How to find the Similarity between two Histograms??

Hi,

I was wondering if there are other methods for finding the similiraty between two histograms quantitatively rather than different distance comparision methods like Battachary distance,KL divergence,EMd............

[Diego Mesa]

What was the problem with those metrics? I'm considering using Jensen-Shannon for comparing two histograms (I'm fiting a kernel distribution to the histogram first)

Answer 1

[Star Strider]

One option is the chi-square test if you want to test the statistical hypothesis that the two are different. (See Chi-Square Test for Independence (link) for one example.) My File Exchange search for chi square (link) returned 96 contributions.

[arun kumar]

I wanted to find the symmetry between two histograms so that I can tell how similar they are, quantitatively. Does the Chi square test for independence do that??

[Image Analyst]

What does "symmetry between" mean? Did you mean similarity instead of symmetry?

[Star Strider]

You seem to have used all the distance metrics, so I assumed you want something else. The chi-square test will give you the probability that they are the same. The ‘null hypothesis’ is that they are not different, so if the chi-square probability is greater than 0.05, you would accept that hypothesis. If the chi-square probability is less than or equal to 0.05, then the alternate hypothesis that they are different would be true. Certain assumptions (that the bin widths and bin numbers are the same in both) would be necessary to use the chi-square test. Normalization would be necessary (for example that the total number of observations or the total bin frequencies in both were the same).

This is essentially a ‘goodness-of-fit’ test, where you are testing one normalized histogram against the other.

Other options are probably available in the literature. A PubMed (link) search could be worthwhile. You will have to experiment with the search strings you use to find what gives you the most relevant results.

[arun kumar]

Let me explain you in brief.... I have two data sets basically one from left leg(say X1)and other from right leg(say X2),after taking the histogram of X1 and X2 I need to find a way that tells me how much symmetry is there between the two histograms quantatively(I should get a numerical number so that I can say this much of % symmetry is there between the two histogram ). If X1 data is obtained by limp walking and X2 is by normal walk then there will be less symmetry between the histograms. So, I'm in need of various methods I can implement on the histograms that tells the symmetry measure. I hope my question is clear now :)

[Image Analyst]

Not as clear as it would be if you had posted bar charts of a normal histogram and an abnormal histogram.

Answer 2

[Image Analyst]

What is your data? There are different ways of comparing data other than comparing their histograms. For example two completely different looking images may have the exact same histogram. So, what does your data represent and are you sure comparing the histograms is the best way to compare them or the best approach, though comparing histograms may be a perfectly good thing to do?

[arun kumar]

Im working on gait acceleration data. Basically i am interested in finding the symmetry(Quantitatively) between two histograms. I already implemented various distance measures such as KL-divergence, Jensen Shannon,Battacharya,Emd distance measure. I wanted to know any other way to find the symmetry between two histograms so that i can tell how much similar they are quantitatively.

[Image Analyst]

I suggest you check the literature. I'm sure someone has already done that before. See

http://www.visionbib.com/bibliography/contentsmotion-f.html#Motion%20--%20Feature-Based,%20Long%20Range,%20Motion%20and%20Structure%20Estimates,%20Tracking,%20Surveillance,%20Activities

16.7.4.5 Walking, Gait Recognition, Gait Analysis  
    16.7.4.5.1 Walking, Gait Recognition, University of Southampton
    16.7.4.5.2 Cyclic Motion, Periodic Motion, for Walking and Gait Recognition
    16.7.4.5.3 Human ID Using Gait, Recognition of People Through Gait
    16.7.4.5.4 Gait Analysis, Depth, 3-D Data, 3-D from Gait
    16.7.4.5.5 Gait Analysis, Diagnosis of Difference, Joint Information, Motion Capture
    16.7.4.5.6 Rehabilitation Systems, Rehabilitation Techniques
    16.7.4.5.7 Human Motion Capture, Joint Information, Special Activities
    16.7.4.5.8 Human Motion Capture, Dance Activities

[arun kumar]

Thanks for the information. unfortunately i didn't find the particular methods to find the symmetry between the histograms :(