wikipedia.org/wiki/Travelling_salesman_problem
To apply it you can see "elements" in my example as "cities" in TSP and (1-Similarity coefficient) as "distances".
answered Mar 30 at 23:27
NoazertyNoazerty
131 silver badge3 bronze badges
answered Mar 30 at 23:27
NoazertyNoazerty
131 silver badge3 bronze badges
answered Mar 30 at 23:27
NoazertyNoazerty
131 silver badge3 bronze badges
answered Mar 30 at 23:27
NoazertyNoazerty
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131 silver badge3 bronze badges
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