| Title: | Data Analysis Tools over Space of Phylogenetic Trees Using Tropical Geometry |
| Version: | 1.2.1 |
| Maintainer: | Houjie Wang <wanghoujie6688@gmail.com> |
| Description: | Process phylogenetic trees with tropical support vector machine and principal component analysis defined with tropical geometry. Details about tropical support vector machine are available in : Tang, X., Wang, H. & Yoshida, R. (2020) <doi:10.48550/arXiv.2003.00677>. Details about tropical principle component analysis are available in : Page, R., Yoshida, R. & Zhang L. (2020) <doi:10.1093/bioinformatics/btaa564> and Yoshida, R., Zhang, L. & Zhang, X. (2019) <doi:10.1007/s11538-018-0493-4>. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.1.1 |
| Imports: | ape, lpSolve, lpSolveAPI, parallel, Rfast, RcppAlgos, caret |
| Depends: | R (≥ 3.5.0) |
| Suggests: | rmarkdown, knitr, e1071, testthat (≥ 3.0.0) |
| URL: | https://github.com/HoujieWang/Rtropical |
| VignetteBuilder: | knitr |
| Config/testthat/edition: | 3 |
| NeedsCompilation: | no |
| Packaged: | 2021-11-09 12:08:20 UTC; wanghoujie |
| Author: | Houjie Wang [aut, cre], Kaizhang Wang [aut], Grady Weyenberg [aut], Xiaoxian Tang [aut], Ruriko Yoshida [aut] |
| Repository: | CRAN |
| Date/Publication: | 2021-11-09 18:50:08 UTC |
Simulated Tree Data with Different Proximity Parameter Value
Description
Simulated Tree Data with Different Proximity Parameter Value
Usage
data(all_trees)
Format
A list of length 12 with each element a sublist containing an
ape multiPhylo object with 300 rooted trees on 5 tips and the tree categories.
Apicomplexa gene trees sample data set.
Description
Apicomplexa gene trees sample data set.
Usage
apicomplexa
Format
An ape multiPhylo object with 268 rooted trees on 8 tips.
Source
Chih-Horng Kuo, John P. Wares, Jessica C. Kissinger. The Apicomplexan Whole-Genome Phylogeny: An Analysis of Incongruence among Gene Trees Molecular Biology and Evolution, Volume 25, Issue 12, December 2008, Pages 2689–2698.
Vectorize a Set of Phylognetic Trees
Description
Unifies tip labels of all phylogenetic trees in multiPhylo
object the same as the first tree and returns the
cophenetic distance of their corresponding chronogram.
Usage
## S3 method for class 'multiPhylo'
as.matrix(x, tipOrder = x[[1]]$tip.label, parallel = FALSE, ncores = 2, ...)
Arguments
x |
an object of class |
tipOrder |
a numeric vector of order of leaf names to which all trees
in the |
parallel |
a logical value indicating if parallel computing should be used. (default: FALSE) |
ncores |
a numeric value indicating the number of threads utilized for multi-cored CPUs. (default: 2) |
... |
Not used. Other arguments to as.vector |
Value
A data matrix with each row a vector representation of a chronogram. Each element of the vector is the distance between two leaves.
Examples
data(apicomplexa)
data <- as.matrix(apicomplexa[1: 10]) # matrixize first ten trees
Vectorize a Phylogenetic Tree
Description
Computes the cophenetic distance and outputs them in a vector
of a phylogenetic tree in phylo object
Usage
## S3 method for class 'phylo'
as.vector(x, mode = "any")
Arguments
x |
A object of class phylo |
mode |
The same as |
Value
A vector with its elements the distance between two leaves of the tree.
Examples
library(ape)
tree <- rcoal(5)
tree_vec <- as.vector(tree)
Efficient Finder of Best Assignment
Description
Efficient Finder of Best Assignment
Usage
assignment_finder(P, Q, t = 25)
Arguments
P |
a data matrix of the first category. |
Q |
a data matrix of the second category. |
t |
a numeric value controlling the number of selected best assignments. |
Value
A matrix with each row a unique assignment, starting from the best assignment and ending with the worst.
