Help for package KODAMA

Version:

3.0

Date:

2025-06-03

Maintainer:

Stefano Cacciatore <tkcaccia@gmail.com>

Title:

Knowledge Discovery by Accuracy Maximization

Description:

A self-guided, weakly supervised learning algorithm for feature extraction from noisy and high-dimensional data. It facilitates the identification of patterns that reflect underlying group structures across all samples in a dataset. The method incorporates a novel strategy to integrate spatial information, improving the interpretability of results in spatially resolved data.

Depends:

R (≥ 2.10.0), stats, Rtsne, umap

Imports:

Rcpp (≥ 0.12.4), Rnanoflann, methods, Matrix

LinkingTo:

Rcpp, RcppArmadillo, Rnanoflann, Matrix

Suggests:

rgl, knitr, rmarkdown

VignetteBuilder:

knitr

SuggestsNote:

No suggestions

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

Packaged:

2025-06-03 13:22:30 UTC; user

NeedsCompilation:

yes

Repository:

CRAN

Author:

Stefano Cacciatore

[aut, trl, cre], Leonardo Tenori

[aut]

Date/Publication:

2025-06-03 15:10:10 UTC

Knowledge Discovery by Accuracy Maximization

Description

KODAMA (KnOwledge Discovery by Accuracy MAximization) is an unsupervised and semi-supervised learning algorithm that performs feature extraction from noisy and high-dimensional data.

Usage

KODAMA.matrix (data,                 
               spatial = NULL,     
               samples = NULL,
               M = 100, Tcycle = 20, 
               FUN = c("fastpls","simpls"), 
               ncomp = min(c(50,ncol(data))),
               W = NULL, metrics="euclidean",
               constrain = NULL, fix = NULL,  landmarks = 10000,  
               splitting = ifelse(nrow(data) < 40000, 100, 300), 
               spatial.resolution = 0.3 , 
               simm_dissimilarity_matrix=FALSE,
               seed=1234)

Arguments

data

A numeric matrix where rows are samples and columns are variables.

spatial

Optional matrix of spatial coordinates or NULL. Used to apply spatial constraints.

samples

An optional vector indicating the identity for each sample. Can be used to guide the integration of prior sample-level information.

M

Number of iterative processes.

Tcycle

Number of cycles to optimize cross-validated accuracy.

FUN

Classifier to be used. Options are "fastpls" or "simpls".

ncomp

Number of components for the PLS classifier. Default is min(50, ncol(data)).

W

A vector of initial class labels for each sample (length = nrow(data)). Defaults to unique labels for each sample if NULL.

metrics

Distance metric to be used (default is "euclidean").

constrain

An optional vector indicating group constraints. Samples sharing the same value in this vector will be forced to stay in the same cluster.

fix

A logical vector indicating whether each sample's label in W should be fixed during optimization. Defaults to all FALSE.

landmarks

Number of landmark points used to approximate the similarity structure. The default is 10000.

splitting

Number of random sample splits used during optimization. The default is 100 for small datasets (<40000 samples) and 300 otherwise.

spatial.resolution

A numeric value (default 0.3) controlling the resolution of spatial constraints.

simm_dissimilarity_matrix

Logical. If TRUE, the function returns a similarity/dissimilarity matrix. Default is FALSE.

seed

Random seed for reproducibility. The default is 1234.

Details

KODAMA consists of five steps. These can be in turn divided into two parts: (i) the maximization of cross-validated accuracy by an iterative process (step I and II), resulting in the construction of a proximity matrix (step III), and (ii) the definition of a dissimilarity matrix (step IV and V). The first part entails the core idea of KODAMA, that is, the partitioning of data guided by the maximization of the cross-validated accuracy. At the beginning of this part, a fraction of the total samples (defined by FUN_SAM) are randomly selected from the original data. The whole iterative process (step I-III) is repeated M times to average the effects owing to the randomness of the iterative procedure. Each time that this part is repeated, a different fraction of samples is selected. The second part aims at collecting and processing these results by constructing a dissimilarity matrix to provide a holistic view of the data while maintaining their intrinsic structure (steps IV and V). Then, KODAMA.visualization function is used to visualise the results of KODAMA dissimilarity matrix.

