SOCR EduMaterials Activities 2D PointSegmentation EM Mixture - Revision history

Dinov at 22:32, 6 January 2023

2023-01-06T22:32:26Z

IvoDinov: /* See also */

2013-05-01T17:14:02Z

‎See also

IvoDinov: /* See also */

2012-09-19T00:30:44Z

‎See also

IvoDinov: /* See also */

2012-07-28T20:08:10Z

‎See also

IvoDinov: /* Exercise 1: SOCR Charts Activity */

2009-05-19T19:10:13Z

‎Exercise 1: SOCR Charts Activity

IvoDinov: /* References */

2009-01-22T17:35:42Z

‎References

IvoDinov: /* References */

2009-01-22T17:34:24Z

‎References

IvoDinov: /* References */

2009-01-22T17:33:39Z

‎References

IvoDinov: /* References */

2009-01-22T17:31:15Z

‎References

IvoDinov: /* References */ expanded the references

2008-12-08T19:34:51Z

‎References: expanded the references

@@ Line 3: / Line 3: @@
 == Summary ==
 This activity demonstrates mixture modeling and expectation maximization (EM) applied to the problem of 2D point cluster segmentation.
 == Background==

@@ Line 60: / Line 60: @@
 * [[SOCR_EduMaterials_AnalysisActivities_HierarchicalClustering|SOCR Hierarchical Clustering Analysis Activity]]
 * [[SOCR_Data_KneePainData_041409| Knee Pain Simulated Data]]
 <hr>

@@ Line 59: / Line 59: @@
 * [[SOCR_EduMaterials_ModelerActivities_MixtureModel_1 | SOCR 1D Mixture Modeling Activity]]
 * [[SOCR_EduMaterials_AnalysisActivities_HierarchicalClustering|SOCR Hierarchical Clustering Analysis Activity]]
 <hr>

@@ Line 58: / Line 58: @@
 * [http://socr.ucla.edu/htmls/dist/Mixture_Distribution.html SOCR Mixture-Distribution applet]
 * [[SOCR_EduMaterials_ModelerActivities_MixtureModel_1 | SOCR 1D Mixture Modeling Activity]]
 <hr>

@@ Line 13: / Line 13: @@
 * ''Data'': You can enter data (paired X,Y observations) either via the Data-Tab, using copy-and-paste, or via the add random points button ('''RandomPts'''). This applet was designed specifically so that you may enter your own paired observations in tabular form. If you are not interested in data analysis, but want to explore more the properties of the EM mixture model, you may try the second SOCR applet ([http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments], select '''Mixture Model EM Experiment''' from the drop down list of [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] on the top-left), which allows you to manually add points by clicking on the graphing canvas. At the end of this document, the [[SOCR_EduMaterials_Activities_2D_PointSegmentation_EM_Mixture#Step-by-Step_Data_Analysis_Protocol | step-by-step protocol]] is included for running the algorithm on any dataset.
 * ''Applet Specifications'': You can fit one of two models to your data (Linear or elliptical Gaussian), see the '''GaussianMix''' button. Linear model will only show the main direction of variation for a sub-cluster. A Gaussian model will illustrate additional information, including the scope of the kernel coverage. The '''Normal''' button allows you to choose ''Slow'', ''Normal'' or ''Fast'' speed for the iterative EM estimation. The '''ClearPts''' will remove all data and reset the applet. The '''InitKernels''' button re-initializes the kernels (location and size) and is useful for shaking the EM algorithm to escape the local minimum. A kernel is roughly a weighting function used in non-parametric techniques. Kernel locations are generally non trivial to choose - we use random initial kernel locations ('''InitKernels''' button). The '''drop-down list''' on the top-right allows you to select the number of kernels you want to fit to this data. There is no exact method for determining this number in all situations (manually or automatically). Typically, one uses the physical or biological properties of the studied data/process to determine the appropriate integer value. On the top, the '''Step''', '''Run''' and '''Stop''' buttons have the natural functions associated with driving the iterative EM algorithm. The '''Segment''' button allows labeling/classification of the points once the EM algorithm has converged or stopped.
@@ Line 18: / Line 19: @@
 * ''Segmentation Results'': Once the EM algorithm converges to a visually satisfactory result you should stop the iterative process ('''Stop''' button) and click on the '''Segment''' button. You will obtain a color classification of all points in 2D based on which of the kernels is most likely to contain the point in its neighborhood. In addition to this visual classification, the Data tab-panel will contain a couple of result columns that contain the complete analytical description of the kernels (as 2D Gaussian), the [http://en.wikipedia.org/wiki/Mixture_model mixture-model] weight coefficients, the [http://en.wikipedia.org/wiki/Log-likelihood log-likelihood function] (quantifying the match between the mixture model and the data), and color-coded membership of all data points to one of the kernels.
 <center>[[Image:SOCR_Activities_EMMixtureModel_Dinov_040407_Fig4.jpg|400px]]</center>
 === '''Exercise 2''': 1D and 3D Examples of [[SOCR]] EM Mixture Modeling===

@@ Line 64: / Line 64: @@
 ==References==
 * Ivo D. Dinov, [http://repositories.cdlib.org/socr/EM_MM Expectation Maximization and Mixture Modeling Tutorial] (December 9, 2008). Statistics Online Computational Resource. Paper EM_MM, http://repositories.cdlib.org/socr/EM_MM.
 * [http://www.cs.tut.fi/~jupeto/2504tohkaj.pdf Genetic Algorithms and Mixture Modeling]
 * [http://www.stat.ucla.edu/%7Edinov/courses_students.dir/07/Winter/PN284.dir/NITP_PN_M284_Inference2.pdf Lecture notes on Statistical Methods in Neuroimaging]

@@ Line 63: / Line 63: @@
 ==References==
-* [http://repositories.cdlib.org/socr/EM_MM  The Mathematics of EM Mixture Modeling]
+* [http://repositories.cdlib.org/socr/EM_MM  Notes on parameter estimation, expectation maximization and mixture modeling] and the corresponding [[SOCR_EduMaterials_Activities_2D_PointSegmentation_EM_Mixture | Java applets and activities]].
 * [http://www.cs.tut.fi/~jupeto/2504tohkaj.pdf Genetic Algorithms and Mixture Modeling]