So I expect noisy data for clustering. There's no pre-assumed number of clusters and I don't want the isolated noise points to result in smaller clusters. How can I remove them ?
Thanks.
There are algorithms such as DBSCAN and k-means-- that can handle such isolated points, without having to remove them.
There are two ways that you can handle this.
The way that you asked about - removing the noise points - outliers. In order to do that you must detect the outliers. For that, you could compute Local Outlier Factor using the lof function in the package Rlof.
Use a clustering algorithm that specifically identifies noise. The one that I would recommend is DBSCAN. You can get an R implementation of that algorithm in the package called dbscan.
Related
I did clustering on spatial datasets using DBSCAN algorithm and generating a lot of noise 193000 of 250000 data. is that a reasonable amount?
Depends on your data and problem.
If I generate random coordinates, 100% noise would be appropriate because the data is random noise.
First, to address the question in your title. By making eps
very large, it is easy to get no noise points and all the points are
in one big cluster. By making eps very small, you can easily
make all points be noise points. In general, somewhere in between
is what you are looking for. Your job is to find a value that produces
a meaningful clustering. That is where the remark of
#Anony-Mousse comes into play.
Depends on your data and problem
As he suggested, if you have uniform random data, maybe all
noise is the best answer. If you have Gaussian random data,
maybe one big cluster with a few outliers is good. But this is
supposed to help you understand the structure of your data.
What happens as you change eps? From your current clustering
with many noise points, what happens as you gradually increase eps?
Does it gradually add a few noise points into the existing clusters?
Is there some place where two clusters get merged into one? Is there
someplace that there is a sudden change in the number of clusters?
Also, can you interpret the clusters in terms of your variables?
Perhaps the difference between two clusters is that in one all the
values of some variable are low and in another cluster they are high. Considering whatever problem you are trying to solve,
do the clusters divide the data into meaningful groups? Try to use
the clusterings to find meaning in your data.
Let me explain what I'm trying to do.
I have plot of an Image's points/pixels in the RGB space.
What I am trying to do is find elongated clusters in this space. I'm fairly new to clustering techniques and maybe I'm not doing things correctly, I'm trying to cluster using MATLAB's inbuilt k-means clustering but it appears as if that is not the best approach in this case.
What I need to do is find "color clusters".
This is what I get after applying K-means on an image.
This is how it should look like:
for an image like this:
Can someone tell me where I'm going wrong, and what I can to do improve my results?
Note: Sorry for the low-res images, these are the best I have.
Are you trying to replicate the results of this paper? I would say just do what they did.
However, I will add since there are some issues with the current answers.
1) Yes, your clusters are not spherical- which is an assumption k-means makes. DBSCAN and MeanShift are two more common methods for handling such data, as they can handle non spherical data. However, your data appears to have one large central clump that spreads outwards in a few finite directions.
For DBSCAN, this means it will put everything into one cluster, or everything is its own cluster. As DBSCAN has the assumption of uniform density and requires that clusters be separated by some margin.
MeanShift will likely have difficulty because everything seems to be coming from one central lump - so that will be the area of highest density that the points will shift toward, and converge to one large cluster.
My advice would be to change color spaces. RGB has issues, and it the assumptions most algorithms make will probably not hold up well under it. What clustering algorithm you should be using will then likely change in the different feature space, but hopefully it will make the problem easier to handle.
k-means basically assumes clusters are approximately spherical. In your case they are definitely NOT. Try fit a Gaussian to each cluster with non-spherical covariance matrix.
Basically, you will be following the same expectation-maximization (EM) steps as in k-means with the only exception that you will be modeling and fitting the covariance matrix as well.
Here's an outline for the algorithm
init: assign each point at random to one of k clusters.
For each cluster estimate mean and covariance
For each point estimate its likelihood to belong to each cluster
note that this likelihood is based not only on the distance to the center (mean) but also on the shape of the cluster as it is encoded by the covariance matrix
repeat stages 2 and 3 until convergence or until exceeded pre-defined number of iterations
Take a look at density-based clustering algorithms, such as DBSCAN and MeanShift. If you are doing this for segmentation, you might want to add pixel coordinates to your vectors.
I've been looking around scipy and sklearn for clustering algorithms for a particular problem I have. I need some way of characterizing a population of N particles into k groups, where k is not necessarily know, and in addition to this, no a priori linking lengths are known (similar to this question).
