Dear Sandip,

I hope my answer is not too late.

Mean silhouette width (MSW) below 0 definitely suggests that your classification is weak. However, if you get such low values with different numbers of clusters, I suspect that your classification method produces clusters of peculiar shape or size distribution. For example, single linkage clustering results in very unequal-sized clusters (usually one large and many small) and very variable shape. Such classifications often get low MSW because the original form of silhouette prefers clusters of similar size and spherical shape. Ward's method or flexible-beta with beta near -0.25 used to get much higher MSW.

Sorry for the self-promotion but I have a recent paper on an extension of silhouette width where its size- and shape-preference can be relaxed. You can find it here: Article Silhouette width using generalized mean—A flexible method fo...

Best regards,

Attila

Dear Attila Lengyel,

Can I further ask regarding the silhouette width? In my case, the average silhouette width is at 0.7 indicates quite good structure of clusters. However, some objects have negative silhouette width which I understand that these objects might belong to the wrong cluster. Would we try to change the cluster of these objects in this case? Thank you

Dear Rattiya Suddeephong Lippe ,

yes, it is possible to re-assign objects in order to improve a classification. If you want to avoid objects with negative silhouette width, I can recommend the method REMOS that we recently published (again, sorry for the self-promotion). Article Comparison of silhouette‐based reallocation methods for vege...

After re-assignment, cluster memberships change, and therefore all silhouette widths should be re-calculated. This may result in negative silhouettes for other objects, so further re-allocations may be necessary. The number of negative silhouette widths thus can be iteratively optimized until reaching the minimum. Notably, it is not rare that this algorithm stucks into a loop without finding a single best solution. Such loops must be broken with some criteria.

Best regards,

Attila

Thank you Attila Lengyel

Dear Rattiya Suddeephong Lippe ,

per se there is no 'wrong' classification of single objects to a group or class by the chosen cluster analysis algorithm. However, the negative WSS scores indicate, that there is no clear distinction among the objects of one and (minimum one) other classes.

Since clusterring is an algorithm based process, the question should be whether or not the method/algorithm used is the optimal cluster analysis algorithm and if certain parameters for the cluster analysis were defined in an optimal way. Furthermore the data used may lack sufficient preprocessing.

Best regards

André