| Title: | A Fast, User-Friendly Implementation of Self-Organizing Maps (SOMs) |
|---|---|
| Description: | Methods for building self-organizing maps (SOMs) with a number of distinguishing features such automatic centroid detection and cluster visualization using starbursts. For more details see the paper "Improved Interpretability of the Unified Distance Matrix with Connected Components" by Hamel and Brown (2011) in <ISBN:1-60132-168-6>. The package provides user-friendly access to two models we construct: (a) a SOM model and (b) a centroid based clustering model. The package also exposes a number of quality metrics for the quantitative evaluation of the map, Hamel (2016) <doi:10.1007/978-3-319-28518-4_4>. Finally, we reintroduced our fast, vectorized training algorithm for SOM with substantial improvements. It is about an order of magnitude faster than the canonical, stochastic C implementation <doi:10.1007/978-3-030-01057-7_60>. |
| Authors: | Lutz Hamel [aut, cre], Benjamin Ott [aut], Gregory Breard [aut], Robert Tatoian [aut], Michael Eiger [aut], Vishakh Gopu [aut] |
| Maintainer: | Lutz Hamel <[email protected]> |
| License: | GPL-3 |
| Version: | 7.1.0 |
| Built: | 2025-03-02 18:30:38 UTC |
| Source: | https://github.com/cran/popsom7 |
Construct a self-organizing map and return an object of class ‘map’
map.build(data,labels=NULL,xdim=10,ydim=5, alpha=0.3,train=1000,normalize=FALSE, seed=NULL,minimal=FALSE)map.build(data,labels=NULL,xdim=10,ydim=5, alpha=0.3,train=1000,normalize=FALSE, seed=NULL,minimal=FALSE)
data |
A dataframe where each row contains an unlabeled training instance. |
labels |
A vector or dataframe with one label for each observation in data. |
xdim |
The x-dimension of the map. |
ydim |
The y-dimension of the map. |
alpha |
The learning rate, should be a value greater than zero and less or equal to one. |
train |
The number of training iterations. |
normalize |
Boolean switch indicating whether or not to normalize the data. |
seed |
A seed value for repeatablity of random initialization and selection. |
minimal |
Boolean switch indicating whether to build a ‘map.minimal’ or ‘map’ object. |
The function ‘map.build’ constructs an object of type ‘map’. The object contains two models: (1) A self-organizing map model expressed through its trained neurons and its quality of fit can be ascertained by the ‘convergence’ (see below). (2) A cluster model expressed by the discovered centroids. The quality of these models can be ascertained by the ‘map convergence’, ‘within cluster sum of squares’, and the ‘between cluster sum of squares’ (see below).
An object of type ‘map’. The object has the following member fields:
Data frame contining the possibly normalized training data.
Vector of labels, one for each observation in data or NULL if no labels were given.
The x dimension of the neuron map.
The y dimension of the neuron map.
The given learning rate for the neural network.
The training iterations applied to the neural network.
A list of neurons for the network. The dimensionality of this data frame is the same as the training data. The following two formulas come in handy when working with the neural data. The first set of computations provide the x and y coordinate on the map of the neuron in row ‘rowix’ of the ‘neurons’ data frame,
x <- (rowix-1)%%map$xdim+1
y <- (rowix-1)%/%map$xdim+1
The second formula computes the row of the neuron in position (x,y) on the map,
rowix <- x+(y-1)*map$xdim
This is the representation of the map which is the basis for the ‘starburst’ plot.
List of indexes of the best matching neuron for each observation. Each index is an row index into the ‘neuron’ data frame.
This is a data frame of (x,y)-locations where each cell points to the the (x,y)-location on the map where the corresponding centroid is located. Centroids point to themselves.
A vector of actual centroid (x,y)-locations on the map. Hint: to compute the number of clusters on the map take the length of this vector.
A data frame where the (x,y)-locations of actual centroids have a label associated with them. All other locations are NULL. If the training data is unlabeled then popsom invents a label for each centroid.
A label-to-centroid lookup table (hash). A lookup in this table will return a list of indexes into the ‘unique.centroids’ table. Note: a label can be associated with multiple centroids.
A vector of lists of observations per centroid indexed by the centroid number from ‘unique.centroids’. The observations on the list are row numbers of the ‘data’ data frame.
A quality measure of how well the map fits the training data.
The average ‘within cluster sum of squares’. This is the average distance variance within the clusters of the underlying cluster model.
The ‘between cluster sum of squares’. This is the distance variance between the cluster centroids of the underlying cluster model.