Value

The function returns a list with 4 items:

dissimilarity

a dissimilarity matrix.

acc

a vector with the M cross-validated accuracies.

proximity

a proximity matrix.

v

a matrix containing all classifications obtained maximizing the cross-validation accuracy.

res

a matrix containing all classification vectors obtained through maximizing the cross-validation accuracy.

knn_Rnanoflann

dissimilarity matrix used as input for the KODAMA.visualization function.

data

original data.

res_constrain

the constrins used.

Author(s)

Stefano Cacciatore and Leonardo Tenori

References

Abdel-Shafy EA, Kassim M, Vignol A, et al.
KODAMA enables self-guided weakly supervised learning in spatial transcriptomics.
bioRxiv 2025. doi: 10.1101/2025.05.28.656544. doi:10.1101/2025.05.28.656544

Cacciatore S, Luchinat C, Tenori L
Knowledge discovery by accuracy maximization.
Proc Natl Acad Sci U S A 2014;111(14):5117-5122. doi: 10.1073/pnas.1220873111. doi:10.1073/pnas.1220873111

L.J.P. van der Maaten and G.E. Hinton.
Visualizing High-Dimensional Data Using t-SNE.
Journal of Machine Learning Research 9 (Nov): 2579-2605, 2008.

L.J.P. van der Maaten.
Learning a Parametric Embedding by Preserving Local Structure.
In Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics (AISTATS), JMLR W&CP 5:384-391, 2009.

McInnes L, Healy J, Melville J.
Umap: Uniform manifold approximation and projection for dimension reduction.
arXiv preprint:1802.03426. 2018 Feb 9.

Examples



 data(iris)
 data=iris[,-5]
 labels=iris[,5]
 kk=KODAMA.matrix(data,ncomp=2)
 cc=KODAMA.visualization(kk,"t-SNE")
 plot(cc,col=as.numeric(labels),cex=2)

Visualization of KODAMA output

Description

Provides a simple function to transform the KODAMA dissimilarity matrix in a low-dimensional space.

Usage

KODAMA.visualization(kk,
                     method=c("UMAP", "t-SNE", "MDS"),
                     config=NULL)

Arguments

kk

output of KODAMA.matrix function.

method

method to be considered for transforming the dissimilarity matrix into a low-dimensional space. Choices are "t-SNE", "MDS", and "UMAP".

config

object of class umap.config or tsne.config.

Value

The function returns a matrix that contains the coordinates of the datapoints in a low-dimensional space.

Author(s)

Stefano Cacciatore and Leonardo Tenori

References

Cacciatore S, Luchinat C, Tenori L
Knowledge discovery by accuracy maximization.
Proc Natl Acad Sci U S A 2014;111(14):5117-5122. doi: 10.1073/pnas.1220873111. doi:10.1073/pnas.1220873111

L.J.P. van der Maaten and G.E. Hinton.
Visualizing High-Dimensional Data Using t-SNE.
Journal of Machine Learning Research 9 (Nov) : 2579-2605, 2008.

L.J.P. van der Maaten.
Learning a Parametric Embedding by Preserving Local Structure.
In Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics (AISTATS), JMLR W&CP 5:384-391, 2009.

McInnes L, Healy J, Melville J.
Umap: Uniform manifold approximation and projection for dimension reduction.
arXiv preprint:1802.03426. 2018 Feb 9.

Examples



 data(iris)
 data=iris[,-5]
 labels=iris[,5]
 kk=KODAMA.matrix(data,ncomp=2)
 cc=KODAMA.visualization(kk,"t-SNE")
 plot(cc,col=as.numeric(labels),cex=2)

Default configuration for RMDS

Description

A list with parameters customizing an MDS embedding.

Usage

  MDS.defaults

Format

An object of class MDS.defaults of length 1.

