nFCA (version 0.3)

nfca: Numerical Formal Concept Analysis for Systematic Clustering

Description

The R function nfca() is an implementation of the numerical Formal Concept Analysis (nFCA), a modern unsupervised learning tool for analyzing general numerical data developed in [3]. nfca() provides two nFCA graphs: a H-graph and an I-graph that reveal systematic, hierarchical clustering and inherent structure of the data.

Usage

nfca(data, type = 0, method = 'hist', choice = 1, n = 30, alpha = 0.05)

Arguments

data

The input numerical data. It can be a correlation matrix, a distance matrix, or a general data matrix of n x p dimensions, where n is the number of subjects and p is the dimension of variables. If the input is a general data matrix, nfca is performed ba

type

The type of input data. The default type=0 represents a correlation matrix, while type=1 represents a distance matrix and type=2 represents a general data matrix.

method

The method of choosing a sequence of thresholds to scale FCA in building nFCA. The default method=`hist' implements the `histogram' method, applicable to all data types, type=0, 1, or 2. The method=`CI' uses the `confidence interval' method, currently ap

choice

The choice of how to choose the thresholds for the `histogram' method. The default choice=1 chooses the thresholds automatically while choice=0 allows the user to choose thresholds based on histograms shown on the screen manually.

n

The sample size used to compute the correlation matrix if the input data is 0, ie. correlation matrix. Required only if the threshold selection method is `confidence interval'. The default value is 30.

alpha

The significance level used for `confidence interval' method. The default value is 0.05.

Value

• Hgraph.dot
  a dot file containing systematic clustering result.
• Igraph.dot
  a dot file containing inherited clustering information.
• To visualize H-graph.dot and I-graph.dot in Graphviz, choose `fdp' as the LAYOUT engine for the H-graph, and choose `neato' for the I-graph. These selections can be done in GUI versions of Graphviz in Window or Mac. In a Mac running macport or Linux machine on which Graphviz is installed, use the following commands to generate graphics outside R: fdp -Tpng Hgraph.dot -o Hgraph.png neato -Tpng Igraph.dot -o Igraph.png

Details

Numerical Formal Concept Analysis (nFCA) combines the merit of statistics, formal concept analysis (FCA), and a graphical visualization tool (Graphviz) to analyze the clustering and inherent structure of data. Its output is a pair of nFCA graphs, H- and I-graphs. H-graph maps systematic relations of hierarchical clusters. I-graph is a directed acyclic graph (DAG) that complements the H-graph by revealing inherent structures and connections from one member to the relevant member of another cluster. The nFCA package includes our main R code and a supporting program in Ruby that implements the faster concept analysis algorithm developed by Dr. Zhang's team (Troy et al. 2007). If needed, Ruby compiler can be downloaded from https://www.ruby-lang.org. The two nFCA outcome files, Hgraph.dot and Igraph.dot, can be visualized using Graphviz. Graphviz is a standard, powerful graphic visualization software, available at http://www.graphviz.org/. We have tested selected versions of Graphviz. Versions 2.26, 2.30, 2.38 for Mac OS Lion and Window work with this package. Do not use version 2.28, which has a known bug. For further instructions on how to use Graphviz for nFCA, see the `Value' below or: http://sr2c.case.edu/nfca, for detailed installation instructions and examples of figures from Graphviz.

References

Troy, A. D., Zhang, G.-Q. and Tian, Y. (2007) Faster Concept Analysis. Proceedings of the 15th International Conference on Conceptual Structures (ICCS 2007), 4604, 206--219. Ma, J. (2010) Contributions to Numerical Formal Concept Analysis, Bayesian Predictive Inference, and Sample Size Determination. PhD thesis, Case Western Reserve University. http://rave.ohiolink.edu/etdc/view?acc_num=case1285341426 Ma, J., Sun, J. and Zhang, G.-Q. (2014) Numerical Formal Concept Analysis (nFCA): a New Systematic Clustering Technique. Under review.

Examples

# View a build-in correlation matrix: nfca_example
data("nfca_example", package = "nFCA")
nfca_example
     
# 1. using the default 'histogram' method and choosing threshold
# automatically   
nfca(data = nfca_example)

# 2. using 'confidence interval' method with sample size 30 and 
# choosing threshold automatically 
nfca(data = nfca_example, method = "CI")

# The output files Hgraph.dot and Igraph.dot from #1 and #2 can
# be visualized as H- and I-graphs in Graphviz. In this example,
# the I-graphs from both 'histogram' and 'confidence interval' 
# methods are identical, while two H-graphs are consistent to
# each other.