Anybody have any notes on what Modal Cluster in Bivariate is doing? It's an option under the Nonpar Density LRT Menu. The doc's have 1 sentence on page 146 and nothing in the statistical details.
Thanks!
M
Here's what tech support came back with:"Modal clustering is just finding peaks in the density and collecting all the points that are on the downhill of the gradient to that peak. SAS Proc MODECLUS does this, though it is in more dimensions, not just two, and it uses near-neighbor estimates rather than kernel estimates. The default kernel is chosen according to the Bowman-Foster recommendation: .5*stdDev*n^(1/6). [Link to paper]"There's a link to the paper included - it's open content, so anyone can download if they want to go really deep into the weeds.
Hi Mike,
Not sure if this is at all helpful, but I found in it in a SAS document on clustering.
"Recent research has tended to de-emphasize mixture models in favor of nonparametric models in which clusters correspond to modes in the probability density function.Hartigan and Hartigan (1985) and Hartigan (1985) developed a test of unimodalityversus bimodality in the univariate case.Nonparametric tests for the number of clusters can also be based on nonparametricdensity estimates. This approach requires much weaker assumptions than mixturemodels, namely, that the observations are sampled independently and that the distribution can be estimated nonparametrically. Silverman (1986) describes a bootstraptest for the number of modes using a Gaussian kernel density estimate, but problemshave been reported with this method under the uniform null distribution. FurtherSAS OnlineDoc: Version 8References 131developments in nonparametric methods are given by Mueller and Sawitzki (1991),Minnotte (1992), and Polonik (1993). All of these methods suffer from heavy computational requirements.One useful descriptive approach to the number-of-clusters problem is provided byWong and Schaack (1982), based on a kth-nearest-neighbor density estimate. Thekth-nearest-neighbor clustering method developed by Wong and Lane (1983) is applied with varying values of k. Each value of k yields an estimate of the number ofmodal clusters. If the estimated number of modal clusters is constant for a wide rangeof k values, there is strong evidence of at least that many modes in the population. Aplot of the estimated number of modes against k can be highly informative. Attemptsto derive a formal hypothesis test from this diagnostic plot have met with difficulties,but a simulation approach similar to Silverman’s (1986) does seem to work (Girman1994). The simulation, of course, requires considerable computer time."
Best,
Bill
I didn’t know this cool feature, but now I’ve played with it since your post. It seems it has been available in JMP a long time.
The modal clustering classifies data points into clusters through the kernel density estimation. Using Big Class as an example I ran Fit Height by Weight and then select the Nonpar Density and Modal Clustering. It automatically saves a Cluster column to the data table. In this example there are 14 clusters assigned based on the contours drawn ( i.e., there are 14 peaks in the bivariate density). To makes sense of it I ran Distribution and GB, and placed them in a dashboard.
To illustrate the modal clustering, I allow the quadratic curve in GB automatically updating with the Cluster selection but keep the curve in the Bivariare fixed to the whole data set. As you can see, overall there is a strong upward curvature between Height and Weight, but for Cluster 9 it’s downward. You can also see where these data points are.