Details

dims: integer, Output dimensionality

Examples

  # display all default settings
  MDS.defaults
  
  # create a new settings object with perplexity set to 100
  custom.settings = MDS.defaults
  custom.settings$dims = 3
  custom.settings

Nuclear Magnetic Resonance Spectra of Urine Samples

Description

The data belong to a cohort of 22 healthy donors (11 male and 11 female) where each provided about 40 urine samples over the time course of approximately 2 months, for a total of 873 samples. Each sample was analysed by Nuclear Magnetic Resonance Spectroscopy. Each spectrum was divided in 450 spectral bins.

Usage

data(MetRef)

Value

A list with the following elements:

data

Metabolomic data. A matrix with 873 rows and 450 columns.

gender

Gender index. A vector with 873 elements.

donor

Donor index. A vector with 873 elements.

References

Assfalg M, Bertini I, Colangiuli D, et al.
Evidence of different metabolic phenotypes in humans.
Proc Natl Acad Sci U S A 2008;105(5):1420-4. doi: 10.1073/pnas.0705685105. doi:10.1073/pnas.0705685105

Cacciatore S, Luchinat C, Tenori L
Knowledge discovery by accuracy maximization.
Proc Natl Acad Sci U S A 2014;111(14):5117-5122. doi: 10.1073/pnas.1220873111. doi:10.1073/pnas.1220873111

Examples


data(MetRef)
u=MetRef$data;
u=u[,-which(colSums(u)==0)]
u=normalization(u)$newXtrain
u=scaling(u)$newXtrain
class=as.numeric(as.factor(MetRef$donor))

u_pca=pca(u)$x[,1:5]

kk=KODAMA.matrix(u_pca,ncomp=2)
cc=KODAMA.visualization(kk,"t-SNE")
plot(cc,pch=21,bg=rainbow(22)[class])

State of the Union Data Set

Description

This dataset consists of the spoken, not written, addresses from 1900 until the sixth address by Barack Obama in 2014. Punctuation characters, numbers, words shorter than three characters, and stop-words (e.g., "that", "and", and "which") were removed from the dataset. This resulted in a dataset of 86 speeches containing 834 different meaningful words each. Term frequency-inverse document frequency (TF-IDF) was used to obtain feature vectors. It is often used as a weighting factor in information retrieval and text mining. The TF-IDF value increases proportionally to the number of times a word appears in the document, but is offset by the frequency of the word in the corpus, which helps to control for the fact that some words are generally more common than others.

Usage

data(USA)

Value

A list with the following elements:

data

TF-IDF data. A matrix with 86 rows and 834 columns.

year

Year index. A vector with 86 elements.

president

President index. A vector with 86 elements.

Author(s)

Stefano Cacciatore and Leonardo Tenori

References

Cacciatore S, Luchinat C, Tenori L
Knowledge discovery by accuracy maximization.
Proc Natl Acad Sci U S A 2014;111(14):5117-5122. doi: 10.1073/pnas.1220873111. doi:10.1073/pnas.1220873111

Examples


# Here is reported the analysis on the State of the Union
# of USA president as shown in Cacciatore, et al. (2014)

data(USA)

pp=pca(USA$data)$x[,1:50]

kk=KODAMA.matrix(pp,ncomp=2)
custom.settings=tsne.defaults
custom.settings$perplexity = 10
cc=KODAMA.visualization(kk,"t-SNE",config=custom.settings)
oldpar <- par(cex=0.5,mar=c(15,6,2,2));
plot(USA$year,cc[,1],axes=FALSE,pch=20,xlab="",ylab="First Component");
axis(1,at=USA$year,labels=rownames(USA$data),las=2);
axis(2,las=2);
box()

par(oldpar)

Maximization of Cross-Validateed Accuracy Methods

Description

This function performs the maximization of cross-validated accuracy by an iterative process

Usage

core_cpp(x,
         xTdata = NULL, 
         clbest, 
         Tcycle = 20, 
         FUN = c("fastpls","simpls"), 
         f.par.pls = 5, 
         constrain = NULL, 
         fix = NULL)

Arguments

x

a matrix.

xTdata

a matrix for projections. This matrix contains samples that are not used for the maximization of the cross-validated accuracy. Their classification is obtained by predicting samples on the basis of the final classification vector.

clbest

a vector to optimize.

Tcycle

number of iterative cycles that leads to the maximization of cross-validated accuracy.

