categorical dataclusteringunsupervised learning
I have a list of categorical data and I want to apply an unsupervised classification method to cluster this data.
Which method could be used?
Example:
gene1
gene2
gene3
gene4
gene5
gene6
gene7
gene8
My goal is to cluster these genes.
Could anyone suggest me how to do clustering with these labels?
With mixed data types the basic answer is to use Gower's distance (see @ttnphns' thorough explainer here: Hierarchical clustering with mixed type data - what distance/similarity to use?). The gist of it is that you get the distance measure of your preference for each variable individually, then average them. You can also do a weighted average of the constituent distances, if you think some should be given more credibility than others.
For your continuous variable, the absolute difference should be fine. Simple matching is presumably fine for your categorical variable, creator. That is, $1$, if two rows have the same creator, and $0$ otherwise. Then you just need to find a metric for your multivalue categorical variable. I think it is fine for you to think of this as a single variable, but I suspect it is ultimately better to think of it as a set of binary variables, where all possible options constitutes the set. From there, if the option is listed, that amounts to having a $1$ in that column, and $0$ otherwise. Thus, you have a high-dimensional binary space. There have been lots of measures defined for binary data (see: Choi, Cha, & Tappert, A Survey of Binary Similarity and Distance Measures, pdf, for a list of 76!). You need to decide which makes sense. The constituent distance measures each gets normalized, and then you use whichever clustering algorithm you like that can work with a distance matrix instead of the raw data (see, e.g., my answer here: How to use both binary and continuous variables together in clustering?).
K-means produces a set of cluster centroids that approximately minimize the cost function. A cluster is defined as the set of points that share a common closest centroid. So, suppose you've trained k-means on some training set, and now want to cluster new points in a test set. Simply find the nearest centroid to each new point. Note that this applies to k-means, but not other clustering methods.
Geometrically, k-means induces a Voronoi partition on input space, with the centroids as seeds. All points within the Voronoi cell of a particular centroid are assigned to the same cluster. For example, in this image from Wikipedia, the black points would correspond to centroids, and all points in the corresponding colored regions (Voronoi cells) would be clustered together:
Best Answer
I'm going to answer this as an approach to clustering categorical data.
The standard k-means performs poorly in case of categorical data since in the sample space is discrete. The cost function defined by k-means computes the Euclidean Distance (or something similar) which is relevant only for continuous variables. Instead of computing the Euclidean distance, one could use the Hammer Distance (for categorical) or Gower Distance (for mixed). Instead of computing the mean, one can compute the mode. The most occurring value of a nominal variable is used as its representative (centers of cluster). Such a cost function is used in a variation of k-means called k-modes. Modes are analogous to centroids in k-means.
If you are using python then you could probably use this package. The method was first presented in this paper. You can read about it's usage methods in their documentation. There's another extension of the k-modes called k-prototypes which works well for mixed datatypes (included in the python package).