Self-organized neural networks (Kohonen algorithm) can be what you are looking for. using your measurements as input data, you can create an output layer with as many units as clusters you wish to conform.

For additional information there is a shareware software: http://databionic-esom.sourceforge.net/

Sorry to say but i have no idea in this field

Juan Barcelo: Thank you! I will take a look at that. Actually I just realized last week that Neural Networks may be the answer to a part that comes next, but I was still sticking to more traditional methods in terms of clustering...

Sadaf Afrin: No problem, that makes two of us. :)

I just found out about something called constrained k-means.... maybe that is a simpler way to solve the problem...

Preprocessing of data is crucial in case of clustering. Are all the measures in the same range? (if not do normalization or rescale them). Are you going to process a huge amount of data like this or just this single measurement? k-means is looking for rounded compact clusters in your n-dimensional space, it might not be your case. Try to assign some labels to your data and visualize them. For constrained clustering you need must-link or can-not-link constraints. If your constrains wouldn't make sense in your space and distance metric you might skew results which might match your expectations, however it won't have any statistical significance.

Tomas Barton: yes, I do understand that. I have actually lots of measures, but they will be treated almost individually, so every subset of measures will be on the same scale, but with different (meaningful) ranges in some cases.

This is an ecological study. I have 12 sampling locations where I measure a set of variables, and each variable is measured 6 times per location (6 replicates).

What I want to do is cluster the locations while forcing replicates within sites to link (I don't want to include any "cannot link" constraints), in a way that a lot of these variables (individually) are similar within clusters.

So what I did was build a separate euclidean distance matrix for each subset of variables I wanted, some containing only 1 variable, some containing more than one (depending on whether the variables "belong" together or can be treated alone). What I thought was that, even in the cases where variables have different ranges (for my data), they are in the exact same units and scale, so the range in this case is meaningful and therefore I'm not interested in normalization (is this right?).

Then I need to run a separate k-means cluster analysis for each distance matrix (approx 10 matrices), but initially I need to define k for each one (I don't know the number of clusters in advance and they are likely to be different in each matrix), using that curve that shows the within group variability decreasing as k increases and selecting the number where it stabilizes. In this step replicates within sites must link together (so I must use a constrained k-means algorithm).

My dataset is not huge at all, as you can see, and the must-link constrain will not go completely against my data. Without constraints, I get only 1 case where the 6 replicates are split 3/3 to different clusters (in other cases I get 5/1 and 4/2 and 6/0), but this made me think I need constraints because I want to cluster locations and not replicate measurements individually...

Maybe k-means is not suited, but I wanted to non-hierarchically separate clusters in a way that variables (or sets of variables) have a more or less cohesive pattern within them, so I thought it was the best, but I wouldn't be surprised if I was wrong.

The thing is a lot of methods are published detailing the algorithms and how the thing works, but without providing some kind of user interface for dummies like me to apply as a tool... The cop-kmeans method has some kind of thing in C++ that I need to do something with it, but I have no idea what to do with C++. I can only go as far as R packages or even matlab tools if there is a comprehensive step by step procedure explaining what the commands mean and the order in which they should be performed. There is an improved version called icop-kmeans that solves some constrain violations that doesn't have any code available, just an explanation of how it works but in a language that is too advanced (like a cookbook for chefs)...

Do you think my lines of thought are right? Am I violating something mathematically speaking? If these methods can be applied in my case I will try to solve the interface or code problem (by contacting the authors if needed). If not, I won't lose any more time chasing these algorithms and go for something readily available for application.

Levente Kriston, thank you. Yes, I don't like to make assumptions regarding distributions with ecological data in general... So perhaps k-means is parametric (and my despair just made me overlook that) and I will look at non-parametric clustering methods, like those you refer...

Ecology includes so many things that a lot of time I find myself to be too ignorant to even try to address all the issues... I need to always be looking at biology, physics, chemistry, geology and statistics to see if they are all fitting and sometimes I don't think they all fit my brain at once...