FUN

classifier to be consider. Choices are "fastpls" and "simpls".

f.par.pls

parameters of the classifier. If the classifier is KNN, fpar represents the number of neighbours. If the classifier is PLS-DA, fpar represents the number of components.

constrain

a vector of nrow(data) elements. Supervised constraints can be imposed by linking some samples in such a way that if one of them is changed, all other linked samples change in the same way (i.e., they are forced to belong to the same class) during the maximization of the cross-validation accuracy procedure. Samples with the same identifying constrain will be forced to stay together.

fix

a vector of nrow(data) elements. The values of this vector must be TRUE or FALSE. By default all elements are FALSE. Samples with the TRUE fix value will not change the class label defined in W during the maximization of the cross-validation accuracy procedure. For more information refer to Cacciatore, et al. (2014).

Value

The function returns a list with 3 items:

clbest

a classification vector with a maximized cross-validated accuracy.

accbest

the maximum cross-validated accuracy achieved.

vect_acc

a vector of all cross-validated accuracies obtained.

vect_proj

a prediction of samples in xTdata matrix using the vector clbest. This output is present only if xTdata is not NULL.

Author(s)

Stefano Cacciatore and Leonardo Tenori

References

Cacciatore S, Luchinat C, Tenori L
Knowledge discovery by accuracy maximization.
Proc Natl Acad Sci U S A 2014;111(14):5117-5122. doi: 10.1073/pnas.1220873111. doi:10.1073/pnas.1220873111

Examples

# Here, the famous (Fisher's or Anderson's) iris data set was loaded
data(iris)
u=as.matrix(iris[,-5])
s=sample(1:150,150,TRUE)

# The maximization of the accuracy of the vector s is performed
results=core_cpp(u, clbest=s,f.par.pls  = 4)


print(as.numeric(results$clbest))

Ulisse Dini Data Set Generator

Description

This function creates a data set based upon data points distributed on a Ulisse Dini's surface.

Usage

dinisurface(N=1000)

Arguments

N

Number of data points.

Value

The function returns a three dimensional data set.

Author(s)

Stefano Cacciatore and Leonardo Tenori

References

Cacciatore S, Luchinat C, Tenori L
Knowledge discovery by accuracy maximization.
Proc Natl Acad Sci U S A 2014;111(14):5117-5122. doi: 10.1073/pnas.1220873111. doi:10.1073/pnas.1220873111

Examples

require("rgl")
x=dinisurface()
open3d()
plot3d(x, col=rainbow(1000),box=FALSE,size=3)

Find Shortest Paths Between All Nodes in a Graph

Description

The floyd function finds all shortest paths in a graph using Floyd's algorithm.

Usage

floyd(data)

Arguments

data

matrix or distance object

Value

floyd returns a matrix with the total lengths of the shortest path between each pair of points.

References

Floyd, Robert W
Algorithm 97: Shortest Path.
Communications of the ACM 1962; 5 (6): 345. doi:10.1145/367766.368168.

Examples

# build a graph with 5 nodes
x=matrix(c(0,NA,NA,NA,NA,30,0,NA,NA,NA,10,NA,0,NA,NA,NA,70,50,0,10,NA,40,20,60,0),ncol=5)
print(x)

# compute all path lengths
z=floyd(x)
print(z)

Internal Grid Functions

Description

Internal Grid functions

Details

These are not to be called by the user (or in some cases are just waiting for proper documentation to be written :).

Value

The return values of these function are used for internal usage.

Helicoid Data Set Generator

Description

This function creates a data set based upon data points distributed on a Helicoid surface.

Usage

helicoid(N=1000)

Arguments

N

Number of data points.

Value

The function returns a three dimensional data set.