If the ‘minimal’ switch is set to TRUE then a ‘map.minimal’ object is returned which only contains the trained neurons together with the training parameters. Observe that none of the POPSOM interface functions will work with this kind of object.
If your training data is unlabeled popsom will automatically generate a label for each of the centroids it discovers.
Lutz Hamel, Benjamin Ott, Gregory Breard
VSOM: Efficient, Stochastic Self-Organizing Map Training, Lutz Hamel, Intelligent Systems Conference (IntelliSys) 2018, K. Arai et al. (Eds.): Intelligent Systems and Applications, Advances in Intelligent Systems and Computing 869, pp 805-821, Springer, 2018.
Self-Organizing Map Convergence, Robert Tatoian and Lutz Hamel. Proceedings of the 2016 International Conference on Data Mining (DMIN'16), pp92-98, July 25-28, 2016, Las Vegas, Nevada, USA, ISBN: 1-60132-431-6, CSREA Press.
Evaluating Self-Organizing Map Quality Measures as Convergence Criteria, Gregory Breard and Lutz Hamel, Proceedings of the 2018 International Conference on Data Science (ICDATA'18), Robert Stahlbock, Gary M. Weiss, Mahmoud Abou-Nasr (Eds.), ISBN: 1-60132-481-2, pp 86-92, CSREA Press, 2018.
SOM Quality Measures: An Efficient Statistical Approach, Lutz Hamel, Proceedings of the 11th International Workshop WSOM 2016, Houston, Texas USA, E. Merenyi et al. (eds.), Advances in Self-Organizing Maps and Learning Vector Quantization, Advances in Intelligent Systems and Computing 428, Springer, pp 49-59, DOI 10.1007/978-3-319-28518-4_4, 2016.
# training data data(iris) df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) # build a map m <- map.build(df,labels,xdim=15,ydim=10,train=10000,seed=42) # look at the characteristics of the maps map.summary(m) # plot the map map.starburst(m)# training data data(iris) df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) # build a map m <- map.build(df,labels,xdim=15,ydim=10,train=10000,seed=42) # look at the characteristics of the maps map.summary(m) # plot the map map.starburst(m)
Evaluate the quality of a SOM using embedding accuracy and estimated topographical accuracy.
map.convergence(map,conf.int=.95,k=50,verb=TRUE,ks=TRUE)map.convergence(map,conf.int=.95,k=50,verb=TRUE,ks=TRUE)
map |
an object of type 'map'. |
conf.int |
is the confidence interval of the quality assessment. |
k |
number of samples to use in the computation of the estimated topographical accuracy. |
verb |
if true reports the two convergence components separately, otherwise it will report a linear combination of the two indices. |
ks |
if true uses the Kolmogorov-Smirnov convergence test otherwise a convergence test based on variance and means is performed. |
A single value or a pair of values: 1) embedding accuracy 2) estimated topographic accuracy. The structure of the return value depends on the 'verb' switch.
Lutz Hamel
"SOM Quality Measures: A Statistical Approach," Lutz Hamel, WSOM16, 2016.
data(iris) ## set data frame and labels df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) ## build a map m <- map.build(df, labels, xdim=15, ydim=10, train=1000) ## map quality map.convergence(m)data(iris) ## set data frame and labels df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) ## build a map m <- map.build(df, labels, xdim=15, ydim=10, train=1000) ## map quality map.convergence(m)
Computes a vector of labels assigned to each of the observations in the training data through the constructed cluster model. If the training data is unlabeled then machine-generated labels are used.
map.fitted(map)map.fitted(map)
map |
An object of type 'map'. |
A vector of predicted labels, one for each observations in the training data.
Lutz Hamel
data(iris) df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) m <- map.build(df,labels,xdim=15,ydim=10,train=10000) map.fitted(m)data(iris) df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) m <- map.build(df,labels,xdim=15,ydim=10,train=10000) map.fitted(m)
Generate a plot that shows the marginal probability distribution of the neurons and data.
map.marginal(map,marginal)map.marginal(map,marginal)
map |
An object of type 'map'. |
marginal |
The name of a training data dimension or index. |
No return value, called for side effects.
Lutz Hamel, Robert Tatoian
data(iris) ## set data frame and labels df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) ## build a map m <- map.build(df,labels,xdim=15,ydim=10,train=10000) ## display marginal distribution of dimension 1 map.marginal(m,1)data(iris) ## set data frame and labels df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) ## build a map m <- map.build(df,labels,xdim=15,ydim=10,train=10000) ## display marginal distribution of dimension 1 map.marginal(m,1)
Compute the (x,y)-positions of points on the map.
map.position(map,points)map.position(map,points)
map |
An object of type 'map'. |
points |
A data frame of points to be mapped. |
A data frame with (x,y)-positions. The data frame has two columns:
The x-position of the corresponding point in the 'points' data frame.
