Description Usage Arguments Details Value Author(s) References See Also Examples
Computes cross-validated nonparametric p-values for the potential class memberships of the training data. The p-values are based on 'k nearest neighbors'.
1 2 |
X |
matrix containing training observations, where each observation is a row vector. |
Y |
vector indicating the classes which the training observations belong to. |
k |
number of nearest neighbors. If |
distance |
the distance measure: |
cova |
estimator for the covariance matrix: |
Computes cross-validated nonparametric p-values for the potential class memberships of the training data. Precisely, for each feature vector X[i,]
and each class b
the number PV[i,b]
is a p-value for the null hypothesis that Y[i] = b.
This p-value is based on a permutation test applied to an estimated Bayesian likelihood ratio, using 'k nearest neighbors' with estimated prior probabilities N(b)/n. Here N(b) is the number of observations of class b and n is the total number of observations.
If k
is a vector, the program searches for the best k
. To determine the best k
for the p-value PV[i,b]
, the class label of the training observation X[i,] is set temporarily to b
and then for all training observations with Y[j] != b
the proportion of the k
nearest neighbors of X[j,]
belonging to class b
is computed. Then the k
which minimizes the sum of these values is chosen.
If k = NULL
, it is set to 2:ceiling(length(Y)/2).
PV
is a matrix containing the cross-validated p-values. Precisely, for each feature vector X[i,]
and each class b
the number PV[i,b]
is a p-value for the null hypothesis that Y[i] = b.
If k
is a vector or NULL
, PV
has an attribute "opt.k"
, which is a matrix and opt.k[i,b]
is the best k
for observation X[i,]
and class b
(see section 'Details'). opt.k[i,b]
is used to compute the p-value for observation X[i,]
and class b
.
Niki Zumbrunnen niki.zumbrunnen@gmail.com
Lutz Dümbgen lutz.duembgen@stat.unibe.ch
www.imsv.unibe.ch/duembgen/index_ger.html
Zumbrunnen N. and Dümbgen L. (2017) pvclass: An R Package for p Values for Classification. Journal of Statistical Software 78(4), 1–19. doi:10.18637/jss.v078.i04
Dümbgen L., Igl B.-W. and Munk A. (2008) P-Values for Classification. Electronic Journal of Statistics 2, 468–493, available at http://dx.doi.org/10.1214/08-EJS245.
Zumbrunnen N. (2014) P-Values for Classification – Computational Aspects and Asymptotics. Ph.D. thesis, University of Bern, available at http://boris.unibe.ch/id/eprint/53585.
cvpvs, cvpvs.gaussian, cvpvs.wnn, cvpvs.logreg
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setosa versicolor virginica
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[85,] 0.01960784 0.38000000 0.01960784
[86,] 0.01960784 0.30000000 0.03921569
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[88,] 0.01960784 0.38000000 0.01960784
[89,] 0.01960784 0.96000000 0.01960784
[90,] 0.01960784 0.96000000 0.01960784
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[97,] 0.01960784 0.96000000 0.01960784
[98,] 0.01960784 1.00000000 0.01960784
[99,] 0.01960784 0.96000000 0.01960784
[100,] 0.01960784 0.96000000 0.01960784
[101,] 0.01960784 0.01960784 1.00000000
[102,] 0.01960784 0.01960784 0.32000000
[103,] 0.01960784 0.01960784 1.00000000
[104,] 0.01960784 0.01960784 0.44000000
[105,] 0.01960784 0.01960784 1.00000000
[106,] 0.01960784 0.01960784 1.00000000
[107,] 0.01960784 0.31372549 0.02000000
[108,] 0.01960784 0.01960784 1.00000000
[109,] 0.01960784 0.01960784 1.00000000
[110,] 0.01960784 0.01960784 1.00000000
[111,] 0.01960784 0.03921569 0.32000000
[112,] 0.01960784 0.01960784 0.32000000
[113,] 0.01960784 0.01960784 1.00000000
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[115,] 0.01960784 0.01960784 0.44000000
[116,] 0.01960784 0.01960784 1.00000000
[117,] 0.01960784 0.01960784 0.44000000
[118,] 0.01960784 0.01960784 1.00000000
[119,] 0.01960784 0.01960784 1.00000000
[120,] 0.01960784 0.03921569 0.12000000
[121,] 0.01960784 0.01960784 1.00000000
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[124,] 0.01960784 0.03921569 0.16000000
[125,] 0.01960784 0.01960784 1.00000000
[126,] 0.01960784 0.01960784 1.00000000
[127,] 0.01960784 0.03921569 0.12000000
[128,] 0.01960784 0.03921569 0.12000000
[129,] 0.01960784 0.01960784 1.00000000
[130,] 0.01960784 0.01960784 1.00000000
[131,] 0.01960784 0.01960784 1.00000000
[132,] 0.01960784 0.01960784 1.00000000
[133,] 0.01960784 0.01960784 1.00000000
[134,] 0.01960784 0.03921569 0.12000000
[135,] 0.01960784 0.03921569 0.32000000
[136,] 0.01960784 0.01960784 1.00000000
[137,] 0.01960784 0.01960784 1.00000000
[138,] 0.01960784 0.01960784 0.44000000
[139,] 0.01960784 0.07843137 0.04000000
[140,] 0.01960784 0.01960784 1.00000000
[141,] 0.01960784 0.01960784 1.00000000
[142,] 0.01960784 0.01960784 0.44000000
[143,] 0.01960784 0.01960784 0.32000000
[144,] 0.01960784 0.01960784 1.00000000
[145,] 0.01960784 0.01960784 1.00000000
[146,] 0.01960784 0.01960784 1.00000000
[147,] 0.01960784 0.01960784 0.32000000
[148,] 0.01960784 0.01960784 0.44000000
[149,] 0.01960784 0.01960784 1.00000000
[150,] 0.01960784 0.03921569 0.20000000
attr(,"opt.k")
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