Author(s)

Stefano Cacciatore and Leonardo Tenori

References

Cacciatore S, Luchinat C, Tenori L
Knowledge discovery by accuracy maximization.
Proc Natl Acad Sci U S A 2014;111(14):5117-5122. doi: 10.1073/pnas.1220873111. doi:10.1073/pnas.1220873111

Examples

require("rgl")
x=helicoid()
open3d()
plot3d(x, col=rainbow(1000),box=FALSE,size=3)

Kabsch Algorithm

Description

Aligns two sets of points via rotations and translations. Given two sets of points, with one specified as the reference set, the other set will be rotated so that the RMSD between the two is minimized. The format of the matrix is that there should be one row for each of n observations, and the number of columns, d, specifies the dimensionality of the points. The point sets must be of equal size and with the same ordering, i.e. point one of the second matrix is mapped to point one of the reference matrix, point two of the second matrix is mapped to point two of the reference matrix, and so on.

Usage

kabsch (pm, qm)

Arguments

pm

n x d matrix of points to align to to qm.

qm

n x d matrix of reference points.

Value

Matrix pm rotated and translated so that the ith point is aligned to the ith point of qm in the least-squares sense.

Author(s)

James Melville

Examples

data=iris[,-5]
pp1=pca(data)$x
pp2=pca(scale(data))$x
pp3=kabsch(pp1,pp2)
plot(pp1,pch=21,bg=rep(2:4,each=50))
points(pp3,pch=21,bg=rep(2:4,each=50),col=5)

Lymphoma Gene Expression Dataset

Description

This dataset consists of gene expression profiles of the three most prevalent adult lymphoid malignancies: diffuse large B-cell lymphoma (DLBCL), follicular lymphoma (FL), and B-cell chronic lymphocytic leukemia (B-CLL). The dataset consists of 4,682 mRNA genes for 62 samples (42 samples of DLBCL, 9 samples of FL, and 11 samples of B-CLL). Missing value are imputed and data are standardized as described in Dudoit, et al. (2002).

Usage

data(lymphoma)

Value

A list with the following elements:

data

Gene expression data. A matrix with 62 rows and 4,682 columns.

class

Class index. A vector with 62 elements.

References

Cacciatore S, Luchinat C, Tenori L
Knowledge discovery by accuracy maximization.
Proc Natl Acad Sci U S A 2014;111(14):5117-5122. doi: 10.1073/pnas.1220873111. doi:10.1073/pnas.1220873111

Cacciatore S, Tenori L, Luchinat C, Bennett PR, MacIntyre DA
KODAMA: an updated R package for knowledge discovery and data mining.
Bioinformatics 2017;33(4):621-623. doi: 10.1093/bioinformatics/btw705. doi:10.1093/bioinformatics/btw705

Alizadeh AA, Eisen MB, Davis RE, et al.
Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling.
Nature 2000;403(6769):503-511.

Dudoit S, Fridlyand J, Speed TP
Comparison of discrimination methods for the classification of tumors using gene expression data.
J Am Stat Assoc 2002;97(417):77-87.

Examples


data(lymphoma)
class=1+as.numeric(lymphoma$class)
cc=pca(lymphoma$data)$x[,1:50]
plot(cc,pch=21,bg=class)

kk=KODAMA.matrix(cc,ncomp=2)

custom.settings=tsne.defaults
custom.settings$perplexity = 10
cc=KODAMA.visualization(kk,"t-SNE",config=custom.settings)

plot(cc,pch=21,bg=class)

Evaluation of the Monte Carlo accuracy results

Description

This function can be used to plot the accuracy values obtained during KODAMA procedure.

Usage

mcplot(model)

Arguments

model

output of KODAMA.

Value

No return value.

Author(s)

Stefano Cacciatore

References

Cacciatore S, Luchinat C, Tenori L
Knowledge discovery by accuracy maximization.
Proc Natl Acad Sci U S A 2014;111(14):5117-5122. doi: 10.1073/pnas.1220873111. doi:10.1073/pnas.1220873111

Examples


 data=as.matrix(iris[,-5])
 kk=KODAMA.matrix(data)
 mcplot(kk)

Normalization Methods

Description

Collection of Different Normalization Methods.

Usage

normalization(Xtrain,Xtest=NULL, method = "pqn",ref=NULL)

Arguments

Xtrain

a matrix of data (training data set).

