| Type: | Package |
| Title: | Construct an Unsupervised Hidden Markov Model |
| Version: | 1.0 |
| Date: | 2016-03-18 |
| Author: | Emilie POISSON-CAILLAULT [aut], Paul TERNYNCK [aut, cre] |
| Maintainer: | Paul TERNYNCK <ternynck@lisic.univ-littoral.fr> |
| Description: | Construct a Hidden Markov Model with states learnt by unsupervised classification. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| RoxygenNote: | 5.0.1 |
| LazyData: | TRUE |
| Depends: | R (≥ 3.0.0), stats, grDevices |
| Imports: | tcltk, tcltk2, tkrplot, HMM, clValid, class, cluster, FactoMineR, corrplot, chron |
| NeedsCompilation: | no |
| Packaged: | 2016-04-22 13:03:49 UTC; ternynck |
| Repository: | CRAN |
| Date/Publication: | 2016-04-22 16:25:47 |
Construct an unsupervised Hidden Markov Model
Description
This package proposes an interface to detect usual or extreme events in a dataset and to characterize their dynamic, by building an unsupervised Hidden Markov Model (use uHMMinterface to launch the interface).
Functions can also be used out of the interface to build an uHMM.
Details
| Package: | uHMM |
| Version: | 1.0 |
| Date: | 2016-04-13 |
| Depends: | R (>= 3.0.0), stats, grDevices |
| Import: | tcltk, tcltk2, tkrplot, HMM, clValid, class, cluster, FactoMineR, corrplot, chron |
| License: | GPL (>=2) |
| LazyLoad: | yes |
Author(s)
Emilie Poisson-Caillault and Paul Ternynck
Maintainer: <emilie.caillault@lisic.univ-littoral.fr>
Source
Rousseeuw, Kevin, et al. "Hybrid hidden Markov model for marine environment monitoring." Selected Topics in Applied Earth Observations and Remote Sensing, IEEE Journal of 8.1 (2015): 204-213.
Jordan Fast Spectral Algorithm
Description
Perform the Jordan spectral algorithm for large databases. Data are sampled, using K-means with Elbow criteria, before being classified.
Usage
FastSpectralNJW(data, nK = NULL, Kech = 2000, StopCriteriaElbow = 0.97,
neighbours = 7, method = "", nb.iter = 10, uHMMinterface = FALSE,
console = NULL, tm = NULL)
Arguments
data |
numeric matrix or dataframe. |
nK |
number of clusters desired. If NULL, optimal number of clusters will be computed using gap criteria. |
Kech |
maximum number of representative points in sampled data. |
StopCriteriaElbow |
maximum (minimum ?) de variance expliquees des points representatifs souhaite. |
neighbours |
number of neighbours considered for the computation of local scale parameters. |
method |
string specifying the spectral classification method desired, either "PAM" (for spectral kmedoids) or "" (for "spectral kmeans"). |
nb.iter |
number of iterations. |
uHMMinterface |
logical indicating whether the function is used via the uHMMinterface. |
console |
frame of the uHMM interface in which messages should be displayed (only if uHMMinterface=TRUE). |
tm |
a one row dataframe containing text to display in the uHMMinterface (only if uHMMinterface=TRUE). |
Details
Algorithme de Jordan pour un grand jeu de donnees : echantillonage puis spectral
Value
The function returns a list containing:
sim |
similarity matrix of representative points, multiplied by its transpose ( |
label |
vector of cluster sequencing. |
gap |
number of clusters. |
labelElbow |
vector of prototype sequencing. |
vpK |
matrix containing, in columns, the K first normalised eigen vectors of the data similarity matrix. |
valp |
vector containing the K first eigen values of the data similarity matrix. |
echantillons |
matrix of prototypes coordinates. |
label.echantillons |
vector containing the cluster of each prototype. |
numSymbole |
vector containing the nearest prototype of each data item. |
See Also
KmeansAutoElbow ZPGaussianSimilarity knn
silhouette dunn connectivity dist
Examples
x=(runif(1000)*4)-2;y=(runif(1000)*4)-2
keep<-which((x**2+y**2<0.5)|(x**2+y**2>1.5**2 & x**2+y**2<2**2 ))
data<-data.frame(x,y)[keep,]
cl<-FastSpectralNJW(data,2)
plot(data,col=cl$label)
Hidden Markov Model parameter estimation
Description
This function is used by the uHMMinterface to estimate parameters of a Hidden Markov Model.
