I have a question about using a clustering method vs fitting the same data with a distribution.
Assuming that I have a dataset with 2 features (feat_A and feat_B) and let's assume that I use a clustering algorithm to divide the data in an optimal number of clusters...say 3.
My goal is to assign for each of the input data [feat_Ai,feat_Bi] a probability (or something similar) that the point belongs to cluster 1 2 3.
a. First approach with clustering:
I cluster the data in the 3 clusters and I assign to each point the probability of belonging to a cluster depending on the distance from the center of that cluster.
b. Second approach using mixture model:
I fit a mixture model or mixture distribution to the data. Data are fit to the distribution using an expectation maximization (EM) algorithm, which assigns posterior probabilities to each component density with respect to each observation. Clusters are assigned by selecting the component that maximizes the posterior probability.
In my problem I find the cluster centers (or I fit the model if approach b. is used) with a subsample of data. Then I have to assign a probability to a lot of other data... I would like to know in presence of new data which approach is better to use to still have meaningful assignments.
I would go for a clustering method for example a kmean because:
If the new data come from a distribution different from the one used to create the mixture model, the assignment could be not correct.
With new data the posterior probability changes.
The clustering method minimizes the variance of the clusters in order to find a kind of optimal separation border, the mixture model take into consideration the variance of the data to create the model (not sure that the clusters that will be formed are separated in an optimal way).
More info about the data:
Features shouldn't be assumed dependent.
Feat_A represents the duration of a physical activity Feat_B the step counts In principle we could say that with an higher duration of the activity the step counts increase, but it is not always true.
Please help me to think and if you have any other point please let me know..
Related
I was reading through all (or most) previously asked questions, but couldn't find an answer to my problem...
I have 13 variables measured on an ordinal scale (thy represent knowledge transfer channels), which I want to cluster (HCA) for a following binary logistic regression analysis (including all 13 variables is not possible due to sample size of N=208). A Factor Analysis seems inappropriate due to the scale level. I am using SPSS (but tried R as well).
Questions:
1: Am I right in using the Chi-Squared measure for count data instead of the (squared) euclidian distance?
2. How can I justify a choice of method? I tried single, complete, Ward and average, but all give different results and I can't find a source to base my decision on.
Thanks a lot in advance!
Answer 1: Since the variables are on ordinal scale, the chi-square test is an appropriate measurement test. Because, "A Chi-square test is designed to analyze categorical data. That means that the data has been counted and divided into categories. It will not work with parametric or continuous data (such as height in inches)." Reference.
Again, ordinal scaled data is essentially count or frequency data you can use regular parametric statistics: mean, standard deviation, etc Or non-parametric tests like ANOVA or Mann-Whitney U test to compare 2 groups or Kruskal–Wallis H test to compare three or more groups.
Answer 2: In a clustering problem, the choice of distance method solely depends upon the type of variables. I recommend you to read these detailed posts 1, 2,3
I'm looking for a method to perform density based clustering. The resulting clusters should have a representative unlike DBSCAN.
Mean-Shift seems to fit those needs but doesn't scale enough for my needs. I have looked into some subspace clustering algorithms and only found CLIQUE using representatives, but this part is not implemented in Elki.
As I noted in the comments on the previous iteration of your question,
https://stackoverflow.com/questions/34720959/dbscan-java-library-with-corepoints
Density-based clustering does not assume there is a center or representative.
Consider the following example image from Wikipedia user Chire (BY-CC-SA 3.0):
Which object should be the representative of the red cluster?
Density-based clustering is about finding "arbitrarily shaped" clusters. These do not have a meaningful single representative object. They are not meant to "compress" your data - this is not a vector quantization method, but structure discovery. But it is the nature of such complex structure that it cannot be reduced to a single representative. The proper representation of such a cluster is the set of all points in the cluster. For geometric understanding in 2D, you can also compute convex hulls, for example, to get an area as in that picture.
Choosing representative objects is a different task. This is not needed for discovering this kind of structure, and thus these algorithms do not compute representative objects - it would waste CPU.
You could choose the object with the highest density as representative of the cluster.
It is a fairly easy modification to DBSCAN to store the neighbor count of every object.
But as Anony-Mousse mentioned, the object may nevertheless be a rather bad choice. Density-based clustering is not designed to yield representative objects.
You could try AffinityPropagation, but it will also not scale very well.
I read the concept of GMM from Understanding concept of Gaussian Mixture Models. It is helpful for me. I have implemented GMM for fisheriris also but I didn't use fitgmdist function because I didn't have it. So I used code from http://chrisjmccormick.wordpress.com/2014/08/04/gaussian-mixture-models-tutorial-and-matlab-code/.
