My problem is that it is difficult to get the optimal cluster number by using k-means, so I thought of using a hierarchical algorithm to find the optimal cluster number. After defining my ideal classification I want to use this classification to find the centroids with k-means, without iteration.
data= rand(300,5);
D = pdist(data);
Z = linkage(D,'ward');
T = cluster(Z,'maxclust',6);
Now I want to use the clusters defined in vector T and the positions in to k-means algorithm without iterations. Can anyone give a tip how to do?
Thank you.
If you are looking for the centroids given that you already clustered them in T, then you only need to compute the mean of data grouped according to T.
Related
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.
How can I apply KMEANS algorithm with determined cluster position which has specified from PSO algorithm ??
Just do it.
K-means allows you to specify the initial centroids.
Without any information on the nature of the data you're dealing with (number if dimensions, datatypes, outliers, overlap etc), it is impossible to give specific answers.
I don't know of any genuine k-means implementation where you can pass in a list of centroids that the algorithm uses to initialize the k-means centroids. Usually these are selected randomly. (Can't you write your own implementation of k-means that does this initialization? Simple take an open-source implementaion and add an argument)
However, In the python sklearn implementation of kmeans, there is a kmeans++ implementation, where you can pass in the initial centers as an array.
init : {‘k-means++’, ‘random’ or an ndarray}
Method for initialization, defaults to ‘k-means++’:
‘k-means++’ : selects initial cluster centers for k-mean clustering
in a smart way to speed up convergence.
...
If an ndarray is passed, it should be of shape
(n_clusters, n_features) and gives the initial centers.
Haven't used it, though.
And I wrote this before I remembered/looked up kmeans++:
This is a poor-man's approach:
You can run kmeans with a k parameter equal to the length of the list/array that the PSO algorithm (whatever it did) has given you.
Then kmeans will quickly find its own centroids. Do this several times, maybe with different distance-measures (Euclidean, manhattan, shortest, longest, avg...), and different seeds for your random-number generator. Each time, afterwards, compare the coordinates of the k-means centroids with the coordinates of the PSO centroids.
When there is a near 1:1 correspondence (depending on your requirements), you've found a match. then do something with your list of k-means classfication-results.
So I am using fastcluster with SciPy to do agglomerative clustering. I can do dendrogram to get the dendrogram for the clustering. I can do fcluster(Z, sqrt(D.max()), 'distance') to get a pretty good clustering for my data. What if I want to manually inspect a region in the dendrogram where say k=3 (clusters) and then I want to inspect k=6 (clusters)? How do I get the clustering at a specific level of the dendrogram?
I see all these functions with tolerances, but I don't understand how to convert from tolerance to number of clusters. I can manually build the clustering using a simple data set by going through the linkage (Z) and piecing the clusters together step by step, but this is not practical for large data sets.
If you want to cut the tree at a specific level, then use:
fl = fcluster(cl,numclust,criterion='maxclust')
where cl is the output of your linkage method and numclust is the number of clusters you want to get.
Hierarchical clustering allows you to zoom in and out to get fine or coarse grained views of the clustering. So, it might not be clear in advance which level of the dendrogram to cut. A simple solution is to get the cluster membership at every level. It is also possible to select the desired number of clusters.
import numpy as np
from scipy import cluster
np.random.seed(23)
X = np.random.randn(20, 4)
Z = cluster.hierarchy.ward(X)
cutree_all = cluster.hierarchy.cut_tree(Z)
cutree1 = cluster.hierarchy.cut_tree(Z, n_clusters=[5, 10])
print("membership at all levels \n", cutree_all)
print("membership for 5 and 10 clusters \n", cutree1)
Ok so let me propose one way. I don't think it is the right or best way, but at least it is a start.
Choose k we are interested in
Note that linkage Z has N-1 lists where N is the number of data points. The mth list entry will produce N-m clusters. Therefore grab the list in Z with index where k = N-m-1.
Grab the distance value which is the 3rd column of that list
Call fcluster with that particular distance as the tolerance (or perhaps the distance plus some really small delta).
The only problem with this is that there are ties, but really this is not a problem if you can detect that a tie has taken place.
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.
How can I do K-means clustering of time series data?
I understand how this works when the input data is a set of points, but I don't know how to cluster a time series with 1XM, where M is the data length. In particular, I'm not sure how to update the mean of the cluster for time series data.
I have a set of labelled time series, and I want to use the K-means algorithm to check whether I will get back a similar label or not. My X matrix will be N X M, where N is number of time series and M is data length as mentioned above.
Does anyone know how to do this? For example, how could I modify this k-means MATLAB code so that it would work for time series data? Also, I would like to be able to use different distance metrics besides Euclidean distance.
To better illustrate my doubts, here is the code I modified for time series data:
% Check if second input is centroids
if ~isscalar(k)
c=k;
k=size(c,1);
else
c=X(ceil(rand(k,1)*n),:); % assign centroid randomly at start
end
% allocating variables
g0=ones(n,1);
gIdx=zeros(n,1);
D=zeros(n,k);
% Main loop converge if previous partition is the same as current
while any(g0~=gIdx)
% disp(sum(g0~=gIdx))
g0=gIdx;
% Loop for each centroid
for t=1:k
% d=zeros(n,1);
% Loop for each dimension
for s=1:n
D(s,t) = sqrt(sum((X(s,:)-c(t,:)).^2));
end
end
% Partition data to closest centroids
[z,gIdx]=min(D,[],2);
% Update centroids using means of partitions
for t=1:k
% Is this how we calculate new mean of the time series?
c(t,:)=mean(X(gIdx==t,:));
end
end
Time series are usually high-dimensional. And you need specialized distance function to compare them for similarity. Plus, there might be outliers.
k-means is designed for low-dimensional spaces with a (meaningful) euclidean distance. It is not very robust towards outliers, as it puts squared weight on them.
Doesn't sound like a good idea to me to use k-means on time series data. Try looking into more modern, robust clustering algorithms. Many will allow you to use arbitrary distance functions, including time series distances such as DTW.
It's probably too late for an answer, but:
k-means can be used to cluster longitudinal data
Anony-Mousse is right, DWT distance is the way to go for time series
The methods above use R. You'll find more methods by looking, e.g., for "Iterative Incremental Clustering of Time Series".
I have recently come across the kml R package which claims to implement k-means clustering for longitudinal data. I have not tried it out myself.
Also the Time-series clustering - A decade review paper by S. Aghabozorgi, A. S. Shirkhorshidi and T. Ying Wah might be useful to you to seek out alternatives. Another nice paper although somewhat dated is Clustering of time series data-a survey by T. Warren Liao.
If you did really want to use clustering, then dependent on your application you could generate a low dimensional feature vector for each time series. For example, use time series mean, standard deviation, dominant frequency from a Fourier transform etc. This would be suitable for use with k-means, but whether it would give you useful results is dependent on your specific application and the content of your time series.
I don't think k-means is the right way for it either. As #Anony-Mousse suggested you can utilize DTW. In fact, I had the same problem for one of my projects and I wrote my own class for that in Python. The logic is;
Create your all cluster combinations. k is for cluster count and n is for number of series. The number of items returned should be n! / k! / (n-k)!. These would be something like potential centers.
For each series, calculate distances for each center in each cluster groups and assign it to the minimum one.
For each cluster groups, calculate total distance within individual clusters.
Choose the minimum.
And, the Python implementation is here if you're interested.