cvpvs.knn: Cross-Validated P-Values (k Nearest Neighbors)
In pvclass: P-Values for Classification
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
Computes cross-validated nonparametric p-values for the potential class memberships of the training data. The p-values are based on 'k nearest neighbors'.
Usage
1
2
Arguments
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 k is a vector or k = NULL, the program searches for the best k. For more information see section 'Details'.
distance
the distance measure:
"euclidean": fixed Euclidean distance,
"ddeuclidean": data driven Euclidean distance (component-wise standardization),
"mahalanobis": Mahalanobis distance.
cova
estimator for the covariance matrix:
'standard': standard estimator,
'M': M-estimator,
'sym': symmetrized M-estimator.
Details
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).
Value
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.
Author(s)
Niki Zumbrunnen niki.zumbrunnen@gmail.com
Lutz Dümbgen lutz.duembgen@stat.unibe.ch
www.imsv.unibe.ch/duembgen/index_ger.html
References
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.
See Also
cvpvs, cvpvs.gaussian, cvpvs.wnn, cvpvs.logreg
Examples
1
2
3
4
Example output
setosa versicolor virginica
[1,] 0.90000000 0.01960784 0.01960784
[2,] 0.90000000 0.01960784 0.01960784
[3,] 0.90000000 0.01960784 0.01960784
[4,] 0.90000000 0.01960784 0.01960784
[5,] 0.90000000 0.01960784 0.01960784
[6,] 0.90000000 0.01960784 0.01960784
[7,] 0.90000000 0.01960784 0.01960784
[8,] 0.90000000 0.01960784 0.01960784
[9,] 0.90000000 0.01960784 0.01960784
[10,] 0.90000000 0.01960784 0.01960784
[11,] 0.90000000 0.01960784 0.01960784
[12,] 0.90000000 0.01960784 0.01960784
[13,] 0.90000000 0.01960784 0.01960784
[14,] 0.90000000 0.01960784 0.01960784
[15,] 0.90000000 0.01960784 0.01960784
[16,] 0.90000000 0.01960784 0.01960784
[17,] 0.90000000 0.01960784 0.01960784
[18,] 0.90000000 0.01960784 0.01960784
[19,] 0.90000000 0.01960784 0.01960784
[20,] 1.00000000 0.01960784 0.01960784
[21,] 0.90000000 0.01960784 0.01960784
[22,] 0.90000000 0.01960784 0.01960784
[23,] 0.90000000 0.01960784 0.01960784
[24,] 0.90000000 0.01960784 0.01960784
[25,] 1.00000000 0.01960784 0.01960784
[26,] 0.90000000 0.01960784 0.01960784
[27,] 0.90000000 0.01960784 0.01960784
[28,] 0.90000000 0.01960784 0.01960784
[29,] 0.90000000 0.01960784 0.01960784
[30,] 0.90000000 0.01960784 0.01960784
[31,] 0.90000000 0.01960784 0.01960784
[32,] 1.00000000 0.01960784 0.01960784
[33,] 0.90000000 0.01960784 0.01960784
[34,] 0.90000000 0.01960784 0.01960784
[35,] 0.90000000 0.01960784 0.01960784
[36,] 0.90000000 0.01960784 0.01960784
[37,] 1.00000000 0.01960784 0.01960784
[38,] 0.90000000 0.01960784 0.01960784
[39,] 0.90000000 0.01960784 0.01960784
[40,] 0.90000000 0.01960784 0.01960784
[41,] 0.90000000 0.01960784 0.01960784
[42,] 0.90000000 0.01960784 0.01960784
[43,] 0.90000000 0.01960784 0.01960784
[44,] 0.90000000 0.01960784 0.01960784
[45,] 1.00000000 0.01960784 0.01960784
[46,] 0.90000000 0.01960784 0.01960784
