One model for clusters in multivariate data is that the data are sampled from a density with many modes, one mode for each cluster. Methods of estimating multivariate densities may therefore be converted to clustering techniques, and clustering techniques may be helpful in estimating multivariate densities. Graphical techniques for representing clusters are closely related to multivariate histograms. Block histograms in two dimensions are constructed by finding a rectangle of minimum area containing a fixed number of points, deleting this rectangle and the points it contains, then finding another rectangle of minimum area containing a fixed number of points and so on. These histograms are simple visual representations of a density estimate in two dimensions. Analogous block histograms in many dimensions are useful but more difficult to represent graphically. A different approach represents each point by a box drawn in three or more dimensions. If the points are first ordered by some other clustering techn...
[1]
R. Sokal,et al.
Principles of numerical taxonomy
,
1965
.
[2]
H. Chernoff.
Estimation of the mode
,
1964
.
[3]
C. Quesenberry,et al.
A nonparametric estimate of a multivariate density function
,
1965
.
[4]
J. H. Venter.
On Estimation of the Mode
,
1967
.
[5]
Tim Robertson,et al.
On Estimating a Density which is Measurable with Respect to a $\sigma$-Lattice
,
1967
.
[6]
R. Kronmal,et al.
The Estimation of Probability Densities and Cumulatives by Fourier Series Methods
,
1968
.
[7]
Raymond M. Wright,et al.
Numerical classification applied to certain Jamaican eocene nummulitids
,
1971
.
[8]
E. Wegman.
Nonparametric probability density estimation
,
1972
.
[9]
E. Wegman.
Nonparametric Probability Density Estimation: I. A Summary of Available Methods
,
1972
.
[10]
Herman Chernoff,et al.
The Use of Faces to Represent Points in k- Dimensional Space Graphically
,
1973
.
[11]
John A. Hartigan,et al.
Clustering Algorithms
,
1975
.