I've tried kmeans, which works well if you know how many clusters you want. I've tried dbscan, which does poorly unless you tell it a characteristic length scale on which to stop looking (or start looking) for clusters. The problem is, I have potentially thousands of these clusters of particles, and I cannot spend the time to tell kmeans/dbscan algorithms what they should go off of.
Here is an example of what dbscan find:
You can see that there really are two separate populations here, though adjusting the epsilon factor (the max. distance between neighboring clusters parameter), I simply cannot get it to see those two populations of particles.
Is there any other algorithms which would work here? I'm looking for minimal information upfront - in other words, I'd like the algorithm to be able to make "smart" decisions about what could constitute a separate cluster.
I've found one that requires NO a priori information/guesses and does very well for what I'm asking it to do. It's called Mean Shift and is located in SciKit-Learn. It's also relatively quick (compared to other algorithms like Affinity Propagation).
Here's an example of what it gives:
I also want to point out that in the documentation is states that it may not scale well.
When using DBSCAN it can be helpful to scale/normalize data or
distances beforehand, so that estimation of epsilon will be relative.
There is a implementation of DBSCAN - I think its the one
Anony-Mousse somewhere denoted as 'floating around' - , which comes
with a epsilon estimator function. It works, as long as its not fed
with large datasets.
There are several incomplete versions of OPTICS at github. Maybe
you can find one to adapt it for your purpose. Still
trying to figure out myself, which effect minPts has, using one and
the same extraction method.
You can try a minimum spanning tree (zahn algorithm) and then remove the longest edge similar to alpha shapes. I used it with a delaunay triangulation and a concave hull:http://www.phpdevpad.de/geofence. You can also try a hierarchical cluster for example clusterfck.
Your plot indicates that you chose the minPts parameter way too small.
Have a look at OPTICS, which does no longer need the epsilon parameter of DBSCAN.
I am trying to differentiate two populations. Each population is an NxM matrix in which N is fixed between the two and M is variable in length (N=column specific attributes of each run, M=run number). I have looked at PCA and K-means for differentiating the two, but I was curious of the best practice.
To my knowledge, in K-means, there is no initial 'calibration' in which the clusters are chosen such that known bimodal populations can be differentiated. It simply minimizes the distance and assigns the data to an arbitrary number of populations. I would like to tell the clustering algorithm that I want the best fit in which the two populations are separated. I can then use the fit I get from the initial clustering on future datasets. Any help, example code, or reading material would be appreciated.
-R
K-means and PCA are typically used in unsupervised learning problems, i.e. problems where you have a single batch of data and want to find some easier way to describe it. In principle, you could run K-means (with K=2) on your data, and then evaluate the degree to which your two classes of data match up with the data clusters found by this algorithm (note: you may want multiple starts).
It sounds to like you have a supervised learning problem: you have a training data set which has already been partitioned into two classes. In this case k-nearest neighbors (as mentioned by #amas) is probably the approach most like k-means; however Support Vector Machines can also be an attractive approach.
I frequently refer to The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition (Springer Series in Statistics) by Trevor Hastie (Author), Robert Tibshirani (Author), Jerome Friedman (Author).
It really depends on the data. But just to let you know K-means does get stuck at local minima so if you wanna use it try running it from different random starting points. PCA's might also be useful how ever like any other spectral clustering method you have much less control over the clustering procedure. I recommend that you cluster the data using k-means with multiple random starting points and c how it works then you can predict and learn for each the new samples with K-NN (I don't know if it is useful for your case).
Check Lazy learners and K-NN for prediction.
I have many 3D data points, and I wish to find 'connected components' in this graph. This is where clusters are formed that exhibit the following properties:
Each cluster contains points all of which are at most distance from another point in the cluster.
All points in two distinct clusters are at least distance from each other.
This problem is described in the question and answer here.
Is there a MATLAB implementation of such an algorithm built-in or available on the FEX? Simple searches have not thrown up anything useful.
Perhaps a density-based clustering algorithm can be applied in this case. See this related question for a description of the DBscan algorithm.
I do not think that it is possible to satisfy both conditions in all cases.
If you decide to concentrate on the first condition, you can use Complete-Linkage hierarichical clustering, in which points or groups of points are merged based on the maximum distance between any two points. In Matlab, this is implemented in CLUSTERDATA (see help for the individual function steps).
To calculateyour cluster indices, you'd run
clusterIndex = clusterdata(coordiantes,maxDistance,'criterion','distance','linkage','complete','distance','euclidean')
In case you then want to simply eliminate points of different clusters that are less than minDistance apart, you can run pdist between clusters to clean up your connected components.
k-means or k-medoid algorithm may be useful in this case.