Xtest

a matrix of data (test data set).(by default = NULL).

method

the normalization method to be used. Choices are "none", "pqn", "sum", "median", "sqrt" (by default = "pqn"). A partial string sufficient to uniquely identify the choice is permitted.

ref

Reference sample for Probabilistic Quotient Normalization. (by default = NULL).

Details

A number of different normalization methods are provided:

"none": no normalization method is applied.
"pqn": the Probabilistic Quotient Normalization is computed as described in Dieterle, et al. (2006).
"sum": samples are normalized to the sum of the absolute value of all variables for a given sample.
"median": samples are normalized to the median value of all variables for a given sample.
"sqrt": samples are normalized to the root of the sum of the squared value of all variables for a given sample.

Value

The function returns a list with 2 items or 4 items (if a test data set is present):

newXtrain

a normalized matrix (training data set).

coeXtrain

a vector of normalization coefficient of the training data set.

newXtest

a normalized matrix (test data set).

coeXtest

a vector of normalization coefficient of the test data set.

Author(s)

Stefano Cacciatore and Leonardo Tenori

References

Dieterle F,Ross A, Schlotterbeck G, Senn H.
Probabilistic Quotient Normalization as Robust Method to Account for Diluition of Complex Biological Mixtures. Application in 1H NMR Metabolomics.
Anal Chem 2006;78:4281-90.

Cacciatore S, Luchinat C, Tenori L
Knowledge discovery by accuracy maximization.
Proc Natl Acad Sci U S A 2014;111(14):5117-5122. doi: 10.1073/pnas.1220873111. doi:10.1073/pnas.1220873111

Examples

data(MetRef)
u=MetRef$data;
u=u[,-which(colSums(u)==0)]
u=normalization(u)$newXtrain
u=scaling(u)$newXtrain
class=as.numeric(as.factor(MetRef$gender))
cc=pca(u)
plot(cc$x,pch=21,bg=class)

Principal Components Analysis

Description

Performs a principal components analysis on the given data matrix and returns the results as an object of class "prcomp".

Usage

pca(x, ...)

Arguments

x

a matrix of data.

...

arguments passed to prcomp function.

Value

The function returns a list with class prcomp containing the following components:

sdev

the standard deviations of the principal components (i.e., the square roots of the eigenvalues of the covariance/correlation matrix, though the calculation is actually done with the singular values of the data matrix).

rotation

the matrix of variable loadings (i.e., a matrix whose columns contain the eigenvectors). The function princomp returns this in the element loadings.

x

if retx is TRUE the value of the rotated data (the centred (and scaled if requested) data multiplied by the rotation matrix) is returned. Hence, cov(x) is the diagonal matrix diag(sdev^2). For the formula method, napredict() is applied to handle the treatment of values omitted by the na.action.

center, scale

the centering and scaling used, or FALSE.

txt

the component of variance of each Principal Component.

Author(s)

Stefano Cacciatore

References

Pearson, K
On Lines and Planes of Closest Fit to Systems of Points in Space.
Philosophical Magazine 1901;2 (11): 559-572. doi:10.1080/14786440109462720. Link

Examples

data(MetRef)
u=MetRef$data;
u=u[,-which(colSums(u)==0)]
u=normalization(u)$newXtrain
u=scaling(u)$newXtrain
class=as.numeric(as.factor(MetRef$gender))
cc=pca(u)
plot(cc$x,pch=21,bg=class)

Scaling Methods

Description

Collection of Different Scaling Methods.

Usage

scaling(Xtrain,Xtest=NULL, method = "autoscaling")

Arguments

Xtrain

a matrix of data (training data set).

Xtest

a matrix of data (test data set).(by default = NULL).

method

the scaling method to be used. Choices are "none", "centering", "autoscaling", "rangescaling", "paretoscaling" (by default = "autoscaling"). A partial string sufficient to uniquely identify the choice is permitted.

Details

A number of different scaling methods are provided:

"none": no scaling method is applied.
"centering": centers the mean to zero.
"autoscaling": centers the mean to zero and scales data by dividing each variable by the variance.
"rangescaling": centers the mean to zero and scales data by dividing each variable by the difference between the minimum and the maximum value.
"paretoscaling": centers the mean to zero and scales data by dividing each variable by the square root of the standard deviation. Unit scaling divides each variable by the standard deviation so that each variance equal to 1.