The y-position of the corresponding point in the 'points' data frame.
Lutz Hamel
data(iris) df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) m <- map.build(df,labels,xdim=15,ydim=10,train=10000) map.position(m,df)data(iris) df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) m <- map.build(df,labels,xdim=15,ydim=10,train=10000) map.position(m,df)
Compute classification labels for points in a given data frame using the underlying clustering model. If the training data is unlabeled then machine-generated labels are used.
map.predict(map,points)map.predict(map,points)
map |
An object of type 'map'. |
points |
A data frame of points to be classified. |
A data frame with classification results. The data frame has two columns:
The assigned label to the observation at the same row in the 'points' data frame.
A confidence value assigned to the label prediction.
Lutz Hamel
data(iris) df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) m <- map.build(df,labels,xdim=15,ydim=10,train=10000) map.predict(m,df)data(iris) df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) m <- map.build(df,labels,xdim=15,ydim=10,train=10000) map.predict(m,df)
Computes the relative significance of each feature and plots it.
map.significance(map,graphics=FALSE,feature.labels=TRUE)map.significance(map,graphics=FALSE,feature.labels=TRUE)
map |
An object of type 'map'. |
graphics |
A switch that controls whether a plot is generated or not. |
feature.labels |
A switch to allow the plotting of feature names vs feature indices. |
If graphics=FALSE a vector containing the significance for each feature is returned.
We use a Bayesian approach to compute the relative significance of features based on variance.
Lutz Hamel
Bayesian Probability Approach to Feature Significance for Infrared Spectra of Bacteria, Lutz Hamel, Chris W. Brown, Applied Spectroscopy, Volume 66, Number 1, 2012.
data(iris) df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) m <- map.build(df,labels,xdim=15,ydim=10,train=10000) ## show the relative feature significance map.significance(m)data(iris) df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) m <- map.build(df,labels,xdim=15,ydim=10,train=10000) ## show the relative feature significance map.significance(m)
Generate a starburst representation of the clusters on the heat map for the self-organizing map model.
map.starburst(map)map.starburst(map)
map |
An object of type 'map' |
No return value, called for side effects.
Lutz Hamel, Benjamin Ott, Gregory Breard, Robert Tatoian, Vishakh Gopu
Improved Interpretability of the Unified Distance Matrix with Connected Components, Lutz Hamel and Chris W. Brown. Proceeding of the 7th International Conference on Data Mining (DMIN'11), July 18-21, 2011, Las Vegas Nevada, USA, ISBN: 1-60132-168-6, pp338-343, CSREA Press, 2011.
data(iris) df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) m <- map.build(df,labels,xdim=15,ydim=10,train=10000) map.starburst(m)data(iris) df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) m <- map.build(df,labels,xdim=15,ydim=10,train=10000) map.starburst(m)
Generate a summary object for 'map' objects.
map.summary(map,verb=TRUE)map.summary(map,verb=TRUE)
map |
An object of type 'map'. |
verb |
A switch controlling the output. |
An object of type 'summary.map' which contains two structures:
A dataframe containing the parameters the map was trained with.
A dataframe containing the quality assessments of the map. In particular, it contains the 'convergence' of the map which is a linear combination of variance capture and topographic fidelity of the map. A value close to 1 means a converged map (for more details see the reference below). Furthermore, it contains the 'separation' of the clusters. This is computed by the formula,
1 - wcss/bcss
In general, a value close to 1 means well separated clusters.
If 'verb' is TRUE the summar.map object will be formatted and printed to the screen, otherwise it will be returned as a data structure.
Lutz Hamel
Self-Organizing Map Convergence, Robert Tatoian and Lutz Hamel. Proceedings of the 2016 International Conference on Data Mining (DMIN'16), pp92-98, July 25-28, 2016, Las Vegas, Nevada, USA, ISBN: 1-60132-431-6, CSREA Press.
data(iris) ## set data frame and labels df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) ## build a map m <- map.build(df,labels,xdim=15,ydim=10,train=10000) ## compute a summary object and display it s <- map.summary(m,verb=FALSE) sdata(iris) ## set data frame and labels df <- subset(iris,select=-Species) labels <- subset(iris,select=Species) ## build a map m <- map.build(df,labels,xdim=15,ydim=10,train=10000) ## compute a summary object and display it s <- map.summary(m,verb=FALSE) s