Remove outliers from a set of 3d points before clustering Matlab - matlab

I have a set of 3d points in Matlab but the problem is that my data found here. And as you can see there are some outliers which are affecting my clustering results. So if anyone could please advise how I can delete these outliers from my data.

Having looked at your data, I don't think any clustering algorithm will do what you want. Instead, you will probably need to train a classifier. This is what the Kinect people did, train a classifier using millions of real and synthetic postures, to have it label limbs, head, etc.
The reason why I don't think density based clustering will work either is because your data is a single, density-connected, body-with-two-boxes-shaped blob. But without knowing what a "body" and a "box" is, segmentation will be rather arbitrary. Or in the case of density based clustering: it will not segment at all, or it will segment e.g. by the rather low resultion of your z axis. Furthermore, your X and Y axes come from a grid based image scan (I assume), so you have a very uniform density on the X and Y axes - but the arms, for example, are not of a lower density than the body or boxes.
You can, however, use DBSCAN with rather broad (and easy to set) parameters to remove the noise.
E.g. in ELKI the following parameters yield reasonable results:
java -jar elki.jar -dbc.in /tmp/XX.csv -algorithm clustering.DBSCAN \
-dbscan.epsilon 0.05 -dbscan.minpts 100
The majority cluster is your data with the outliers removed; even with this blob near the foot removed.
To speed up the clustering process, you can add the parameters
-db.index tree.spatial.rstarvariants.rstar.RStarTreeFactory \
-pagefile.pagesize 1000 -spatial.bulkstrategy SortTileRecursiveBulkSplit
which yields a runtime opf 4.5 seconds here. This obviously is not good enough for realtime operation as on a Kinect; but it is not surprising to see a directed classification algorithm to outperform an unsupervised method - this is in fact to be expected.
Here is the result of clustering the data set with the parameters above:

Related

Removing outliers with PCA in multidmension (100+) cluster problem

I have two dataframes that I need to clusterize where I am trying to do the following:
Apply PCA to remove outliers and use PCA with 3 components to visualize it.I am using a total of explained variance of 97,5% for the outlier removal process.
Inverse transform and get the MSE score between the inversed tranformed dataframes and the original ones.
Use the IQR upper bracket limit using the calculated MSE score to remove the outliers.
Applying the PCA with 3 components to visualize and determine the number of clusters on the new dataframe.
My main issues are:
Is the IQR on MSE a good criteria for removal?
I have limited to the upper bracket since we are working with absolute values. If not and I am mixing concepts, what would be a good criteria for this type of transformation?
Or I should drop PCA and go for other methods of outliers detection, if so which?
And ultimately I still visualize points very far from the clusters when doing the x,y,z plot, does this mean they aren't outliers, just a few scattered far away points that represent a small cluster? Or the outlier detecting isn't being effective?
Finally on the second dataframe a 3D visualization has roughly 40% of explained variance, is it fair to apply the same decision making process?
The pca library provides functionalities that can be of use for vizualization, outlier detection, playing with explained variance. In general, the Hotelling T2 test and SPE/dmodx are techniques used to remove outliers when using PCA. A previous post with outlier detection can be found here: https://stackoverflow.com/a/63043840/13730780
But in general, if your aim is to detect outliers, it depends on the type of data you have (continuous, categorical, one-hot, mixed datasets), whether you want/need to include context. If you approach is by clustering, you can try the clusteval library which includes methods such as dbscan.

Selecting the K value for Kmeans clustering [duplicate]

This question already has answers here:
Cluster analysis in R: determine the optimal number of clusters
(8 answers)
Closed 3 years ago.
I am going to build a K-means clustering model for outlier detection. For that, I need to identify the best number of clusters needs to be selected.
For now, I have tried to do this using Elbow Method. I plotted the sum of squared error vs. the number of clusters(k) but, I got a graph like below which makes confusion to identify the elbow point.
I need to know, why do I get a graph like this and how do I identify the optimal number of clusters.
K-means is not suitable for outlier detection. This keeps popping up here all the time.
K-means is conceptualized for "pure" data, with no false points. All measurements are supposed to come from the data, and only vary by some Gaussian measurement error. Occasionally this may yield some more extreme values, but even these are real measurements, from the real clusters, and should be explained not removed.
K-means itself is known to not work well on noisy data where data points do not belong to the clusters
It tends to split large real clusters in two, and then points right in the middle of the real cluster will have a large distance to the k-means centers
It tends to put outliers into their own clusters (because that reduces SSQ), and then the actual outliers will have a small distance, even 0.
Rather use an actual outlier detection algorithm such as Local Outlier Factor, kNN, LOOP etc. instead that were conceptualized with noisy data in mind.
Remember that the Elbow Method doesn't just 'give' the best value of k, since the best value of k is up to interpretation.
The theory behind the Elbow Method is that we in tandem both want to minimize some error function (i.e. sum of squared errors) while also picking a low value of k.
The Elbow Method thus suggests that a good value of k would lie in a point on the plot that resembles an elbow. That is the error is small, but doesn't decrease drastically when k increases locally.
In your plot you could argue that both k=3 and k=6 resembles elbows. By picking k=3 you'd have picked a small k, and we see that k=4, and k=5 doesn't do much better in minimizing the error. Same goes with k=6.

