The following examples illustrate the functionality of the KernelKnn package for classification tasks. I’ll make use of the ionosphere data set,
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## 256 281 244 266 243 263 245 263 2When using an algorithm where the ouput depends on distance calculation (as is the case in k-nearest-neighbors) it is recommended to first scale the data,
# recommended is to scale the data
X = scale(ionosphere[, -ncol(ionosphere)])
y = ionosphere[, ncol(ionosphere)]important note : In classification, both functions KernelKnn and KernelKnnCV accept a numeric vector as a response variable (here y) and the unique values of the labels should begin from 1. This is important otherwise the internal functions do not work. Furthermore, both functions (by default) return predictions in form of probabilities, which can be converted to labels by using either a threshold (if binary classification) or the maximum value of each column (if multiclass classification).
# labels should be numeric and begin from 1:Inf
y = c(1:length(unique(y)))[ match(ionosphere$class, sort(unique(ionosphere$class))) ]
# random split of data in train and test
spl_train = sample(1:length(y), round(length(y) * 0.75))
spl_test = setdiff(1:length(y), spl_train)
str(spl_train)## int [1:263] 57 280 33 27 91 226 85 30 338 55 ...## int [1:88] 3 4 5 8 21 26 52 56 59 64 ...# evaluation metric
acc = function (y_true, preds) {
out = table(y_true, max.col(preds, ties.method = "random"))
acc = sum(diag(out))/sum(out)
acc
}The KernelKnn function takes a number of arguments. To read details for each one of the arguments type ?KernelKnn::KernelKnn in the console.
A simple k-nearest-neighbors can be run with weights_function = NULL and the parameter ‘regression’ should be set to FALSE. In classification the Levels parameter takes the unique values of the response variable,
library(KernelKnn)
preds_TEST = KernelKnn(X[spl_train, ], TEST_data = X[spl_test, ], y[spl_train], k = 5 ,
method = 'euclidean', weights_function = NULL, regression = F,
Levels = unique(y))
head(preds_TEST)## class_1 class_2
## [1,] 0.0 1.0
## [2,] 0.0 1.0
## [3,] 0.2 0.8
## [4,] 0.8 0.2
## [5,] 0.0 1.0
## [6,] 0.0 1.0
There are two ways to use a kernel in the KernelKnn function.
The first option is to choose one of the existing
kernels (uniform, triangular, epanechnikov,
biweight, triweight, tricube,
gaussian, cosine, logistic,
silverman, inverse, gaussianSimple,
exponential). Here, I use the canberra metric and the
tricube kernel because they give optimal results (according to
my RandomSearchR package),
preds_TEST_tric = KernelKnn(X[spl_train, ], TEST_data = X[spl_test, ], y[spl_train], k = 10 ,
method = 'canberra', weights_function = 'tricube', regression = F,
Levels = unique(y))
head(preds_TEST_tric)## class_1 class_2
## [1,] 0.0000000 1.00000000
## [2,] 0.9414972 0.05850276
## [3,] 0.0000000 1.00000000
## [4,] 1.0000000 0.00000000
## [5,] 0.0000000 1.00000000
## [6,] 0.4430946 0.55690537
The second option is to give a self defined
kernel function. Here, I’ll pick the density function of the normal
distribution with mean = 0.0 and standard deviation = 1.0 (the data are
scaled to have mean zero and unit variance),
norm_kernel = function(W) {
W = dnorm(W, mean = 0, sd = 1.0)
W = W / rowSums(W)
return(W)
}
preds_TEST_norm = KernelKnn(X[spl_train, ], TEST_data = X[spl_test, ], y[spl_train], k = 10 ,
method = 'canberra', weights_function = norm_kernel, regression = F,
Levels = unique(y))
head(preds_TEST_norm)## class_1 class_2
## [1,] 0.0000000 1.0000000
## [2,] 0.8281746 0.1718254
## [3,] 0.0000000 1.0000000
## [4,] 1.0000000 0.0000000
## [5,] 0.0000000 1.0000000
## [6,] 0.4008593 0.5991407The computations can be speed up by using the parameter
threads (multiple cores can be run in parallel). There
is also the option to exclude extrema (minimum and
maximum distances) during the calculation of the k-nearest-neighbor
distances using extrema = TRUE. The bandwidth of the existing
kernels can be tuned using the h parameter.