Extract Optimal Tropical Hyperplane from a cv.tropsvm object
Description
Obtain the optimal tropical hyperplane in the form of vectors from a cv.tropsvm object.
Usage
## S3 method for class 'cv.tropsvm'
coef(object, ...)
Arguments
object |
a fitted |
... |
Not used. Other arguments. |
Value
An output of the apex of the fitted optimal tropical hyperplane.
Extract Optimal Tropical Hyperplane from a tropsvm object
Description
Obtain the optimal tropical hyperplane in the form of vectors from a tropsvm object.
Usage
## S3 method for class 'tropsvm'
coef(object, ...)
Arguments
object |
a fitted |
... |
Not used. Other arguments. |
Value
An output of the apex of the fitted optimal tropical hyperplane.
Cross-Validation for Tropical Support Vector Machines
Description
Conduct k-fold cross validation for tropsvm and return an object "cv.tropsvm".
Usage
cv.tropsvm(x, y, parallel = FALSE, nfold = 10, nassignment = 10, ncores = 2)
Arguments
x |
a data matrix, of dimension nobs x nvars; each row is an observation vector. |
y |
a response vector with one label for each row/component of x. |
parallel |
a logical value indicating if parallel computing should be used. (default: FALSE) |
nfold |
a numeric value of the number of data folds for cross-validation. (default: 10) |
nassignment |
a numeric value indicating the size of the parameter grid of assignments. (default: 10) |
ncores |
a numeric value indicating the number of threads utilized for multi-cored CPUs. (default: 2) |
Value
object with S3 class cv.tropsvm containing the fitted model, including:
apex |
The negative apex of the fitted optimal tropical hyperplane. |
assignment |
The best |
index |
The best classification method tuned by cross-validation. |
levels |
The name of each category, consistent with categories in |
accuracy |
The validation accuracy for each fold. |
nfold |
The number of folds used in cross-validation. |
See Also
summary, predict, coef and the tropsvm function.
Examples
# data generation
library(Rfast)
set.seed(101)
e <- 20
n <- 10
N <- 10
s <- 5
x <- rbind(
rmvnorm(n, mu = c(5, -5, rep(0, e - 2)), sigma = diag(s, e)),
rmvnorm(n, mu = c(-5, 5, rep(0, e - 2)), sigma = diag(s, e))
)
y <- as.factor(c(rep(1, n), rep(2, n)))
newx <- rbind(
rmvnorm(N, mu = c(5, -5, rep(0, e - 2)), sigma = diag(s, e)),
rmvnorm(N, mu = c(-5, 5, rep(0, e - 2)), sigma = diag(s, e))
)
newy <- as.factor(rep(c(1, 2), each = N))
# train the tropical svm
cv_tropsvm_fit <- cv.tropsvm(x, y, parallel = FALSE)
summary(cv_tropsvm_fit)
coef(cv_tropsvm_fit)
# test with new data
pred <- predict(cv_tropsvm_fit, newx)
# check with accuracy
table(pred, newy)
# compute testing accuracy
sum(pred == newy) / length(newy)
Tropical Determinants for Small Matrices
Description
Tropical Determinants for Small Matrices
Usage
trop_det2d(X)
trop_det3d(X)
trop_det4d(X)
trop_det5d(X)
Arguments
X |
a square matrix |
Value
Tropical determinant of a given matrix
Convert Tropical Linear Space to Convex Hull
Description
Convert Tropical Linear Space to Convex Hull
Usage
linsp_to_poly(V)
Arguments
V |
a data matrix, of dimension s x e, with each row a basis of tropical linear space. e is the dimension of the tropical space and s is the dimension of the linear space. |
Value
the return is a e choose s-1 x e matrix.
Coelacanths genome and transcriptome data
Description
Coelacanths genome and transcriptome data
Usage
lungfish
Format
An ape multiPhylo object with 1193 rooted trees on 10 tips.