Value

The function returns a list with 1 item or 2 items (if a test data set is present):

newXtrain

a scaled matrix (training data set).

newXtest

a scale matrix (test data set).

Author(s)

Stefano Cacciatore and Leonardo Tenori

References

van den Berg RA, Hoefsloot HCJ, Westerhuis JA, et al.
Centering, scaling, and transformations: improving the biological information content of metabolomics data.
BMC Genomics 2006;7(1):142.

Cacciatore S, Luchinat C, Tenori L
Knowledge discovery by accuracy maximization.
Proc Natl Acad Sci U S A 2014;111(14):5117-5122. doi: 10.1073/pnas.1220873111. doi:10.1073/pnas.1220873111

Examples

data(MetRef)
u=MetRef$data;
u=u[,-which(colSums(u)==0)]
u=normalization(u)$newXtrain
u=scaling(u)$newXtrain
class=as.numeric(as.factor(MetRef$gender))
cc=pca(u)
plot(cc$x,pch=21,bg=class,xlab=cc$txt[1],ylab=cc$txt[2])

Spirals Data Set Generator

Description

Produces a data set of spiral clusters.

Usage

spirals(n=c(100,100,100),sd=c(0,0,0))

Arguments

n

a vector of integer. The length of the vector is the number of clusters and each number corresponds to the number of data points in each cluster.

sd

amount of noise for each spiral.

Value

The function returns a two dimensional data set.

Author(s)

Stefano Cacciatore and Leonardo Tenori

References

Cacciatore S, Luchinat C, Tenori L
Knowledge discovery by accuracy maximization.
Proc Natl Acad Sci U S A 2014;111(14):5117-5122. doi: 10.1073/pnas.1220873111. doi:10.1073/pnas.1220873111

Examples


v1=spirals(c(100,100,100),c(0.1,0.1,0.1))
plot(v1,col=rep(2:4,each=100))
v2=spirals(c(100,100,100),c(0.1,0.2,0.3))
plot(v2,col=rep(2:4,each=100))
v3=spirals(c(100,100,100,100,100),c(0,0,0.2,0,0))
plot(v3,col=rep(2:6,each=100))
v4=spirals(c(20,40,60,80,100),c(0.1,0.1,0.1,0.1,0.1))
plot(v4,col=rep(2:6,c(20,40,60,80,100)))

Swiss Roll Data Set Generator

Description

Computes the Swiss Roll data set of a given number of data points.

Usage

swissroll(N=1000)

Arguments

N

Number of data points.

Value

The function returns a three dimensional matrix.

Author(s)

Stefano Cacciatore and Leonardo Tenori

References

Balasubramanian M, Schwartz EL
The isomap algorithm and topological stability.
Science 2002;295(5552):7.

Roweis ST, Saul LK
Nonlinear dimensionality reduction by locally linear embedding.
Science 2000;290(5500):2323-6.

Cacciatore S, Luchinat C, Tenori L
Knowledge discovery by accuracy maximization.
Proc Natl Acad Sci U S A 2014;111(14):5117-5122. doi: 10.1073/pnas.1220873111. doi:10.1073/pnas.1220873111

Examples

require("rgl")
x=swissroll()
open3d()
plot3d(x, col=rainbow(1000),box=FALSE,size=3)

Conversion Classification Vector to Matrix

Description

This function converts a classification vector into a classification matrix.

Usage

transformy(y)

Arguments

y

a vector or factor.

Details

This function converts a classification vector into a classification matrix.

Value

A matrix.

Author(s)

Stefano Cacciatore and Leonardo Tenori

References

Examples

y=rep(1:10,3)
print(y)
z=transformy(y)
print(z)

Default configuration for Rtsne

Description

A list with parameters customizing a Rtsne embedding. Each component of the list is an effective argument for Rtsne_neighbors().

Usage

  tsne.defaults

Format

An object of class tsne.defaults of length 11.