[47,] 0.90000000 0.01960784 0.01960784
[48,] 0.90000000 0.01960784 0.01960784
[49,] 0.90000000 0.01960784 0.01960784
[50,] 0.90000000 0.01960784 0.01960784
[51,] 0.01960784 0.30000000 0.03921569
[52,] 0.01960784 0.38000000 0.03921569
[53,] 0.01960784 0.14000000 0.03921569
[54,] 0.01960784 0.96000000 0.01960784
[55,] 0.01960784 0.30000000 0.03921569
[56,] 0.01960784 0.96000000 0.01960784
[57,] 0.01960784 0.30000000 0.03921569
[58,] 0.01960784 0.96000000 0.01960784
[59,] 0.01960784 0.96000000 0.01960784
[60,] 0.01960784 0.96000000 0.01960784
[61,] 0.01960784 0.96000000 0.01960784
[62,] 0.01960784 0.96000000 0.01960784
[63,] 0.01960784 0.96000000 0.01960784
[64,] 0.01960784 0.14000000 0.03921569
[65,] 0.01960784 0.96000000 0.01960784
[66,] 0.01960784 0.96000000 0.01960784
[67,] 0.01960784 0.96000000 0.01960784
[68,] 0.01960784 0.96000000 0.01960784
[69,] 0.01960784 0.14000000 0.03921569
[70,] 0.01960784 0.96000000 0.01960784
[71,] 0.01960784 0.08000000 0.03921569
[72,] 0.01960784 1.00000000 0.01960784
[73,] 0.01960784 0.08000000 0.05882353
[74,] 0.01960784 0.30000000 0.03921569
[75,] 0.01960784 0.96000000 0.01960784
[76,] 0.01960784 0.96000000 0.01960784
[77,] 0.01960784 0.30000000 0.03921569
[78,] 0.01960784 0.08000000 0.05882353
[79,] 0.01960784 0.30000000 0.03921569
[80,] 0.01960784 0.96000000 0.01960784
[81,] 0.01960784 0.96000000 0.01960784
[82,] 0.01960784 0.96000000 0.01960784
[83,] 0.01960784 0.96000000 0.01960784
[84,] 0.01960784 0.02000000 0.23529412
[85,] 0.01960784 0.38000000 0.01960784
[86,] 0.01960784 0.30000000 0.03921569
[87,] 0.01960784 0.38000000 0.01960784
[88,] 0.01960784 0.38000000 0.01960784
[89,] 0.01960784 0.96000000 0.01960784
[90,] 0.01960784 0.96000000 0.01960784
[91,] 0.01960784 0.96000000 0.01960784
[92,] 0.01960784 0.16000000 0.03921569
[93,] 0.01960784 0.96000000 0.01960784
[94,] 0.01960784 0.96000000 0.01960784
[95,] 0.01960784 0.96000000 0.01960784
[96,] 0.01960784 0.96000000 0.01960784
[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
[114,] 0.01960784 0.03921569 0.20000000
[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
[122,] 0.01960784 0.03921569 0.14000000
[123,] 0.01960784 0.01960784 1.00000000
[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")
[,1] [,2] [,3]
[1,] 15 15 15
[2,] 15 15 15
[3,] 15 15 15
[4,] 15 15 15
[5,] 15 15 15
[6,] 15 15 15
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[58,] 15 15 15
[59,] 15 15 15
[60,] 15 15 15
[61,] 15 15 15
[62,] 15 15 15
[63,] 15 15 15
[64,] 15 15 15
[65,] 15 15 15
[66,] 15 15 15
[67,] 15 15 15
[68,] 15 15 15
[69,] 15 15 15
[70,] 15 15 15
[71,] 15 15 15
[72,] 15 15 15
[73,] 15 15 15
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[80,] 15 15 15
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[86,] 15 15 15
[87,] 15 15 15
[88,] 15 15 15
[89,] 15 15 15
[90,] 15 15 15
[91,] 15 15 15
[92,] 15 15 15
[93,] 15 15 15
[94,] 15 15 15
[95,] 15 15 15
[96,] 15 15 15
[97,] 15 15 15
[98,] 15 15 15
[99,] 15 15 15
[100,] 15 15 15
[101,] 15 15 15
[102,] 15 15 15
[103,] 15 15 15
[104,] 15 15 15