Source
Tom M. W. Nye, Xiaoxian Tang, Grady Weyenberg and Ruriko Yoshida. Principal component analysis and the locus of the Fréchet mean in the space of phylogenetic trees, Biometrika, Volume 104, Issue 4, December 2017, Pages 901–922.
Plot the Tropical Principal Components with Data Projections
Description
Visualize the second order tropical principle components in troppca
as a tropical triangle with projections on a two-dimensional plot via tropical isometry.
Usage
## S3 method for class 'troppca'
plot(x, plab = NULL, fw = FALSE, ...)
Arguments
x |
a fitted |
plab |
a vector of labels of all points in the given data matrix. Not needed for unlabeled data. (default: NULL) |
fw |
a logical variable to determine if to add Fermat-Weber point of the data projection. (default: FALSE) |
... |
Not used. Other arguments to plot |
Value
plot.troppca does not return anything other than the plot.
Dimension Reduction by Isometry
Description
Dimension Reduction by Isometry
Usage
polytope_iso(D, P)
Arguments
D |
a data matrix of size s x e whose rows are vertices of a tropical polytope. |
P |
a vector of a point in row spaces of |
Value
A vector of a point corresponding to P in column span of D.
Predict Method for Tropical Support Vector Machines based on Cross-Validation
Description
Predicts values based upon a model trained by cv.tropsvm.
Usage
## S3 method for class 'cv.tropsvm'
predict(object, newx, ...)
Arguments
object |
a fitted |
newx |
a data matrix, of dimension nobs x nvars used as testing data. |
... |
Not used. Other arguments to predict. |
Value
A vector of predicted values of a vector of labels.
See Also
summary, coef and the cv.tropsvm function.
Examples
# data generation
library(Rfast)
e <- 20
n <- 10
N <- 10
s <- 5
x <- rbind(
rmvnorm(n, mu = c(5, -5, rep(0, e - 2)), sigma = diag(s, e)),
rmvnorm(n, mu = c(-5, 5, rep(0, e - 2)), sigma = diag(s, e))
)
y <- as.factor(c(rep(1, n), rep(2, n)))
newx <- rbind(
rmvnorm(N, mu = c(5, -5, rep(0, e - 2)), sigma = diag(s, e)),
rmvnorm(N, mu = c(-5, 5, rep(0, e - 2)), sigma = diag(s, e))
)
newy <- as.factor(rep(c(1, 2), each = N))
# train the tropical svm
cv_tropsvm_fit <- cv.tropsvm(x, y, parallel = FALSE)
# test with new data
pred <- predict(cv_tropsvm_fit, newx)
# check with accuracy
table(pred, newy)
# compute testing accuracy
sum(pred == newy) / length(newy)
Predict Method for Tropical Support Vector Machines
Description
Predicts values based upon a model trained by tropsvm.
Usage
## S3 method for class 'tropsvm'
predict(object, newx, ...)
Arguments
object |
a fitted |
newx |
a data matrix, of dimension nobs x nvars used as testing data. |
... |
Not used. Other arguments to predict. |
Value
A vector of predicted values of a vector of labels.
See Also
summary, coef and the tropsvm function.
Examples
# data generation
library(Rfast)
e <- 100
n <- 10
N <- 10
s <- 5
x <- rbind(
rmvnorm(n, mu = c(5, -5, rep(0, e - 2)), sigma = diag(s, e)),
rmvnorm(n, mu = c(-5, 5, rep(0, e - 2)), sigma = diag(s, e))
)
y <- as.factor(c(rep(1, n), rep(2, n)))
newx <- rbind(
rmvnorm(N, mu = c(5, -5, rep(0, e - 2)), sigma = diag(s, e)),
rmvnorm(N, mu = c(-5, 5, rep(0, e - 2)), sigma = diag(s, e))
)
newy <- as.factor(rep(c(1, 2), each = N))
# train the tropical svm
tropsvm_fit <- tropsvm(x, y, auto.assignment = TRUE, ind = 1)
# test with new data
pred <- predict(tropsvm_fit, newx)
# check with accuracy
table(pred, newy)
# compute testing accuracy
sum(pred == newy) / length(newy)
Read NEXUS-formatted trees from two categories into a data matrix
Description
Read NEXUS-formatted trees from two categories into a data matrix
Usage
read.nexus.to.data.matrix(data.file1, data.file2)
Arguments
data.file1 |
A data set with trees from one category. |
data.file2 |
A data set with trees from the other category. |
Value
A data matrix with the first x rows corresponding the x trees in the first file and the last y rows are the trees from the second file.