Details

dims: integer, Output dimensionality

perplexity: numeric, Perplexity parameter (should not be bigger than 3 * perplexity < nrow(X) - 1, see details for interpretation)

theta: numeric, Speed/accuracy trade-off (increase for less accuracy), set to 0.0 for exact TSNE

max_iter: integer, Number of iterations

verbose: logical, Whether progress updates should be printed (default: global "verbose" option, or FALSE if that is not set)

Y_init: matrix, Initial locations of the objects. If NULL, random initialization will be used (default: NULL). Note that when using this, the initial stage with exaggerated perplexity values and a larger momentum term will be skipped.

momentum: numeric, Momentum used in the first part of the optimization

final_momentum: numeric, Momentum used in the final part of the optimization

eta: numeric, Learning rate

exaggeration_factor:

num_threads: integer, Number of threads to use when using OpenMP, default is 1. Setting to 0 corresponds to detecting and using all available cores

Examples

  # display all default settings
  tsne.defaults
  
  # create a new settings object with perplexity set to 100
  custom.settings = tsne.defaults
  custom.settings$perplexity = 100
  custom.settings

Default configuration for umap

Description

A list with parameters customizing a Rumap embedding. Each component of the list is an effective argument for Rumap_neighbors().

Usage

  umap.defaults

Format

An object of class umap.defaults of length 24.

Details

n_neighbors: integer; number of nearest neighbors

n_components: integer; dimension of target (output) space

metric: character or function; determines how distances between data points are computed. When using a string, available metrics are: euclidean, manhattan. Other available generalized metrics are: cosine, pearson, pearson2. Note the triangle inequality may not be satisfied by some generalized metrics, hence knn search may not be optimal. When using metric.function as a function, the signature must be function(matrix, origin, target) and should compute a distance between the origin column and the target columns

n_epochs: integer; number of iterations performed during layout optimization

input: character, use either "data" or "dist"; determines whether the primary input argument to umap() is treated as a data matrix or as a distance matrix

init: character or matrix. The default string "spectral" computes an initial embedding using eigenvectors of the connectivity graph matrix. An alternative is the string "random", which creates an initial layout based on random coordinates. This setting.can also be set to a matrix, in which case layout optimization begins from the provided coordinates.

min_dist: numeric; determines how close points appear in the final layout

set_op_ratio_mix_ratio: numeric in range [0,1]; determines who the knn-graph is used to create a fuzzy simplicial graph

local_connectivity: numeric; used during construction of fuzzy simplicial set

bandwidth: numeric; used during construction of fuzzy simplicial set

alpha: numeric; initial value of "learning rate" of layout optimization

gamma: numeric; determines, together with alpha, the learning rate of layout optimization

negative_sample_rate: integer; determines how many non-neighbor points are used per point and per iteration during layout optimization

a: numeric; contributes to gradient calculations during layout optimization. When left at NA, a suitable value will be estimated automatically.

b: numeric; contributes to gradient calculations during layout optimization. When left at NA, a suitable value will be estimated automatically.

spread: numeric; used during automatic estimation of a/b parameters.

random_state: integer; seed for random number generation used during umap()

transform_state: integer; seed for random number generation used during predict()

knn: object of class umap.knn; precomputed nearest neighbors

knn.repeat: number of times to restart knn search

verbose: logical or integer; determines whether to show progress messages

umap_learn_args: vector of arguments to python package umap-learn

Examples


# display all default settings
umap.defaults

# create a new settings object with n_neighbors set to 5
custom.settings = umap.defaults
custom.settings$n_neighbors = 5
custom.settings

Knowledge Discovery by Accuracy Maximization

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Visualization of KODAMA output

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Default configuration for RMDS

Description

Usage

Format

Details

Examples

Nuclear Magnetic Resonance Spectra of Urine Samples

Description

Usage

Value

References

Examples

State of the Union Data Set

Description

Usage

Value

Author(s)

References

Examples

Maximization of Cross-Validateed Accuracy Methods

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Ulisse Dini Data Set Generator

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Find Shortest Paths Between All Nodes in a Graph

Description

Usage

Arguments

Value

References

Examples

Internal Grid Functions

Description

Details

Value

Helicoid Data Set Generator

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Kabsch Algorithm

Description

Usage

Arguments