Finding elongated clusters using MATLAB

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.

Resampling data with minimal loss of information in time-domain

I am trying to resample/recreate already recorded data for plotting purposes. I thought this is best place to ask the question (besides dsp.se).
The data is sampled at high frequency, contains to much data points and not suitable for plotting in time domain (not enough memory). i want to sample it with minimal loss. The sampling interval of the resulting data doesn't need to be same (well it is again for plotting purposes, not analysis) although input data in equally sampled.
When we use the regular resample command from matlab/octave, it can distort stiff pieces of the curve.
What is the best approach here?
For reference I put two pictures found in tex.se)
First image is regular resample
Second image is a better resampled data that can well behave around peaks.
You should try this set of files from the File Exchange. It computes optimal lookup table based on either the maximum set of points or a given error. You can choose from natural, linear, or spline for the interpolation methods. Spline will have the smallest table size but is slower than linear. I don't use natural unless I have a really good reason.
Sincerely,
Jason

Histogram computational efficiency

I am trying to plot a 2 GB matrix using MATLAB hist on a computer with 4 GB RAM. The operation is taking hours. Are there ways to increase the performance of the computation, by pre-sorting the data, pre-determining bin sizes, breaking the data into smaller groups, deleting the raw data as the data is added to bins, etc?
Also, after the data is plotted, I need to adjust the binning to ensure the curve is smooth. This requires starting over and re-binning the raw data. I assume the strategy involving the least computation would be to first bin the data using very small bins and then manipulate the bin size of the output, rather than re-binning the raw data. What is the best way to adjust bin sizes post-binning (assuming the bin sizes can only grow and not shrink)?
I don't like answers to StackOverflow Questions of the form "well even though you asked how to do X, you don't really want to do X, you really want to do Y, so here's a solution to Y"
But that's what i am going to do here. I think such an answer is justified in this rare instance becuase the answer below is in accord with sound practices in statistical analysis and because it avoids the current problem in front of you which is crunching 4 GB of datda.
If you want to represent the distribution of a population using a non-parametric density estimator, and you wwish to avoid poor computational performance, a kernel density estimator (KDE) will do the job far better than a histogram.
To begin with, there's a clear preference for KDEs versus histograms among the majority of academic and practicing statisticians. Among the numerous texts on this topic, ne that i think is particularly good is An introduction to kernel density estimation )
Reasons why KDE is preferred to histogram
the shape of a histogram is strongly influenced by the choice of
total number of bins; yet there is no authoritative technique for
calculating or even estimating a suitable value. (Any doubts about this, just plot a histogram from some data, then watch the entire shape of the histogram change as you adjust the number of bins.)
the shape of the histogram is strongly influenced by the choice of
location of the bin edges.
a histogram gives a density estimate that is not smooth.
KDE eliminates completely histogram properties 2 and 3. Although KDE doesn't produce a density estimate with discrete bins, an analogous parameter, "bandwidth" must still be supplied.
To calculate and plot a KDE, you need to pass in two parameter values along with your data:
kernel function: the most common options (all available in the MATLAB kde function) are: uniform, triangular, biweight, triweight, Epanechnikov, and normal. Among these, gaussian (normal) is probably most often used.
bandwith: the choice of value for bandwith will almost certainly have a huge effect on the quality of your KDE. Therefore, sophisticated computation platforms like MATLAB, R, etc. include utility functions (e.g., rusk function or MISE) to estimate bandwith given oother parameters.
KDE in MATLAB
kde.m is the function in MATLAB that implementes KDE:
[h, fhat, xgrid] = kde(x, 401);
Notice that bandwith and kernel are not supplied when calling kde.m. For bandwitdh: kde.m wraps a function for bandwidth selection; and for the kernel function, gaussian is used.
But will using KDE in place of a histogram solve or substantially eliminate the very slow performance given your 2 GB dataset?
It certainly should.
In your Question, you stated that the lagging performance occurred during plotting. A KDE does not require mapping of thousands (missions?) of data points a symbol, color, and specific location on a canvas--instead it plots a single smooth line. And because the entire data set doesn't need to be rendered one point at a time on the canvas, they don't need to be stored (in memory!) while the plot is created and rendered.