library("seriation")
packageVersion('seriation')[1] '1.5.5.1'List of Seriation Criteria implemented in the R package seriation
This document contains the seriation criteria for judging the quality of permutations given data implemented in the R package seriation.
This list was created for the following version of seriation:
Register some additional criteria
register_DendSer()
register_smacof()Implemented Criteria
The criteria are organized by methods that evaluate the permutation based on distance data or data matrices.
merit specified if the criteria function increases with better fit or if it is formulated as a loss criteria functions (merit = FALSE).
If a seriation method directly tries to optimize the criterion, than its name is specified under “optimized by”. The names can be used as the method argument in seriate().
Criteria for distances
2SUM
2-Sum Criterion: The 2-Sum loss criterion multiplies the similarity between objects with the squared rank differences (Barnard, Pothen and Simon, 1993).
- merit: FALSE
- optimized by: QAP_2SUM, Spectral, Spectral_norm
- additional parameters: no parameters
AR_deviations
Anti-Robinson deviations: The number of violations of the anti-Robinson form weighted by the deviation (Chen, 2002).
- merit: FALSE
- optimized by: N/A
- additional parameters: no parameters
AR_events
Anti-Robinson events: The number of violations of the anti-Robinson form (Chen, 2002).
- merit: FALSE
- optimized by: N/A
- additional parameters: no parameters
ARc
Anti-Robinson form cost (Earle and Hurley, 2015).
- merit: FALSE
- optimized by: DendSer_ARc
- registered by: register_DendSer()
- additional parameters: no parameters
BAR
Banded Anti-Robinson form criterion: Measure for closeness to the anti-Robinson form in a band of size b (Earle and Hurley, 2015).
merit: FALSE
optimized by: QAP_BAR, DendSer_BAR
additional parameters:
de fault values he lp b NULL band size defaults to a band of 20% of n
Gradient_raw
Gradient measure: Evaluates how well distances increase when moving away from the diagonal of the distance matrix (Hubert et al, 2001).
- merit: TRUE
- optimized by: BBURCG
- additional parameters: no parameters
Gradient_weighted
Gradient measure (weighted): Evaluates how well distances increase when moving away from the diagonal of the distance matrix (Hubert et al, 2001).
- merit: TRUE
- optimized by: BBWRCG
- additional parameters: no parameters
Inertia
Inertia criterion: Measures the moment of the inertia of dissimilarity values around the diagonal of the distance matrix (Caraux and Pinloche, 2005).
- merit: TRUE
- optimized by: QAP_Inertia
- additional parameters: no parameters
Lazy_path_length
Lazy path length: A weighted version of the Hamiltonian path criterion where later distances are less important (Earl and Hurley, 2015).
- merit: FALSE
- optimized by: DendSer_LPL
- additional parameters: no parameters
Least_squares
Least squares criterion: The sum of squared differences between distances and the rank differences (Caraux and Pinloche, 2005).
- merit: FALSE
- optimized by: N/A
- additional parameters: no parameters
LS
Linear Seriation Criterion: Weights the distances with the absolute rank differences (Hubert and Schultz, 1976).
MDS_stress
Normalized stress of a configuration given by a seriation order
merit: FALSE
optimized by: MDS, isoMDS, Sammon_mapping, monoMDS, metaMDS
additional parameters:
de fault values he lp warn FALSE produce a warning if the 1D MDS fit does not preserve the given order (see ? seriation::uniscale).
ME
Measure of effectiveness applied to the reordered similarity matrix (McCormick, 1972).
Moore_stress
Stress criterion (Moore neighborhood) applied to the reordered similarity matrix (Niermann, 2005).
- merit: FALSE
- optimized by: N/A
- additional parameters: no parameters
Neumann_stress
Stress criterion (Neumann neighborhood) applied to the reordered similarity matrix (Niermann, 2005).
- merit: FALSE
- optimized by: N/A
- additional parameters: no parameters
Path_length
Hamiltonian path length: Sum of distances by following the permutation (Caraux and Pinloche, 2005).
