I am trying to extract a fixed (and known) number of clusters from a set of points using Matlab.
An immediate clustering method that I tried is the k-means algorithm which seems to tick all the boxes.
Unfortunately, in some cases, the subsets (or clusters) extracted are intertwined, as shown in the image below for the left-most cluster:
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Is there a way to set the k-means algorithm, so that the generated clusters are disconnected?
Is there a way to post-process the cluster indices returned by the k-means algorithm, so as to obtain "disconnected" clusters?
Alternatively, is there another clustering method that might be more suitable?
Thanks!
Related
I have been experimenting with Lumer-Faieta clustering and I am getting
promising results:
However, as clusters formed I was wondering how to identify the final clusters? Do I run another clustering algorithm to identify the clusters (that seems counter-productive)?
I had the idea of starting each data point in its own cluster. Then, when a laden ant drops a data point, its gets the same cluster as the data points that dominates its neighborhood. The problem with this is that if clusters are broken up, they share share the same cluster number.
I am stuck. Any suggestions?
To solve this problem, I employed DBSCAN as a post processing step. The effect as follows:
Given that we have a projection of a high dimensional problem on a 2D grid, with known distances and uniform densities, DBSCAN is ideal for this problem. Choosing the right value for epsilon and the minimum number of neighbours are trivial (I used 3 for both values). Once the clusters have been identified, it can be projected back to the n-dimension space.
See The 5 Clustering Algorithms Data Scientists Need to Know for a quick overview (and graphic demo) of DBSCAN and some other clustering algorithms.
In the MATLAB version of the K-means algorithm, there is a very useful flag that indicates the action to take if a cluster loses all member observations during the optimization. There are 3 possibilities in MATLAB:
treat empty cluster as an error
remove any clusters that become empty
Create a new cluster consisting of the one point furthest from its centroid
Does any one know what happens in DAAL K-means in that case? I could not find anything in the documentation about this.
In the K-Means implementation of Intel DAAL, clustering information on feature vectors is automatically collected during execution of the program. The feature furthest from their assigned centroids are selected as new cluster centers to compensate for an empty cluster during an iteration.
It is notable that a good choice of cluster initialization can avoid an empty cluster.
Refer https://software.intel.com/en-us/daal-programming-guide-details-5 for further details.
I'm using function fcm from Matlab for overlapping clustering. The output of this function is a matrix of size kxn with k being the number of clusters and n being the number of examples.
Now my problem is that how do I choose clusters for an example? For each example, I have scores for all clusters so I can easily find the best matched cluster, but what about other clusters?
Many thanks.
It depends on the clustering algorithm, but you can probably interpret those soft clustering values as probabilities. This gives two well-founded options for extracting a hard clustering:
Sample each point's cluster from its cluster distribution (a column in your kxn matrix).
Assign each point to its most probable cluster. This corresponds to the MAP (max a posteriori) solution to the clustering problem.
Option 2 is probably the way to go - a single sample may not be a great representation of what's going on; with MAP, you're at least guaranteed to get something probable.
I have test classification datasets from UCI Machine Learning repository which are labelled.
I am stripping of the labels and using the data to benchmark a few clustering algorithm and then I am planning to use external validation methods. I will run the algorithm with different initial configurations, for say, 50 times and then take the mean value. For 50 iterations the algorithm labels the data points of one single cluster with different numbers. Because in each run the cluster labels can change, also because each iteration might have slightly different cluster assignments, how to somehow remap each of the clusters to one uniform numbering.
Primary idea is to remap by checking how many of the points in the class labels intersect the maximum in the actual labels and then making a remap based on that, but this can get incorrect remappings because when the classes will have more or less equal number of points, this will not work.
Another idea is to keep the labels while clustering, but make the clustering algorithm ignore it. This way all the cluster data will have the label tags. This is doable but I have already have a benchmarked cluster assignment data to be processed therefore I am trying to avoid modifying and re-benchmarking my implementation (which will take quite some time and cpu) of the cluster analysis algorithms and include the label tag to the vectors and then ignore it.
Is there any way that I can compute average accuracy from the cluster assignments I have right now?
EDIT:
The domain in which I am studying (metaheuristic clustering algorithms) I could not find a paper comparing these indexes. The paper which compares seems to be incorrect in their values. Can anyone point me to a paper where clustering results are compared using any of these indexes?
What do you do when the number of clusters doesn't agree?
Do not try to map clusters.
Instead, use the proper external validation measures for clustering, which do not require a 1:1 correspondence of clusters. There are plenty, for details see Wikipedia.
When ever we want to cluster some data then It is required to give the number of cluster by user. Like K-Means algorithm we need to specify that how cluster are required.
My question is it possible that the algorithm decides itself that how cluster are feasible for particular data set.
There are several clustering algorithms that do not require a desired number of clusters as an input to the algorithm. An example of such an algorithm is the mean-shift clustering algorithm. However, you will need to specify a kernel as an input to the algorithm. This kernel selection (e.g., the size and shape of the kernel) will impact the number of clusters that you get as an output.
Some more information:
http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/TUZEL1/MeanShift.pdf
http://scikit-learn.org/stable/auto_examples/cluster/plot_mean_shift.html
I'm not expert with that, but to answer to your question, yes there are methods to determine automatically the number of cluster for a kmeans for example.
It's quite complicated but given a dataset and a cluster method you can compute what is called gap statistic in order to estime the number of clusters.
If you are a R user, try to check clusGap and maxSE functions.