Type: Package
Title: Fast Clustering Using Adaptive Density Peak Detection
Version: 0.7
Description: An implementation of ADPclust clustering procedures (Fast Clustering Using Adaptive Density Peak Detection). The work is built and improved upon the idea of Rodriguez and Laio (2014)<doi:10.1126/science.1242072>. ADPclust clusters data by finding density peaks in a density-distance plot generated from local multivariate Gaussian density estimation. It includes an automatic centroids selection and parameter optimization algorithm, which finds the number of clusters and cluster centroids by comparing average silhouettes on a grid of testing clustering results; It also includes a user interactive algorithm that allows the user to manually selects cluster centroids from a two dimensional "density-distance plot". Here is the research article associated with this package: "Wang, Xiao-Feng, and Yifan Xu (2015)<doi:10.1177/0962280215609948> Fast clustering using adaptive density peak detection." Statistical methods in medical research". url: http://smm.sagepub.com/content/early/2015/10/15/0962280215609948.abstract.
Depends: R (≥ 3.0.0),
Imports: dplyr, cluster, fields, knitr
URL: https://github.com/ethanyxu/ADPclust
BugReports: https://github.com/ethanyxu/ADPclust/issues
VignetteBuilder: knitr
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
LazyData: true
Suggests: rmarkdown, testthat
RoxygenNote: 5.0.1
NeedsCompilation: no
Packaged: 2016-10-14 14:59:52 UTC; ethan.xu
Author: Yifan (Ethan) Xu [aut, cre], Xiao-Feng Wang [aut]
Maintainer: Yifan (Ethan) Xu <ethan.yifanxu@gmail.com>
Repository: CRAN
Date/Publication: 2016-10-15 11:37:01

AMISE bandwidth

Description

Calculate the AMISE bandwidth from either a data frame, or from the number of observations and the dimension of the data.

Usage

AMISE(x, y = NULL)

Arguments

x

the number of variables (if y is given), or a data frame or a matrix (if y is missing).

y

the number of observations. If y is missing then x is interpreted as the data matrix.

Details

IMPORTANT NOTE: The standard deviation of each variable is omitted in this formula.

Value

AMISE bandwidth.

Automatically finds centers with diagonal f(x) vs delta(x) thresholds

Description

Automatically finds centers with diagonal f(x) vs delta(x) thresholds. This is used in adpclust() with ac = 2. It finds points that are above and farthest from the diagonal line in the f vs. delta plots, and label them to be centers.

Usage

FindCentersAutoD(f, delta, nclust)

Arguments

f

vector of local distance.

delta

vector of minimal distances to higher ground.

nclust

number of clusters. Can be a single integer or a vector of integers. Duplicates are silently removed.

Value

a list of vectors. Each vector gives the locations of centers.

Author(s)

Ethan Xu

Automatically find centers with vertical threshold

Description

Automatically find centers with vertical threshold vertical f(x) thresholds.

Usage

FindCentersAutoV(f, delta, f.cut = c(0.1, 0.2, 0.3), nclust, rm.dup = TRUE)

Arguments

f

vector of local distance f(x). See the detail section of the help(adpclust).

delta

vector of minimal distances to higher ground delta(x). See the detail section of the help(adpclust).

f.cut

number between (0, 1) or numeric vector of numbers between (0, 1). Data points whose f values are larger than f.cut with large delta values are selected as centers. The default is c(0.1, 0.2, 0.3).

nclust

number of clusters. It can be either a single integer or a vector of integers.

rm.dup

boolean. If TRUE (default) duplicated centers vectors are removed from returned list.

Details

Given f's and delta's, cluster centers are chosen to be the data points whose delta values are high and f values are larger than a fixed threshold. To be more specific, let F denote the set of all f(x). centers are selected as points with the largest m delta values in the set x | f(x) > a'th percentile of F. The number of centers m is given by the parameter nclust. The cutting percentile a is given by the parameter f.cut. When at least one of these two parameters are vectors, centers are selected based all combinations of them, and returned in a list.

Value

a list of vectors. Each vector contains the indices of selected centers.

