Yes, in Non-Parametric Clustering methods the samples or groups are not necessary to be equal, however., in Parametric methods for classification the samples from each group must be equal in number, otherwise the algorithm may not be executed for final classification outcomes.

It might be possible but probably not a good idea. Complete case analysis might be a good choice for this case, as you can use the complete data to estimate the number of clusters and then do cluster analysis on the incomplete data. If you are doing k-means clustering, then you will have to specify the number of clusters in advance, and it is expected for this number to be the same across all the features, so it is up to you to decide if you can provide a meaningful result with the limited data you have. Depending on your dataset, you can do PCA, where you "destroy" dimensions. Have a look at this similar question https://www.researchgate.net/post/Is_there_a_way_of_running_cluster_analysis_with_missing_data

If your features are able to be grouped by tuples (A,B,...F) which represent data collected at the same time for the same object, then I take your stated problem to mean there are empty entries in some sampled tuples for features D, E, and/or F.

If you're comfortable with making a couple of assumptions you can use all of your data. If you assume your features are independent you can create a clustering algorithm for each features (6 in total), then use an ensemble to fuse the results of the clustering algorithm. Or if want to avoid the ensemble and if you make an additional assumption that you can estimate the distribution of the features with missing data (e.g., it's gaussian), you can generate missing data points by taking draws from this estimated distribution, and go back to a single 6-dimensional clustering algorithm.

If you're not comfortable making those assumptions, a less loose assumption would be to assume A-C is independent from D-F, then you could create two clustering algorithms, one's with features A-C, and one with features D-F, and use an ensemble to fuse the results.

If you're not comfortable making any of these assumptions, then you're stuck with data points with tuples with complete information.

Hi Dan Harris,

may I know what kind of ensemble you are referring to? And how can I ensemble the results from multiple clustering solutions if some datapoints were clustered differently for each clustering? Thank you.

Husnir Nasyuha assuming all of your clustering algorithms produce a separate probability vector, Pk = [P1,...,PN], where Pk is the probability vector from clustering algorithm k and Pi is the probability the data came from event/object i; then probably the simplest (and fairly good) ensemble is one I call the robust Bayes Rule.

The traditional Bayes Rule would produce posterior Pi as follows: Pi = Pi_prior * prod_k(Pi_source_k) / sum_j(Pj_prior*prod_k(Pj_source_k)). Prod is short for product; so every k cluster result for Pi (notated as Pi_source_k) is multiplied together. The question is what do you select as your prior. If you know the probability of Pi given no information from clustering, then you could put that value; otherwise, use 1/N AKA uniform priors.

The robust Bayes Rule is a bit of pre-processing before using the traditional Bayes Rule. The pre-processing step is to tone down the confidence of the provided probabilities from the clustering results; e.g., Pk = [Pi*F,...,PN*F] + F/N for each k. I like the factor F to be between 0.95 and 0.99 personally. Bayes Rule doesn't care much for 1's and 0's in different i positions because the result is undefined.

Using the same data points for different clustering algorithms is a bad idea unless you can account for the resulting correlation from clustering solutions, which I'm not sure how to do without looking at the data and how you're using it. I believe all of my recommended approaches above uses the data once in a single clustering algorithm. Is there a reason you cannot do that? Now I take same data point to mean the same information, so using feature A in cluster_A, and B in cluster_B and C in cluster_C from the tuble (A,...,F) is using different information for different clusters--assuming independence in your features then no correlation would result.