[105,] 15 15 15
[106,] 15 15 15
[107,] 15 15 15
[108,] 15 15 15
[109,] 15 15 15
[110,] 15 15 15
[111,] 15 15 15
[112,] 15 15 15
[113,] 15 15 15
[114,] 15 15 15
[115,] 15 15 15
[116,] 15 15 15
[117,] 15 15 15
[118,] 15 15 15
[119,] 15 15 15
[120,] 15 15 15
[121,] 15 15 15
[122,] 15 15 15
[123,] 15 15 15
[124,] 15 15 15
[125,] 15 15 15
[126,] 15 15 15
[127,] 15 15 15
[128,] 15 15 15
[129,] 15 15 15
[130,] 15 15 15
[131,] 15 15 15
[132,] 15 15 15
[133,] 15 15 15
[134,] 15 15 15
[135,] 15 15 15
[136,] 15 15 15
[137,] 15 15 15
[138,] 15 15 15
[139,] 15 15 15
[140,] 15 15 15
[141,] 15 15 15
[142,] 15 15 15
[143,] 15 15 15
[144,] 15 15 15
[145,] 15 15 15
[146,] 15 15 15
[147,] 15 15 15
[148,] 15 15 15
[149,] 15 15 15
[150,] 15 15 15
pvclass documentation built on May 1, 2019, 10:17 p.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
Computes cross-validated nonparametric p-values for the potential class memberships of the training data. The p-values are based on 'k nearest neighbors'.
Usage
1 2 |
Arguments
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: |
Details
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).
Value
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.
Author(s)
Niki Zumbrunnen niki.zumbrunnen@gmail.com
Lutz Dümbgen lutz.duembgen@stat.unibe.ch
www.imsv.unibe.ch/duembgen/index_ger.html
References
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.
See Also
cvpvs, cvpvs.gaussian, cvpvs.wnn, cvpvs.logreg
Examples
1 2 3 4 |
Example output
setosa versicolor virginica
[1,] 0.90000000 0.01960784 0.01960784
[2,] 0.90000000 0.01960784 0.01960784
[3,] 0.90000000 0.01960784 0.01960784
[4,] 0.90000000 0.01960784 0.01960784
[5,] 0.90000000 0.01960784 0.01960784
[6,] 0.90000000 0.01960784 0.01960784
[7,] 0.90000000 0.01960784 0.01960784
[8,] 0.90000000 0.01960784 0.01960784
[9,] 0.90000000 0.01960784 0.01960784
[10,] 0.90000000 0.01960784 0.01960784
[11,] 0.90000000 0.01960784 0.01960784
[12,] 0.90000000 0.01960784 0.01960784
[13,] 0.90000000 0.01960784 0.01960784
[14,] 0.90000000 0.01960784 0.01960784
[15,] 0.90000000 0.01960784 0.01960784
[16,] 0.90000000 0.01960784 0.01960784
[17,] 0.90000000 0.01960784 0.01960784
[18,] 0.90000000 0.01960784 0.01960784
[19,] 0.90000000 0.01960784 0.01960784
[20,] 1.00000000 0.01960784 0.01960784
[21,] 0.90000000 0.01960784 0.01960784
[22,] 0.90000000 0.01960784 0.01960784
[23,] 0.90000000 0.01960784 0.01960784
[24,] 0.90000000 0.01960784 0.01960784
[25,] 1.00000000 0.01960784 0.01960784
[26,] 0.90000000 0.01960784 0.01960784
[27,] 0.90000000 0.01960784 0.01960784
[28,] 0.90000000 0.01960784 0.01960784
[29,] 0.90000000 0.01960784 0.01960784
[30,] 0.90000000 0.01960784 0.01960784
[31,] 0.90000000 0.01960784 0.01960784
[32,] 1.00000000 0.01960784 0.01960784
[33,] 0.90000000 0.01960784 0.01960784
[34,] 0.90000000 0.01960784 0.01960784
[35,] 0.90000000 0.01960784 0.01960784
[36,] 0.90000000 0.01960784 0.01960784
[37,] 1.00000000 0.01960784 0.01960784
[38,] 0.90000000 0.01960784 0.01960784
[39,] 0.90000000 0.01960784 0.01960784