Read Newick-formatted trees in two categories into a data matrix
Description
Read Newick-formatted trees in two categories into a data matrix
Usage
read.tree.to.data.matrix(data.file1, data.file2)
Arguments
data.file1 |
A file containing trees in Newick form in a category. |
data.file2 |
A file containing trees in Newick form in an assumed different category. |
Value
read.tree.to.data.matrix has the same return as read.nexus.to.data.matrix.
Simulated Tree Data
Description
Simulated Tree Data
Usage
data(sim_trees)
Format
An ape multiPhylo object with 300 rooted trees on 5 tips.
Summarize an Analysis of Cross-Validated Tropical Support Vector Machine
Description
Return a summary with a more detailed explanation of the object "cv.tropsvm".
Usage
## S3 method for class 'cv.tropsvm'
summary(object, ...)
Arguments
object |
a fitted |
... |
Not used. Other arguments to summary. |
Value
A summary of the crucial information of a tropical support vector machine is printed, including the selected best assignment and classification methods and the validation accuracy of each data fold. The summary section of classification methods specifies the sectors and their intersections used to classify points of two different categories.
See Also
predict, coef and the cv.tropsvm function.
Examples
# data generation
library(Rfast)
e <- 20
n <- 10
N <- 10
s <- 5
x <- rbind(
rmvnorm(n, mu = c(5, -5, rep(0, e - 2)), sigma = diag(s, e)),
rmvnorm(n, mu = c(-5, 5, rep(0, e - 2)), sigma = diag(s, e))
)
y <- as.factor(c(rep(1, n), rep(2, n)))
newx <- rbind(
rmvnorm(N, mu = c(5, -5, rep(0, e - 2)), sigma = diag(s, e)),
rmvnorm(N, mu = c(-5, 5, rep(0, e - 2)), sigma = diag(s, e))
)
newy <- as.factor(rep(c(1, 2), each = N))
# train the tropical svm with cross-validation
cv_tropsvm_fit <- cv.tropsvm(x, y, parallel = FALSE)
summary(cv_tropsvm_fit)
Tropical Fermat-Weber Point
Description
Compute the tropical Fermat-Weber (FW) point for a given data matrix. The FW point minimizes the summed tropical distance to the trees described in the data matrix.
Usage
tropFW(x)
Arguments
x |
a data matrix, of dimension nobs x nvars; each row is an observation vector. |
Value
A list containing:
fw |
The fermat-weber point. |
distsum |
The sum of distance from each observation to the fermat-weber point. |
Examples
x <- matrix(rnorm(100), ncol = 10)
tropFW(x)
Tropical Determinant of a Matrix
Description
Compute the tropical determinant for a given matrix. This is equivalent to solving an assignment problem.
Usage
tropdet(x)
Arguments
x |
a square matrix |
Value
The determinant of the given matrix,
Examples
R <- matrix(sample(1:9, 9), nrow = 3)
tropdet(R)
Tropical Principal Component Analysis by Tropical Linear Space
Description
Approximate the principal component as a tropical linear space
for a given data matrix and returns the results as an object of class troppca.
Usage
troppca.linsp(x, pcs = 2, iteration = list(), ncores = 2)
Arguments
x |
a data matrix, of size n x e, with each row an observation vector. e is the dimension of the tropical space |
pcs |
a numeric value indicating the order of principal component. (default: 2) |
iteration |
a list with arguments controlling the iteration of the algorithm.
|
ncores |
a numeric value indicating the number of threads utilized for multi-cored CPUs. (default: 2) |
Value
A list of S3 class "troppca", including:
pc |
The principal component as a tropical linear space |
obj |
The tropical PCA objective, the sum of tropical distance from each point to the projection. |
projection |
The projections of all data points. |
type |
The geometry of principal component. |
Examples
library(Rfast)
n <- 100
e <- 10
sig2 <- 1
x <- rbind(rmvnorm(n, mu = c(5, -5, rep(0, e - 2)), sigma = diag(sig2, e)))
troppca_fit <- troppca.linsp(x)
Tropical Principal Component Analysis by Polytope Converted from Linear Space
Description
Approximate the principal component as a tropical polytope converted from tropical linear space for a given data matrix
via MCMC and return the results as an object of class troppca.
