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Clustering algorithms are often categorized into broad kingdoms: Partitioning algorithms (like k-means and it's progeny) Hierarchical clustering (as @Tim describes) Density based clustering (such as … It might help you to read an overview of different types of clustering algorithms. The following might be a place to start: Berkhin, P. "Survey of Clustering Data Mining Techniques" (pdf) …

As other answers have pointed out, determining if the clustering represents 'real' latent groups is a very difficult task. … , and the section on evaluating clusterings in Wikipedia's clustering entry). None of the methods are perfect, however. …

Thus the 'clustering' in $X$ is not necessarily a problem. In addition, data tend to have less leverage* over the fitted regression line the closer they are to the mean of $X$. …

And you can use whatever clustering algorithm you like and find appropriate (e.g., k-means) likewise. …

The clustering algorithms I am familiar with that can do so are fuzzy k-means, Gaussian mixture modeling, and clustering by kernel density estimation. … Clustering via nonparametric density estimation, Statisticis and Computing, 17, 1, pp. 71-80. …

I agree with @Nick Cox. This figure is pretty, but doesn't seem very good to me except as eye candy. In essence, this is a Sankey plot (a.k.a., river plot or flow diagram) with just two levels where …

You can see an example where I do this here: How to use both binary and continuous variables together in clustering? This works out fine with a small number of clusterings. … strength of association / correlation between nominal variables, or Determine the probability that two patterns are consistent across the clusterings in that if they are clustered together in one clustering …

An alternative is to use a clustering algorithm that can operate over a distance matrix. Then you can calculate the distances only once. … here: How to use both binary and continous variables together in clustering? …

I agree with @Anony-Mousse. Using anything in statistics, simply because it is the default will never be the best way to go. Take your situation as an example: At the core of Euclidean distance is …

I want to acknowledge from the beginning that I know relatively little about clustering. However, I don't see the point of the procedure you describe. …

The null hypothesis for a $\chi^2$ analysis of a contingency table is that the rows and columns are independent of each other. Under this null model, the expected count is: $$ \hat E_{ij}=\left(\frac …

It is common to normalize all your variables before clustering. … The fact that you are using complete linkage vs. any other linkage, or hierarchical clustering vs. a different algorithm (e.g., k-means) isn't relevant. …

The most common clustering technique that meets your requirements would be DBSCAN. This finds points that are continuous by virtue of having shared nearest neighbors. …

Having figured out what variables are relevant for what you want to do, and having conducted a clustering, it isn't difficult to see which variables play the strongest roles in determining the the clustering … Concept learning and feature selection based on square-error clustering. Machine Learning, 35:25–39, 1999. …

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?). … How to use both binary and continuous variables together in clustering?). …