Author(s)

Ethan Xu

Automatically find cluster assignment given f and delta.

Description

This is the subroutine that automatically finds cluster assignments from given f and delta by testing various parameter settings and find the one that maximizes the silhouette.

Usage

FindClustersAuto(distm, f, delta, ac = 1, nclust = 2:10, f.cut = c(0.1,
  0.2, 0.3))

Arguments

distm

the distance matrix

f

vector of local distance f(x). See the help of adpclust() for details.

delta

vector of minimal distances to higher ground delta(x). See the help of adpclust() for details.

ac

type of auto selection. The valid options are 1 and 2. See the help of adpclust() for details.

nclust

number of clusters to test. Either a single integer or a vector of integers.

f.cut

number between (0, 1) or numeric vector of numbers between (0, 1). Data points whose f values are larger than f.cut with large delta values are selected as centers. The default is c(0.1, 0.2, 0.3). See the help of FindCentersAutoV() for more details.

Value

list of four elements:

Author(s)

Ethan Xu

Find cluster assignments given centers and distance matrix

Description

Find cluster assignments from given centers and distance matrix. Each point is assigned to the center that has the shortest Euclidean distance.

Usage

FindClustersGivenCenters(distm, centers)

Arguments

distm

distance matrix

centers

vector of integers that gives the indices of centers. Duplications will be silently dropped.

Value

Cluster assignments. A vector of the same length as the number of observations.

User-interactive routine to find clusters

Description

Plot the f vs. delta plot, then wait for the user to select centers of clusters by left clicking the points. In general points with both large f and large delta are good candidates of cluster centroids. Selected centers are highlighted. Press ESC to end the selection.

Usage

FindClustersManual(distm, f, delta)

Arguments

distm

distance matrix.

f

vector of local densities f(x). Same length of the number of observations.

delta

vector of distances to the closest high ground delta(x). Same length of the number of observations.

Value

a list of the following items:

Examples

data(clust3)
distm <- FindDistm(clust3, normalize = TRUE)
## Not run: 
fd <- FindFD(distm, 2, "mnorm")
ans <- FindClustersManual(distm, fd$f, fd$delta)
names(ans)
ans$centers

## End(Not run)

Find the distance matrix from data.

Description

A wrapper of the dist() method, with the option to rescale the data with standard deviation of each dimension before calculating the distance matrix. NOTE: If fdelta='mnorm' is passed to adpclust(), then the distm is calculated from rescaled data internally, i.e. distm <- FindDistm(x, normalize = TRUE).

Usage

FindDistm(x, normalize = FALSE, method = "euclidean")

Arguments

x

data

normalize

boolean. Normalize data before calculating distance?

method

passed to 'dist()'

Value

distance matrix of class dist.

Author(s)

Ethan Xu

Find f and delta from distance matrix.

Description

Calculate f(x) and delta(x) from distm and h.

Usage

FindFD(distm, h, fdelta)

Arguments

distm

distance matrix of class 'dist'.

h

bandwidth.

fdelta

character string that specifies the method used to estimate local density f(x) at each data point x. The default is "mnorm" that uses a multivariate Gaussian density estimation to calculate f. Other options are listed below. Here 'distm' denotes the distance matrix.

  • unorm(f <- 1/(h * sqrt(2 * pi)) * rowSums(exp(-(distm/h)^2/2))); Univariate Gaussian smoother

  • weighted(f <- rowSums(exp(-(distm/h)^2))); Univariate weighted smoother

  • count(f <- rowSums(distm < h) - 1); Histogram estimator (used in Rodriguez [2014])

Value

list of two items: f and delta.

Find bandwidth h.

Description

Find bandwidth h from the number of observations n and the dimension p.

Usage

FindH(p, n, htype)

Arguments

p

dimension of data. The number of variables.

n

the number of observations.

htype

methods to calculate h. The valid options are (case insensitive) "amise" or "rot".

Value

bandwidth h.

Calculate ROT bandwidth

Description

Calculate the ROT bandwidth either from a data frame, or from p and n.