I have looked at my data through unconstrained ordination but sometimes I feel like I'm being too subjective when trying to find patterns, with my brain "polluted" by the previous knowledge I have regarding the locations, and that feels like I will always follow my expectations and it's more likely that I will not detect some unusual or unexpected pattern.

I understood that your variables are numerical, so you don't need methods for categorical variables (like poLCA). When you're computing traditional distance metric (e.g. Euclidean distance) between your samples you're summing over your variables (whether it's sum of squares or some other power it doesn't matter right now). If one variable would be in range between 0 and 10 and other between -1 and 1, the categorization would be done mostly based on the first one. If your variables carry same or similar information (they are highly correlated) you're giving higher importance to this aspect (which you probably don't want to do). You can try PCA or Factor Analysis to better understand your variables.

Hierarchical clustering with Ward's linkage (or complete/average linkage) gives very different results than k-means, moreover you don't have to worry about guessing the number of clusters. You can send me the dataset, I can have a look at it.

Tomas, yes, they are numerical.

I wanted to get to a somewhat consensual clustering of the locations when using different variables to cluster the same cases (in this case, 6 replicate measures of each variable per location).

Some matrices are univariate, because I want to see how some variables alone are grouping the locations, this is the case of a variable like "total number of species" counted per replicate.

Other matrices are subsets that belong together, such as the density of species with different degrees of resistance (High res, Medium res, Low res, Very low res). Individuals belonging to each group are counted and divided by the sampled area. This is also done 6 times per location, for all variables.

Because of having matrices with 1 variable and others with 3-5 variables in the same units, I thought using Euclidean distances was appropriate... but I may be wrong...

In some locations, I had to split the replicates in 2 sets of 3 after looking at the data, because due to local heterogeneity in the location itself, the 2 sets of 3 replicates are quite different, so I don't want to constrain the linkage for all 6 of them... In most locations, however, I can force all 6 to cluster together.

So my idea was to treat each location as a little cloud of 6 points (or 3), instead of a single point when clustering. With this I intend to tell the algorithm that these sets "belong together" since they are from the same place. Then, using this constraint, I would test how many clusters would optimize the cohesion of the groups for each matrix (even if the variability of the 6 replicates tells me there is a single cluster for a given subset of variables, that is still interesting!).

Then, I would get one classification for each matrix and then apply an ensemble or consensus clustering method to try to find locations that are consistently clustered together.

I attached an excel file with the examples I mentioned. There are 2 sheets: matrix 1 is the univariate example, matrix 2 is the multivariate example. Location codes group replicates that "must link" or that belong to the same, relatively homogeneous site.

I found this modification of weka that applies PCKmeans (pairwise constrained k means) and MPCKmeans (metric pairwise constrained k-means), but yet again comes in a code that I need to compile somehow...

http://www.cs.utexas.edu/users/ml/risc/code/

I just wanted to experiment with this method, but I just spent hours trying to find out how to compile this things on windows vista, downloaded lots of things and still can't compile anything... so I just give up... apparently the only thing I know how to do when installing software is run a setup.exe and choose a directory...

Well, if you can help me in some way I am much appreciated... If you ever need to identify a fish or something... I can help. :)

The first attribute (Very low res) has only 2 distinct values, it doesn't make much sense to include it analysis. The "Hres" attribute has very strange distribution of values. The sample with value 20 looks like an outlier, if you don't have any reasonable interpretation for this value, it's much better to exclude it.

Yes, I sent you these examples because they show the kind of data I am facing (attributes with many zeros, outliers). In fact that replicate is an outlier in lots of attributes, and I know why. Excluding is the best option indeed, because I still have 5 left to "represent" the location. I have excluded it in many attempts I have done to treat my data before this, but as some methods just kick outliers out to a cluster of their own, I kept the data completely raw in those sheets. The attribute with lots of zeros can be taken out, I guess. In some distance measures it would not make a difference, in others it would perhaps bring cases a bit closer together, but excluding the attribute completely is probably the best solution.

Thank you for pointing that out. :)