Usage
troppca.linsp2poly(x, pcs = 2, nsample = 1000, ncores = 2)
Arguments
x |
a data matrix, of size n x e, with each row an observation vector. e is the dimension of the tropical space#' |
pcs |
a numeric value indicating the order of principal component. (default: 2) |
nsample |
a numeric value indicating the number of samples of MCMC. (default: 1000) |
ncores |
a numeric value indicating the number of threads utilized for multi-cored CPUs. (default: 2) |
Value
A list of S3 class "troppca", including:
pc |
The principal component as a tropical linear space |
obj |
The tropical PCA objective, the sum of tropical distance from each point to the projection. |
projection |
The projections of all data points. |
type |
The geometry of principal component. |
Examples
library(Rfast)
n <- 50
e <- 50
s <- 5
x <- rbind(
rmvnorm(n, mu = c(5, -5, rep(0, e - 2)), sigma = diag(s, e)),
rmvnorm(n, mu = c(-5, 5, rep(0, e - 2)), sigma = diag(s, e))
)
troppca_fit <- troppca.linsp2poly(x)
Compute Tropical PCA Objective
Description
Compute Tropical PCA Objective
Usage
troppca.obj(pc, x_list, cl)
troppca.obj2(pc, x_list, cl)
Arguments
pc |
a matrix of principal components |
x_list |
a list of vectors |
cl |
cluster for parallel computing |
Value
The numeric value of the objective function of tropical principle component analysis. This is the sum of all tropical distance from each point to its projection on the tropical polytope.
Tropical Principal Component Analysis by Tropical Polytope
Description
Approximates the principal component as a tropical polytope for a given data matrix
via MCMC and return the results as an object of class troppca.
Usage
troppca.poly(x, pcs = 2, nsample = 1000, ncores = 2)
Arguments
x |
a data matrix, of size n x e, with each row an observation vector. e is the dimension of the tropical space#' |
pcs |
a numeric value indicating the order of principal component. (default: 2) |
nsample |
a numeric value indicating the number of samples of MCMC. (default: 1000) |
ncores |
a numeric value indicating the number of threads utilized for multi-cored CPUs. (default: 2) |
Value
A list of S3 class "troppca", including:
pc |
The principal component as a tropical linear space |
obj |
The tropical PCA objective, the sum of tropical distance from each point to the projection. |
projection |
The projections of all data points. |
type |
The geometry of principal component. |
Examples
library(Rfast)
n <- 50
e <- 50
s <- 5
x <- rbind(
rmvnorm(n, mu = c(5, -5, rep(0, e - 2)), sigma = diag(s, e)),
rmvnorm(n, mu = c(-5, 5, rep(0, e - 2)), sigma = diag(s, e))
)
troppca_fit <- troppca.poly(x)
plot(troppca_fit)
Projection on Tropical Linear Space
Description
Compute projection of data points on a given tropical linear space.
Usage
tropproj.linsp(x, V)
Arguments
x |
a data matrix, of size n x e, with each row an observation. |
V |
a data matrix, of dimension s x e, with each row a basis of tropical linear space. e is the dimension of the tropical space and s is the dimension of the linear space. |
Value
A matrix of projections of all data points.
Examples
library(Rfast)
n <- 100
e <- 10
sig2 <- 1
s <- 3
x <- rbind(rmvnorm(n, mu = c(5, -5, rep(0, e - 2)), sigma = diag(sig2, e)))
V <- matrix(runif(s * e, -10, 10), nrow = s, ncol = e)
x_proj <- tropproj.linsp(x, V)
head(x_proj)
Projection on Tropical Polytope
Description
Project a point onto a given tropical polytope.