Usage

ROT(x, y = NULL)

Arguments

x

the number of variables (if y is missing), or a data frame or a matrix (if y is not missing).

y

the number of observations. If y is missing, x should be the data matrix.

Details

IMPORTANT NOTE: The standard deviation of each variable is omitted in this formula.

Value

ROT bandwidth.

Fast Clustering Using Adaptive Density Peak Detection

Description

Clustering of data by finding cluster centers from estimated density peaks. ADPclust is a non-iterative procedure that incorporates multivariate Gaussian density estimation. The number of clusters as well as bandwidths can either be selected by the user or selected automatically through an internal clustering criterion.

Usage

adpclust(x = NULL, distm = NULL, p = NULL, centroids = "auto",
  h = NULL, htype = "amise", nclust = 2:10, ac = 1, f.cut = c(0.1,
  0.2, 0.3), fdelta = "mnorm", dmethod = "euclidean", draw = FALSE)

Arguments

x

numeric data frame where rows are observations and columns are variables. One of x and distm must be provided.

distm

distance matrix of class 'dist'. distm is ignored if x is given.

p

number of variables (ncol(x)). This is only needed if neither x nor h is given.

centroids

character string specifying how cluster centroids are selected. Valid options are "user" and "auto".

h

nonnegative number specifying the bandwidth in density estimation. If h is NULL, the algorithm attempts to find h in a neighborhood centered at either the AMISE bandwidth or ROT bandwidth (see htype).

htype

character string specifying the method used to calculate a reference bandwidth for the density estimation. htype is ignored if h is given. Valid options of are "ROT" and "AMISE" (see details).

nclust

integer, or a vector of integers specifying the pool of the number of clusters in automatic variation. The default is 2:10.

ac

integer indicating which automatic cut method is used. This is ignored if centroids = 'user'. The valid options are:

  • ac = 1: centroids are chosen to be the data points x's with the largest delta values such that f(x) >= a'th percentile of all f(x). The number of centroids is given by the parameter nclust. The cutting percentile(s) is given by the parameter f.cut.

  • ac = 2: let l denote the straight line connecting (min(f), max(delta)) and (max(f), min(delta)). The centroids are selected to be data points above l and farthest away from it. The number of centroids is given by the parameter nclust.

f.cut

number between (0, 1) or numeric vector of numbers between (0, 1). f.cut is used when centroids = "auto" and ac = 1 to automatically select cluster centroids from the decision plot (see ac). The default is c(0.1, 0.2, 0.3).

fdelta

character string that specifies the method used to estimate local density f(x) at each data point x. The default (recommended) is "mnorm" that uses a multivariate Gaussian density estimation to calculate f. Other options are listed below. Here 'distm' denotes the distance matrix.

  • unorm(f <- 1/(h * sqrt(2 * pi)) * rowSums(exp(-(distm/h)^2/2))); Univariate Gaussian smoother

  • weighted(f <- rowSums(exp(-(distm/h)^2))); Univariate weighted smoother

  • count(f <- rowSums(distm < h) - 1); Histogram estimator (used in Rodriguez [2014])

dmethod

character string that is passed to the 'method' argument in function dist(), which is used to calculate the distance matrix if 'distm' is not given. The default is "euclidean".

draw

boolean. If draw = TRUE the clustering result is plotted after the algorithm finishes. The plot is produced by by plot.adpclust(ans), where 'ans' is the outcome of 'adpclust()'

Details

Given n data points x's in p dimensions, adpclust() calculates f(x) and delta(x) for each data point x, where f(x) is the local density at x, and delta(x) is the shortest distance between x and y for all y such that f(x) <= f(y). Data points with large f and large delta values are labeled class centroids. In other words, they appear as isolated points in the upper right corner of the f vs. delta plot (the decision plot). After cluster centroids are determined, other data points are clustered according to their distances to the closes centroids.