Usage
HMMparams(stateSeq, symbolSeq)
Arguments
stateSeq |
a numeric vector of state sequencing. |
symbolSeq |
a numeric vector of symbol sequencing. |
Value
HMMparams returns a list containing :
trans |
The transition matrix. |
emis |
The emission matrix. |
startProb |
The vector of initial probability distribution (initial states are supposed equiprobable). |
See Also
transitionMatrix emissionMatrix
KmeansAutoElbow function
Description
KmeansAutoElbow performs k-means clustering on a dataframe with selection of optimal number of clusters using elbow criteria.
Usage
KmeansAutoElbow(features, Kmax, StopCriteria = 0.99, graph = FALSE)
Arguments
features |
dataframe or matrix of raw data. |
Kmax |
maximum number of clusters allowed. |
StopCriteria |
elbow method cumulative explained variance > criteria to stop K-search. (???) |
graph |
boolean, if TRUE figures are plotted. |
Details
KmeansAutoElbow returns partition and K number of groups according to kmeans clustering and Elbow method
Value
The function returns a list containing the following components:
K |
number of clusters in data according to explained variance and kmeans algorithm. |
res.kmeans |
an object of class "kmeans" (see |
See Also
Examples
x <- rbind(matrix(rnorm(300, mean = 0, sd = 0.3), ncol = 2),
matrix(rnorm(100, mean = 2, sd = 0.3), ncol = 2),
matrix(rnorm(100, mean = 4, sd = 0.3), ncol = 2))
colnames(x) <- c("x", "y")
km<-KmeansAutoElbow(x,round(dim(x)/25,0)[1],StopCriteria=0.99,graph=TRUE)
plot(x,col=km$res.kmeans$cluster)
points(km$res.kmeans$centers, col = 1:km$K, pch = 16)
KpartitionNJW function
Description
Perform spectral classification on the similarity matrix of a dataset (Ng et al. (2001) algorithm), using kmeans algorithm on data projected in the space of its K first eigen vectors.
Usage
KpartitionNJW(similarity, K)
Arguments
similarity |
matrix of similarity. |
K |
number of clusters. |
Value
The function returns a list containing:
label |
vector of cluster sequencing. |
centres |
matrix of cluster centers in the space of the K first normalised eigen vectors. |
vecteursPropresProjK |
matrix containing, in columns, the K first normalised eigen vectors of the similarity matrix. |
valeursPropresK |
vector containing the K first eigen values of the similarity matrix. |
vecteursPropres |
matrix containing, in columns, eigen vectors of the similarity matrix. |
valeursPropres |
vector containing eigen values of the similarity matrix. |
inertieZ |
vector of within-cluster sum of squares, one component per cluster. |
References
Ng Andrew, Y., M. I. Jordan, and Y. Weiss. "On spectral clustering: analysis and an algorithm [C]." Advances in Neural Information Processing Systems (2001).
Examples
#####
x <- rbind(matrix(rnorm(100, mean = 0, sd = 0.3), ncol = 2),
matrix(rnorm(100, mean = 2, sd = 0.3), ncol = 2),
matrix(rnorm(100, mean = 4, sd = 0.3), ncol = 2))
similarity<-ZPGaussianSimilarity(x,7)
similarity=similarity%*%t(similarity)
sp<-KpartitionNJW(similarity,3)
plot(x,col=sp$label)
#####
x <- rbind(data.frame(x=1:100+(runif(100)-0.5)*2,y=runif(100)/5),
data.frame(x=1:100+(runif(100)-0.5)*2,y=runif(100)/5+1),
data.frame(x=1:100+(runif(100)-0.5)*2,y=runif(100)/5+2))
similarity<-ZPGaussianSimilarity(x,7)
similarity=similarity%*%t(similarity)
sp<-KpartitionNJW(similarity,3)
plot(x,col=sp$label)
#####
x=(runif(1000)*4)-2;y=(runif(1000)*4)-2
keep<-which((x**2+y**2<0.5)|(x**2+y**2>1.5**2 & x**2+y**2<2**2 ))
data<-data.frame(x,y)[keep,]
similarity=ZPGaussianSimilarity(data, 7)
similarity=similarity%*%t(similarity)
sp<-KpartitionNJW(similarity,2)
plot(data,col=sp$label)
MarelCarnot dataset
Description
The MarelCarnot data set gives the measurements of 14 physico-chemical and biological parameters performed by the Marel-Carnot station (Boulogne-sur-Mer, France), at high frequency resolution.