K-nearest-neigbor calculations in the KernelKnn function can be
accomplished using the following distance metrics : euclidean,
manhattan, chebyshev, canberra,
braycurtis, minkowski (by default the order ‘p’ of the
minkowski parameter equals k), hamming, mahalanobis,
pearson_correlation, simple_matching_coefficient,
jaccard_coefficient and Rao_coefficient. The last four
are similarity measures and are appropriate for binary data [0,1].
I employed my RandomSearchR package to find the optimal parameters
for the KernelKnn function and the following two pairs of parameters
give an optimal accuracy,
| k | method | kernel |
|---|---|---|
| 10 | canberra | tricube |
| 9 | canberra | epanechnikov |
I’ll use the KernelKnnCV function to calculate the accuracy using 5-fold cross-validation for the previous mentioned parameter pairs,
fit_cv_pair1 = KernelKnnCV(X, y, k = 10 , folds = 5, method = 'canberra',
weights_function = 'tricube', regression = F,
Levels = unique(y), threads = 5, seed_num = 5)## List of 2
## $ preds:List of 5
## ..$ : num [1:71, 1:2] 0.00 5.02e-01 5.90e-18 9.16e-01 0.00 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## ..$ : num [1:70, 1:2] 0 0.0846 0.2507 0.0112 1 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## ..$ : num [1:70, 1:2] 0 0 0 0.056 0 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## ..$ : num [1:70, 1:2] 0 0 0 0 0 0 0 0 0 0 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## ..$ : num [1:70, 1:2] 0 0.986 1 1 0 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## $ folds:List of 5
## ..$ fold_1: int [1:71] 242 237 7 20 25 24 232 31 44 42 ...
## ..$ fold_2: int [1:70] 267 59 84 75 253 269 270 50 73 257 ...
## ..$ fold_3: int [1:70] 102 293 114 124 120 279 113 288 281 132 ...
## ..$ fold_4: int [1:70] 142 302 160 304 321 305 172 138 325 319 ...
## ..$ fold_5: int [1:70] 204 217 219 211 194 190 183 343 225 196 ...fit_cv_pair2 = KernelKnnCV(X, y, k = 9 , folds = 5,method = 'canberra',
weights_function = 'epanechnikov', regression = F,
Levels = unique(y), threads = 5, seed_num = 5)## List of 2
## $ preds:List of 5
## ..$ : num [1:71, 1:2] 0 0.459 0 0.913 0 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## ..$ : num [1:70, 1:2] 0.00 1.18e-01 2.01e-01 3.42e-07 1.00 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## ..$ : num [1:70, 1:2] 0 0 0 0.0825 0 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## ..$ : num [1:70, 1:2] 0 0 0 0 0 0 0 0 0 0 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## ..$ : num [1:70, 1:2] 0 0.957 1 1 0 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## $ folds:List of 5