When I read Understanding concept of Gaussian Mixture Models, Amro could plot the result with its label, i.e. setosa, virginica, and versicolor. How did he do it? After some iterations, I only got mu, Sigma, and weight. There is no label at all. I want to put the label (setosa, virginica, and versicolor) to mixture models from GMM iteration.
There are two sets of "labels" in that plot:
one is the "true" labels of the Fisher Iris dataset (the species variable which contains the class of each instance: setoas, versicolor, or virginica). Normally you wouldn't have those in a real dataset (after all the goal of clustering is to discover those groups within the data, which you don't know beforehand). I just used them here to get an idea of how well the EM clustering performed against the actual truth (the scatter points are color-coded according to the class).
the other set of labels are the clusters we found using GMM. Basically I built a 50x50 grid of 2D points to cover the entire data domain, I then assign a cluster to each of those points by computing the posterior probability and choosing the component with highest likelihood. I showed those clusters in the background color. As a nice consequence, we get to see the discriminant decision boundaries between the clusters.
You can see that the cluster of points on the left got separated quite nicely (and perfectly matched the setosa class). While the points on the right side of the plot got separated in two matching the other two classes, although there were instance "misclassified" if you will (some green points on the wrong side of the boundary).
Typically in a real setting you wouldn't have those actual classes to compare against, so no way to tell how "accurate" your clustering was (there exist other metrics for clustering performance evaluation)...
I have a set of data. I want to build a one class distribution from that data. Based on the learned distribution I want to get a probability value for each of the data instance.
Based on this probability values (thresholding) I want to build a classifier to classify a particular data instance is comming from that distribution or not.
In this case, lets say I have a data of 50x100000 where 50 is the dimension of each data instance, the number of instances are 100000. I am leaning a Gaussian mixture model based on this distribution.
When I try to get the probability values for instances I am getting very low values. So in this case how can I build a clssifier?
I don't think this makes sense. For example, suppose your data is 1 dimensional, and suppose the truth is that it has been sampled from a bimodal distribution. But suppose you haven't worked out that it's from a bimodal distribution and you fit a normal distribution. You'd still have the best possible fit, but it would be the best possible fit to the wrong distribution, and the truth is that none of the points come from that distribution or from any distribution that looks like it.
I'm trying to cluster some images depending on the angles between body parts.
The features extracted from each image are:
angle1 : torso - torso
angle2 : torso - upper left arm
..
angle10: torso - lower right foot
Therefore the input data is a matrix of size 1057x10, where 1057 stands for the number of images, and 10 stands for angles of body parts with torso.
Similarly a testSet is 821x10 matrix.
I want all the rows in input data to be clustered with 88 clusters.
Then I will use these clusters to find which clusters does TestData fall into?
In a previous work, I used K-Means clustering which is very straightforward. We just ask K-Means to cluster the data into 88 clusters. And implement another method that calculates the distance between each row in test data and the centers of each cluster, then pick the smallest values. This is the cluster of the corresponding input data row.
I have two questions:
Is it possible to do this using SOM in MATLAB?
AFAIK SOM's are for visual clustering. But I need to know the actual class of each cluster so that I can later label my test data by calculating which cluster it belongs to.
Do you have a better solution?
Self-Organizing Map (SOM) is a clustering method considered as an unsupervised variation of the Artificial Neural Network (ANN). It uses competitive learning techniques to train the network (nodes compete among themselves to display the strongest activation to a given data)
You can think of SOM as if it consists of a grid of interconnected nodes (square shape, hexagonal, ..), where each node is an N-dim vector of weights (same dimension size as the data points we want to cluster).
The idea is simple; given a vector as input to SOM, we find the node closet to it, then update its weights and the weights of the neighboring nodes so that they approach that of the input vector (hence the name self-organizing). This process is repeated for all input data.
The clusters formed are implicitly defined by how the nodes organize themselves and form a group of nodes with similar weights. They can be easily seen visually.
SOM are in a way similar to the K-Means algorithm but different in that we don't impose a fixed number of clusters, instead we specify the number and shape of nodes in the grid that we want it to adapt to our data.
Basically when you have a trained SOM, and you want to classify a new test input vector, you simply assign it to the nearest (distance as a similarity measure) node on the grid (Best Matching Unit BMU), and give as prediction the [majority] class of the vectors belonging to that BMU node.
For MATLAB, you can find a number of toolboxes that implement SOM:
The Neural Network Toolbox from MathWorks can be used for clustering using SOM (see the nctool clustering tool).
Also worth checking out is the SOM Toolbox