Usage
MarelCarnot
Format
A data frame with 131487 rows and 16 columns.
Details
| Dates | date of measurement | (YYYY:MM:DD) |
| Hours | time of measurement | (HH:MM:SS) |
| C_NI1 | nitrate concentration | (in \mumol/L) |
| C_PO1 | phosphate concentration | (in \mumol/L) |
| C_O21 | corrected dissolved oxygen | (in mg/L) |
| C_SI1 | silicate concentration | (in \mumol/L) |
| CSAL1 | salinity | (in PSU) |
| CSAT1 | oxygen saturation | (in %) |
| ETCO1 | air temperature | (in degrees Celsius) |
| E_LU1 | P.A.R | (in \mumol of photons/s/m2) |
| E_O21 | uncorrected dissolved oxygen | (in mg/L) |
| E_PH1 | pH | |
| E_TU1 | turbidity | (in NTU) |
| ECHL1 | fluorescence | (in FFU) |
| E__TA | water temperature | (in degrees Celsius) |
| XMAHH | water level | (in m) |
Source
Lefebvre Alain (2015). MAREL Carnot data and metadata from Coriolis Data Centre. SEANOE. http://doi.org/10.17882/39754
Similarity matrix with local scale parameter
Description
Compute and return the similarity matrix of a data frame using gaussian kernel with a local scale parameter for each data point, rather than a unique scale parameter.
Usage
ZPGaussianSimilarity(data, K)
Arguments
data |
a matrix or numeric data frame. |
K |
number of neighbours considered to compute scale parameters. |
Value
The matrix of similarity.
References
Zelnik-Manor, Lihi, and Pietro Perona. "Self-tuning spectral clustering." Advances in neural information processing systems. 2004.
Examples
x <- rbind(matrix(rnorm(50, mean = 0, sd = 0.3), ncol = 2))
similarity<-ZPGaussianSimilarity(x,7)
Compute gap between eigenvalues of a similarity matrix
Description
Find the highest gap between eigenvalues of a similarity matrix. The 2 first eigenvalues are considered as equal to each other (the gap between the 2 first eigenvalues is set to 0).
Usage
computeGap(similarity, Gmax)
Arguments
similarity |
a similarity matrix. |
Gmax |
the maximum gap value allowed (only the first Gmax eigenvalues will be taken into account). |
Value
The function returns a list containing the following components:
gap |
a vector indicating the gap between similarity matrix eigenvalues (the gap between the 2 first eigenvalues is set to 0) |
Kmax |
an integer indicating the index of the highest gap (the highest gap is between the Kmax-th and the (Kmax+1)-th eigenvalues) |
Examples
x <- rbind(matrix(rnorm(50, mean = 0, sd = 0.3), ncol = 2),
matrix(rnorm(50, mean = 2, sd = 0.3), ncol = 2),
matrix(rnorm(50, mean = 4, sd = 0.3), ncol = 2))
similarity<-ZPGaussianSimilarity(x,7)
Gap<-computeGap(similarity,10)
plot(1:length(Gap$gap),Gap$gap,type="h",
main=paste("Gap criteria =",Gap$K),ylab="gap value",xlab="eigenvalues")
x=(runif(1000)*4)-2;y=(runif(1000)*4)-2
keep<-which((x**2+y**2<0.5)|(x**2+y**2>1.5**2 & x**2+y**2<2**2 ))
data<-data.frame(x,y)[keep,]
plot(data)
similarity<-ZPGaussianSimilarity(data,1)
Gap<-computeGap(similarity,10)
plot(1:length(Gap$gap),Gap$gap,type="h",
main=paste("Gap criteria =",Gap$K),ylab="gap value",xlab="eigenvalues")
cutCalculation function
Description
Compute intra and inter-cluster cuts from the similarity matrix of a dataset.
