How to measure similarity between two data vectors, as like "Correlation coefficient".
Hi,
There are several different options. You can use some kind of norm between the vectors difference, like L2 norm, L1 norm or other hybrid norm (Huber, Student, etc..).
You can also try to adjust the vectors before extract the difference between then, using the Dynamic Time Warping for instance, and you could also normalize the vectors amplitudes using Z-normalization...
As I say, there several different options and depend of your main goal when compare those vectors, what kind of atribute you want to emphasize and so on.
best regards,
Andre Bulcao
Hi,
There are several different options. You can use some kind of norm between the vectors difference, like L2 norm, L1 norm or other hybrid norm (Huber, Student, etc..).
You can also try to adjust the vectors before extract the difference between then, using the Dynamic Time Warping for instance, and you could also normalize the vectors amplitudes using Z-normalization...
As I say, there several different options and depend of your main goal when compare those vectors, what kind of atribute you want to emphasize and so on.
best regards,
Andre Bulcao
Dear Dr. Susant Kumar Panigrahi,
Dr. André Bulcão has given you right view.
Further, represent your data set as vector and then use MATLAB (many options are there).
Hi,
Really, a good question. The answer should depend on a specific definition of similarity. Many definitions exist now (nonlinearity, complexity, coherence, structure,shape). For example, we have recently introduced with colleagues the concept of shape analysis of time-series using a functional formalism. It allows shape monitoring of a set of curves in presence of both time and amplitude variability after realignment procedure (as Dynamic Time Warping cited in a previous comment). It can be considered as an attempt to do automatically what is done by our eyes in comparing two curves. In this context, the classical correlation method should not work due to the presence of time variability (scale factor or nonlinear transformation).
Regards,
Hi,
Like it is rightly pointed out by others, choice of similarity or dissimilarity measures will depend on what kind of data one is handling and what exactly similarity/dissimilarity measures need to signify i.e what is the application that one is dealing with.
One can use various distance measures e.g. the conventional measures like Eucledian distance, Manhattan/city-block distance, Chebychev distance, Minkowsky dustance. Besides, what we use often in image processing are: Hausdorff Distance (the two data vectors will be considered close if every point of each set is close to some point of the other set), Bhattacharyya Distance (measure of similarity of two probabilty distributions), Bhattacharyya coefficient (measure of relative closeness of the two vectors) and Mahalanobis Distance (a specific case of Bhattacharyya Distance).
Share more detials about the data set and application, then it will be easier to give precise answers.
Regards
Hi,
for computer vision datasets you may want to check out this,and related works
http://people.csail.mit.edu/torralba/research/bias/
Cheers
Hi,
As everyone already said, your question is not that easy to answer.
The way you measure the similarity/dissimilarity will depend on the data set you have, more precisely the nature of your data set, and what exactly you want to do (distance/dependance/correlation/difference of distribution ...).
Since you are mentioning Pearson's correlation coefficient, the use of "distances" like Euclidean distances should not fit your problem.
Therefore, explain more precisely what are your data, what is your goal, and you will obtain more precise answers.
Otherwise, you will have hundreds of various answers that will probably not correspond to your needs.
Regards
+1 for dynamic time warping. It is a measurement that makes sense geometrically and mathematically, but it is somewhat difficult to interpret as the "goodness of fit" is not very well defined.
Dear Dr. Susant Kumar Panigrahi,
It is interesting to note that In computer language Binary data is used. There difference is simple and we use XOR logic to find the difference in the data set. A complete theory GF(n) exist.
Thanks to all for your suggestion, Most of you asked for elaboration of my question, which goes like this - I used five different parameters to measure the quality of binary segmentation or thresholding. However, literature suggests that there is some sort of similarity between the parameters (Performance measures). Hence i need to check the amount of similarity of these indices, quantitatively. So, Please suggest me some measurement coefficients.
Thanks,
you can use dice coefficient/cross correlation which could be the easiest methods to perform. mutual information as probabilistic method could be quite tricky as well or you can simply use RMS error method. All would give you quantitative results.
Hi,
This is quite an interesting question. I think the basic starting point is correlations or you could also distance metrics such as the Euclidean distance and others. However, the best method depend on the type and complexity of your data.
One of the problems with Euclidean distance is that it assumes the same weight to all directions.
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