Dear all researchers,
It is well-known that k-means computes centroid of clusters differently for the different supported distance measures. These distance measures are: sqEuclidean, cityblock, cosine, correlation and Hamming. Except hamming distance which is suitable for binary data, which distance measure do you think has a better performance and great effect on clustering? I will be very appreciated your answers.
Regards,
There is no free lunch, and there is no best distance measure.
There is only a best distance measure for a given dataset. The choice of the distance measure WILL influence your clustering, but it depends on the dataset and on the objective, which distance measure is most adequate for your particular application.
Hi Soheila,
In distance measures very important is to normalize features, i.e. to unify their influence on distance. The common practice is standardization: new_x = (x - mean_of_x)/std_of_x.
See: https://en.wikipedia.org/wiki/Feature_scaling
Regards
Dear Soheila,
I think It strongly depends on your data sets type. And also it depends on your method you apply, dynamin or static. Normally, we use normalized Euclidean for vectorial data sets. But there is no specific or best distance measure.
I think that depending on your problem, you may also find valuable defining your own distance function.
There are actually plenty of different distance measures that can be used in a clustering problem, e.g., Manhattan distance, Chebychev distance, Spearman correlation, Minkowski metric as a generalization of Euclidean and Manhattan distances and edit distance. What distance measure you use is at the heart of the research problem that you are trying to solve. Each of these distances would favor some types of cluster and prohibit other ones. So, you need to look at your data and examine the structure of your clusters (perhaps visually using projections to lower dimensional spaces, for example, using PCA) to get a sense of what your clusters look like and choose the distance measure accordingly. Remember, the shape of your clusters depend exactly on what type of distance you are using. So, there is no best distance that works for all problems. The type of distance that you should use is dictated by the problem.
That depends on the amount of features you are analyzing and the desired computational performances.
If you are working in high dimensional spaces you should see the analyses made by Aggarwal (for example http://kops.uni-konstanz.de/handle/123456789/5849) in which fractional distances are proved to performed better than other Lp norms. Other analyses have also shown that the Manhattan distance (city-block) exhibits a better (computationally) performance that the euclidean distance.
At the end that also depends of the structure of the data you're analyzing. For example in the case of convex clusters, if euclidean distance is used the geometrical results is hyper-spherical clusters, while if the Mahalanobis distance is used, the clusters are hyper-ellipsoids.
Even you can use two measures like Euclidean and Manhattan, compare the results, select the best one
For network intrusion clustering which one will be good- Euclidean or Manhattan?
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