## ..$ fold_1: int [1:71] 242 237 7 20 25 24 232 31 44 42 ...
## ..$ fold_2: int [1:70] 267 59 84 75 253 269 270 50 73 257 ...
## ..$ fold_3: int [1:70] 102 293 114 124 120 279 113 288 281 132 ...
## ..$ fold_4: int [1:70] 142 302 160 304 321 305 172 138 325 319 ...
## ..$ fold_5: int [1:70] 204 217 219 211 194 190 183 343 225 196 ...Each cross-validated object returns a list of length 2 ( the first sublist includes the predictions for each fold whereas the second gives the indices of the folds)
acc_pair1 = unlist(lapply(1:length(fit_cv_pair1$preds),
function(x) acc(y[fit_cv_pair1$folds[[x]]],
fit_cv_pair1$preds[[x]])))
acc_pair1## [1] 0.9154930 0.9142857 0.9142857 0.9285714 0.9571429## accurcay for params_pair1 is : 0.9259557acc_pair2 = unlist(lapply(1:length(fit_cv_pair2$preds),
function(x) acc(y[fit_cv_pair2$folds[[x]]],
fit_cv_pair2$preds[[x]])))
acc_pair2## [1] 0.9014085 0.9142857 0.9000000 0.9142857 0.9571429## accuracy for params_pair2 is : 0.9174245In the KernelKnn package there is also the option to combine kernels (adding or multiplying) from the existing ones. For instance, if I want to multiply the tricube with the gaussian kernel, then I’ll give the following character string to the weights_function, “tricube_gaussian_MULT”. On the other hand, If I want to add the same kernels then the weights_function will be “tricube_gaussian_ADD”. I experimented with my RandomSearchR package combining the different kernels and the following two parameter settings gave optimal results,
| k | method | kernel |
|---|---|---|
| 16 | canberra | biweight_triweight_gaussian_MULT |
| 5 | canberra | triangular_triweight_MULT |
fit_cv_pair1 = KernelKnnCV(X, y, k = 16, folds = 5, method = 'canberra',
weights_function = 'biweight_triweight_gaussian_MULT',
regression = F, Levels = unique(y), threads = 5,
seed_num = 5)## List of 2
## $ preds:List of 5
## ..$ : num [1:71, 1:2] 0.00 4.70e-01 5.79e-05 9.26e-01 4.85e-06 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## ..$ : num [1:70, 1:2] 0 0.0476 0.2602 0.0132 0.9991 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## ..$ : num [1:70, 1:2] 0.00 7.39e-08 0.00 1.78e-02 0.00 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## ..$ : num [1:70, 1:2] 0 0 0 0 0 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## ..$ : num [1:70, 1:2] 0 0.99181 1 1 0.00127 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## $ folds:List of 5
## ..$ fold_1: int [1:71] 242 237 7 20 25 24 232 31 44 42 ...
## ..$ fold_2: int [1:70] 267 59 84 75 253 269 270 50 73 257 ...
## ..$ fold_3: int [1:70] 102 293 114 124 120 279 113 288 281 132 ...
## ..$ fold_4: int [1:70] 142 302 160 304 321 305 172 138 325 319 ...
## ..$ fold_5: int [1:70] 204 217 219 211 194 190 183 343 225 196 ...fit_cv_pair2 = KernelKnnCV(X, y, k = 5, folds = 5, method = 'canberra',
weights_function = 'triangular_triweight_MULT',
regression = F, Levels = unique(y), threads = 5,
seed_num = 5)## List of 2
## $ preds:List of 5
## ..$ : num [1:71, 1:2] 0 0.363 0 1 0 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## ..$ : num [1:70, 1:2] 0 0.00076 0.18937 0 1 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## ..$ : num [1:70, 1:2] 0.00 0.00 0.00 3.44e-24 0.00 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## ..$ : num [1:70, 1:2] 0 0 0 0 0 0 0 0 0 0 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## ..$ : num [1:70, 1:2] 0 1 1 1 0 ...
## .. ..- attr(*, "dimnames")=List of 2
## .. .. ..$ : NULL
## .. .. ..$ : chr [1:2] "class_1" "class_2"
## $ folds:List of 5
## ..$ fold_1: int [1:71] 242 237 7 20 25 24 232 31 44 42 ...
## ..$ fold_2: int [1:70] 267 59 84 75 253 269 270 50 73 257 ...
## ..$ fold_3: int [1:70] 102 293 114 124 120 279 113 288 281 132 ...
## ..$ fold_4: int [1:70] 142 302 160 304 321 305 172 138 325 319 ...
## ..$ fold_5: int [1:70] 204 217 219 211 194 190 183 343 225 196 ...acc_pair1 = unlist(lapply(1:length(fit_cv_pair1$preds),
function(x) acc(y[fit_cv_pair1$folds[[x]]],
fit_cv_pair1$preds[[x]])))
acc_pair1## [1] 0.9014085 0.9142857 0.9285714 0.9285714 0.9571429## accuracy for params_pair1 is : 0.925996acc_pair2 = unlist(lapply(1:length(fit_cv_pair2$preds),
function(x) acc(y[fit_cv_pair2$folds[[x]]],
fit_cv_pair2$preds[[x]])))
acc_pair2## [1] 0.9014085 0.9285714 0.9285714 0.9142857 0.9714286## accuracy for params_pair2 is : 0.9288531