Usage
cutCalculation(similarity, label, K)
Arguments
similarity |
a similarity matrix. |
label |
vector of cluster sequencing. |
K |
number of clusters. (= nbCluster CALCULE DANS LA FONCTION ???) |
Details
intra cluster cut :
Cut(g_{k},g_{l}) = \sum_{i=1,x(i)\in g_{k}}^{N_{p}}\sum_{j=1,x(j)\in g_{l}}^{N_{p}}w(x(i),x(j))
Value
The function returns a list containing:
mncut |
the inter-cluster cut, i.e. K-sum(ratioCutVol). |
ratioCutVol |
vector of intra-cluster cuts, one component per cluster. |
Examples
x<-rbind(matrix(runif(100),ncol=2),matrix(runif(100)+2,ncol=2),matrix(runif(20)*3,ncol=2))
similarity<-ZPGaussianSimilarity(x,7)%*%t(ZPGaussianSimilarity(x,7))
km<-kmeans(similarity,2)
label<-km$cluster
plot(x,col=km$cluster)
cutCalculation(similarity,label,length(unique(label)))
Emission matrix estimation
Description
This function estimates the emission matrix of a Hidden Markov Model from vectors of state and symbol sequencing.
Usage
emissionMatrix(states, symbols)
Arguments
states |
a numeric vector of state sequencing. |
symbols |
a numeric vector of symbol sequencing. |
Value
Estimated emission matrix.
See Also
Examples
states<-c(1,1,3,2,1,2,1,3)
symbols<-c(4,1,3,1,4,4,4,2)
B<-emissionMatrix(states,symbols)
B
Self KNN
Description
This function performs the k-Nearest Neighbour algorithm without class estimation, but only computation of distances and neighbours.
Usage
selfKNN(train, K = 1)
Arguments
train |
numeric matrix or data frame. |
K |
number of neighbours considered. |
Value
The function returns a list with the following components:
D |
matrix of squared root of the distances between observations and their nearest neighbours. |
idx |
Index of K nearest neighbours of each observation. |
Examples
x<-matrix(runif(10),ncol=2)
plot(x,pch=c("1","2","3","4","5"))
selfKNN(x,K=4)
spectralPamClusteringNg function
Description
Perform spectral classification on the similarity matrix of a dataset, using pam algorithm (a more robust version of K-means) on projected data.
Usage
spectralPamClusteringNg(similarity, K)
Arguments
similarity |
matrix of similarity |
K |
number of clusters |
Value
The function returns a list containing:
label |
vector of cluster sequencing. |
centres |
matrix of cluster medoids (similar in concept to means, but medoids are members of the dataset) in the space of the K first normalised eigen vectors. |
id.med |
integer vector of indices giving the medoid observation numbers. |
vecteursPropresProjK |
matrix containing, in columns, the K first normalised eigen vectors of the similarity matrix. |
valeursPropresK |
vector containing the K first eigen values of the similarity matrix. |
vecteursPropres |
matrix containing, in columns, eigen vectors of the similarity matrix. |
valeursPropres |
vector containing eigen values of the similarity matrix. |
cluster.info |
matrix, each row gives numerical information for one cluster. These are the cardinality of the cluster (number of observations), the maximal and average dissimilarity between the observations in the cluster and the cluster's medoid, the diameter of the cluster (maximal dissimilarity between two observations of the cluster), and the separation of the cluster (minimal dissimilarity between an observation of the cluster and an observation of another cluster). |
References
Ng Andrew, Y., M. I. Jordan, and Y. Weiss. "On spectral clustering: analysis and an algorithm [C]." Advances in Neural Information Processing Systems (2001).
See Also
Transition matrix estimation
Description
This function estimates the transition matrix of a (Hidden) Markov Model from a vector of state sequencing.
Usage
transitionMatrix(states)
Arguments
states |
a numeric vector of state sequencing. |
Value
Estimated transition matrix.
See Also
Examples
states<-c(1,1,3,2,1,2,1,3)
A<-transitionMatrix(states)
A
Graphical Interface to Build an uHMM
Description
A user-friendly interface to detect usual or extreme events in a dataset and to characterize their dynamic, by building an unsupervised Hidden Markov Model.
Usage
uHMMinterface(uHMMenv = NULL)
Arguments
uHMMenv |
an environment in which data and results will be stored. If NULL, a local environment will be created. |
Value
Results are saved in the directory chosen by the user.
References
Rousseeuw, Kevin, et al. "Hybrid hidden Markov model for marine environment monitoring." Selected Topics in Applied Earth Observations and Remote Sensing, IEEE Journal of 8.1 (2015): 204-213.