[40,] 0.90000000 0.01960784 0.01960784
[41,] 0.90000000 0.01960784 0.01960784
[42,] 0.90000000 0.01960784 0.01960784
[43,] 0.90000000 0.01960784 0.01960784
[44,] 0.90000000 0.01960784 0.01960784
[45,] 1.00000000 0.01960784 0.01960784
[46,] 0.90000000 0.01960784 0.01960784
[47,] 0.90000000 0.01960784 0.01960784
[48,] 0.90000000 0.01960784 0.01960784
[49,] 0.90000000 0.01960784 0.01960784
[50,] 0.90000000 0.01960784 0.01960784
[51,] 0.01960784 0.30000000 0.03921569
[52,] 0.01960784 0.38000000 0.03921569
[53,] 0.01960784 0.14000000 0.03921569
[54,] 0.01960784 0.96000000 0.01960784
[55,] 0.01960784 0.30000000 0.03921569
[56,] 0.01960784 0.96000000 0.01960784
[57,] 0.01960784 0.30000000 0.03921569
[58,] 0.01960784 0.96000000 0.01960784
[59,] 0.01960784 0.96000000 0.01960784
[60,] 0.01960784 0.96000000 0.01960784
[61,] 0.01960784 0.96000000 0.01960784
[62,] 0.01960784 0.96000000 0.01960784
[63,] 0.01960784 0.96000000 0.01960784
[64,] 0.01960784 0.14000000 0.03921569
[65,] 0.01960784 0.96000000 0.01960784
[66,] 0.01960784 0.96000000 0.01960784
[67,] 0.01960784 0.96000000 0.01960784
[68,] 0.01960784 0.96000000 0.01960784
[69,] 0.01960784 0.14000000 0.03921569
[70,] 0.01960784 0.96000000 0.01960784
[71,] 0.01960784 0.08000000 0.03921569
[72,] 0.01960784 1.00000000 0.01960784
[73,] 0.01960784 0.08000000 0.05882353
[74,] 0.01960784 0.30000000 0.03921569
[75,] 0.01960784 0.96000000 0.01960784
[76,] 0.01960784 0.96000000 0.01960784
[77,] 0.01960784 0.30000000 0.03921569
[78,] 0.01960784 0.08000000 0.05882353
[79,] 0.01960784 0.30000000 0.03921569
[80,] 0.01960784 0.96000000 0.01960784
[81,] 0.01960784 0.96000000 0.01960784
[82,] 0.01960784 0.96000000 0.01960784
[83,] 0.01960784 0.96000000 0.01960784
[84,] 0.01960784 0.02000000 0.23529412
[85,] 0.01960784 0.38000000 0.01960784
[86,] 0.01960784 0.30000000 0.03921569
[87,] 0.01960784 0.38000000 0.01960784
[88,] 0.01960784 0.38000000 0.01960784
[89,] 0.01960784 0.96000000 0.01960784
[90,] 0.01960784 0.96000000 0.01960784
[91,] 0.01960784 0.96000000 0.01960784
[92,] 0.01960784 0.16000000 0.03921569
[93,] 0.01960784 0.96000000 0.01960784
[94,] 0.01960784 0.96000000 0.01960784
[95,] 0.01960784 0.96000000 0.01960784
[96,] 0.01960784 0.96000000 0.01960784
[97,] 0.01960784 0.96000000 0.01960784
[98,] 0.01960784 1.00000000 0.01960784
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[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
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[114,] 0.01960784 0.03921569 0.20000000
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[116,] 0.01960784 0.01960784 1.00000000
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[118,] 0.01960784 0.01960784 1.00000000
[119,] 0.01960784 0.01960784 1.00000000
[120,] 0.01960784 0.03921569 0.12000000
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[122,] 0.01960784 0.03921569 0.14000000
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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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