- merit: FALSE
- optimized by: TSP, GW, GW_single, GW_average, GW_complete, GW_ward, OLO, OLO_single, OLO_average, OLO_complete, OLO_ward, DendSer_PL
- additional parameters: no parameters
RGAR
Relative generalized anti-Robinson events: Counts Anti-Robinson events in a variable band of size w around the main diagonal and normalizes by the maximum of possible events (Tien et al, 2008).
merit: FALSE
optimized by: N/A
additional parameters:
de fault values he lp w NULL window size. Default is to use a pct of 100% of n pct 100 specify w as a percentage of n in (0,100] relative TRUE set to FALSE to get the GAR, i.e., the absolute number of AR events in the window.
Rho
Absolute value of the Spearman rank correlation between original distances and rank differences of the order.
- merit: TRUE
- optimized by: N/A
- additional parameters: no parameters
smacof_stress0
Stress0 calculated for different transformation types from package smacof.
merit: FALSE
optimized by: MDS_smacof
registered by: register_smacof()
additional parameters:
de fault values he lp type “ratio” MDS type (see ? smacof::stress0) warn FALSE produce a warning if the 1D MDS fit does not preserve the given order (see ? seriation::uniscale). more NA more arguments are passed on to smacof::stress0.
Criteria for data matrices, tables and data.frames
Cor_R
Weighted correlation coefficient R: A measure of effectiveness normalized between -1 and 1 (Deutsch and Martin, 1971).
- merit: TRUE
- optimized by: N/A
- additional parameters: no parameters
ME
Measure of effectiveness (McCormick, 1972).
Moore_stress
Stress criterion (Moore neighborhood) applied to the reordered matrix (Niermann, 2005).
- merit: FALSE
- optimized by: N/A
- additional parameters: no parameters
Neumann_stress
Stress criterion (Neumann neighborhood) applied to the reordered matrix (Niermann, 2005).
- merit: FALSE
- optimized by: N/A
- additional parameters: no parameters
References
Barnard, S.T., A. Pothen, and H. D. Simon (1993): A Spectral Algorithm for Envelope Reduction of Sparse Matrices. In Proceedings of the 1993 ACM/IEEE Conference on Supercomputing, 493–502. Supercomputing ’93. New York, NY, USA: ACM.
Caraux, G. and S. Pinloche (2005): Permutmatrix: A Graphical Environment to Arrange Gene Expression Profiles in Optimal Linear Order, Bioinformatics, 21(7), 1280–1281.
Chen, C.-H. (2002): Generalized association plots: Information visualization via iteratively generated correlation matrices, Statistica Sinica, 12(1), 7–29.
Deutsch, S.B. and J.J. Martin (1971): An ordering algorithm for analysis of data arrays. Operational Research, 19(6), 1350–1362.
Earle, D. and C.B. Hurley (2015): Advances in Dendrogram Seriation for Application to Visualization. Journal of Computational and Graphical Statistics, 24(1), 1–25.
Hahsler, M. (2017): An experimental comparison of seriation methods for one-mode two-way data. European Journal of Operational Research, 257, 133–143.
Hubert, L. and J. Schultz (1976): Quadratic Assignment as a General Data Analysis Strategy. British Journal of Mathematical and Statistical Psychology, 29(2). Blackwell Publishing Ltd. 190–241.
Hubert, L., P. Arabie, and J. Meulman (2001): Combinatorial Data Analysis: Optimization by Dynamic Programming. Society for Industrial Mathematics.
Niermann, S. (2005): Optimizing the Ordering of Tables With Evolutionary Computation, The American Statistician, 59(1), 41–46.
McCormick, W.T., P.J. Schweitzer and T.W. White (1972): Problem decomposition and data reorganization by a clustering technique, Operations Research, 20(5), 993-1009.
Robinson, W.S. (1951): A method for chronologically ordering archaeological deposits, American Antiquity, 16, 293–301.
Tien, Y-J., Yun-Shien Lee, Han-Ming Wu and Chun-Houh Chen (2008): Methods for simultaneously identifying coherent local clusters with smooth global patterns in gene expression profiles, BMC Bioinformatics, 9(155), 1–16.