Usage
tropproj.poly(x, tconv)
Arguments
x |
a data vector, of length e. |
tconv |
a data matrix, of size e x s, with each column a vertex of the tropical polytope. e is the dimension of the tropical space and s is the number of vertices of the polytope |
Value
A projected vector on the given tropical polytope.
Examples
# Generate a tropical polytope consisting of three trees each with 5 leaves
library(ape)
pltp <- sapply(1:3, function(i) {
as.vector(rcoal(5))
})
# Generate an observation and vectorize it
tree <- rcoal(5)
tree_vec <- as.vector(tree)
tropproj.poly(tree_vec, pltp)
Compute Tropical Line Segment
Description
Compute Tropical Line Segment
Usage
tropseg(D1, D2, flag = FALSE)
Arguments
D1 |
a vector of length 2. |
D2 |
a vector of length 2. |
flag |
a logical value indicating if to swap |
Value
A list containing the following:
1 |
End points as columns of each line component. |
2 |
Overall length of the tropical line segment |
Tropical Support Vector Machines
Description
Fit a discriminative two-class classifier via linear programming defined by the tropical hyperplane which maximizes the minimum tropical distance from data points to itself in order to separate the data points into sectors (half-spaces) in the tropical projective torus.
Usage
tropsvm(x, y, auto.assignment = FALSE, assignment = NULL, ind = 1)
Arguments
x |
a data matrix, of dimension nobs x nvars; each row is an observation vector. |
y |
a response vector with one label for each row/component of x. |
auto.assignment |
a logical value indicating if to provide an |
assignment |
a numeric vector of length 4 indicating the sectors of tropical hyperplane that the
data will be assigned to. The first and third elements in the |
ind |
a numeric value or a numeric vector ranging from 1 to 70 indicating which classification method
to be used. There are 70 different classification methods. Details of a given method can be retrieved by |
Value
An object with S3 class tropsvm containing the fitted model, including:
apex |
The negative apex of the fitted optimal tropical hyperplane. |
assignment |
The user-input or auto-found |
index |
The user-input classification method. |
levels |
The name of each category, consistent with categories in |
See Also
predict, coef and the cv.tropsvm function.
Examples
# data generation
library(Rfast)
e <- 100
n <- 10
N <- 100
s <- 10
x <- rbind(
rmvnorm(n, mu = c(5, -5, rep(0, e - 2)), sigma = diag(s, e)),
rmvnorm(n, mu = c(-5, 5, rep(0, e - 2)), sigma = diag(s, e))
)
y <- as.factor(c(rep(1, n), rep(2, n)))
newx <- rbind(
rmvnorm(N, mu = c(5, -5, rep(0, e - 2)), sigma = diag(s, e)),
rmvnorm(N, mu = c(-5, 5, rep(0, e - 2)), sigma = diag(s, e))
)
newy <- as.factor(rep(c(1, 2), each = N))
# train the tropical svm
tropsvm_fit <- tropsvm(x, y, auto.assignment = TRUE, ind = 1)
coef(tropsvm_fit)
# test with new data
pred <- predict(tropsvm_fit, newx)
# check with accuracy
table(pred, newy)
# compute testing accuracy
sum(pred == newy) / length(newy)
Helper for cv.tropsvm
Description
Helper for cv.tropsvm
Usage
tropsvm_helper(x, y, assignment = NULL, ind = 1, newx = NULL, newy = NULL)
Arguments
x |
a data matrix, of dimension nobs x nvars; each row is an observation vector. |
y |
a response vector with one label for each row/component of x. |
assignment |
a numeric vector of length 4 indicating the sectors of tropical hyperplane that the
data will be assigned to. The first and third elements in the |
ind |
a numeric value or a numeric vector ranging from 1 to 70 indicating which classification method
to be used. There are 70 different classification methods. Details of a given method can be retrieved by |
newx |
the same as "x" but only needed in |
newy |
the same as "y" but only needed in |
Value
Classification accuracy