A bandwidth (smoothing parameter) h is used to calculate local density f(x) in various ways. See parameter 'fdelta' for details. If centroids = 'user', then h must be explicitly provided. If centroids = 'auto' and h is not specified, then it is automatically selected from a range of testing values: First a reference bandwidth h0 is calculated by one of the two methods: Scott's Rule-of-Thumb value (htype = "ROT") or Wand's Asymptotic-Mean-Integrated-Squared-Error value (htype = "AMISE"), then 10 values equally spread in the range [1/3h0, 3h0] are tested. The value that yields the highest silhouette score is chosen as the final h.

Value

An 'adpclust' object that contains the list of the following items.

References

Examples

# Load a data set with 3 clusters
data(clust3)

# Automatically select cluster centroids
ans <- adpclust(clust3, centroids = "auto", draw = FALSE)
summary(ans)
plot(ans)

# Specify distm instead of data
distm <- FindDistm(clust3, normalize = TRUE)
ans.distm <- adpclust(distm = distm, p = 2, centroids = "auto", draw = FALSE)
identical(ans, ans.distm)

# Specify the grid of h and nclust
ans <- adpclust(clust3, centroids = "auto", h = c(0.1, 0.2, 0.3), nclust = 2:6)

# Specify that bandwidths should be searched around
# Wand's Asymptotic-Mean-Integrated-Squared-Error bandwidth
# Also test 3 to 6 clusters.
ans <- adpclust(clust3, centroids = "auto", htype = "AMISE", nclust = 3:6)

# Set a specific bandwidth value.
ans <- adpclust(clust3, centroids = "auto", h = 5)

# Change method of automatic selection of centers
ans <- adpclust(clust3, centroids = "auto", nclust = 2:6, ac = 2)

# Specify that the single "ROT" bandwidth value by
# using the 'ROT()' function
ans <- adpclust(clust3, centroids = "auto", h = ROT(clust3))

# Centroids selected by user
## Not run: 
ans <- adpclust(clust3, centroids = "user", h = ROT(clust3))

## End(Not run)

# A larger data set
data(clust5)
ans <- adpclust(clust5, centroids = "auto", htype = "ROT", nclust = 3:5)
summary(ans)
plot(ans)

1000 5-dimensional data points that form ten clusters

Description

Generated from the genRandomClust() function of the "clusterGeneration" package with separation value 0.2.

Format

data frame

90 2-dimensional data points that form three clusters

Description

Randomly generated from three normal distributions.

Format

data frame

500 5-dimensional data points that form five clusters

Description

500 5-dim points in 5 clusters. Generated from the genRandomClust() function of the "clusterGeneration" package with separation value 0.1.

Format

data frame

500 5-dimensional data points that form five clusters

Description

Generated from the genRandomClust() function of the "clusterGeneration" package with separation value 0.01 (tightly clustered).

Format

data frame

243-dimensional gene expression data of 38 patients (243 genes)

Description

38 by 243 matrix. Each row represents a patient. Each column represents a gene.

Format

matrix

Default colors

Description

Returns 10 default colors

Usage

defCol()

Value

vector of colors

Visualize the result of adpclust()

Description

Plot the f vs. delta plot with selected centroids.

Usage

## S3 method for class 'adpclust'
plot(x, cols = "default", to.plot = c("cluster.sil",
  "fd"), ...)

Arguments

x

an object of class "adpclust". Result of adpclust().

cols

vector of colors used to distinguish different clusters. Recycled if necessary.

to.plot

string vector that indicate which plot(s) to show. The two options are 'cluster.sil' (nclust vs. silhouette) and 'fd' (f vs. delta).

...

Not used.

Examples

## Load a data set with 3 clusters
data(clust3)
## Automatically select cluster centroids
ans <- adpclust(clust3, centroids = "auto")
plot(ans)
plot(ans, to.plot = "fd")
plot(ans, to.plot = "cluster.sil")
plot(ans, to.plot = c("cluster.sil", "fd")) #Default

Summary of adpclust

Description

Summarizes the result from the adpclust() function.

Usage

## S3 method for class 'adpclust'
summary(object, ...)

Arguments

object

object of class "adpclust" that is returned from adpclust().

...

other arguments. NOT used.

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