## Introduction

Neighbr is a package for performing k-nearest neighbor classification and regression. Highlights include:

• comparison measures that support continuous or logical features
• support for categorical and continuous targets
• neighbor ranking

Neighbr models can also be converted to the PMML (Predictive Model Markup Language) standard using the pmml R package.

This vignette provides examples and advice on using the package.

## Examples

First, load necessary libraries and set the seed and number display options. knitr::kable is used to display data frames.

library(neighbr)
library(knitr)
set.seed(123)
options(digits=3)

### Continuous features and categorical target

This example shows using squared euclidean distance with 3 neighbors to classify the Species of flowers in the iris dataset. Each training instance consists of 4 features and 1 class variable. The categorical target is predicted by a majority vote from the closest k neighbors. The knn() function requires that all columns in test_set are feature columns, and have the same names and are in the same order as the features in train_set. The train_set is assumed to only contain features and targets (one categorical, one continuous, and/or ID for neighbor ranking); i.e., if a column name is not specified as a target, it is assumed to be a feature. The fit object contains predictions for test_set in fit$test_set_scores (there is no predict method for knn). data(iris) train_set <- iris[1:147,] #train set contains all targets and features test_set <- iris[148:150,!names(iris) %in% c("Species")] #test set does not contain any targets #run knn function fit <- knn(train_set=train_set,test_set=test_set, k=3, categorical_target="Species", comparison_measure="squared_euclidean") #show predictions kable(fit$test_set_scores)
categorical_target
148 virginica
149 virginica
150 virginica

The returned data frame contains predictions for the categorical target (Species).

### Mixed targets and neighbor ranking

It is possible to predict categorical and continuous targets simultaneously, as well as to return the IDs of closest neighbors of a given instance. In the next example, an ID column is added to the data for ranking, and Petal.Width is used as a continuous target. By default, the prediction for the continuous target is calculated by averaging the closest k neighbors.

data(iris)
iris$ID <- c(1:150) #an ID column is necessary if ranks are to be calculated train_set <- iris[1:147,] #train set contains all predicted variables, features, and ID column test_set <- iris[148:150,!names(iris) %in% c("Petal.Width","Species","ID")] #test set does not contain predicted variables or ID column fit <- knn(train_set=train_set,test_set=test_set, k=3, categorical_target="Species", continuous_target= "Petal.Width", comparison_measure="squared_euclidean", return_ranked_neighbors=3, id="ID") kable(fit$test_set_scores)
categorical_target continuous_target neighbor1 neighbor2 neighbor3
148 virginica 2.20 146 111 116
149 virginica 2.17 137 116 138
150 virginica 1.93 115 128 84

The ranked neighbor IDs are returned along with the categorical and continuous targets, with neghbor1 being the closest in terms of distance. If a similarity measure were being used, neighbor1 would be the most similar. Any number of neighbors can be returned, as long as return_ranked_neighbors <= k.

### Neighbor ranking without targets

It is possible to get neighbor ranks without a target variable. In this unsupervised learning case, continuous_target and categorical_target are left as NULL by default.

data(iris)
iris$ID <- c(1:150) #an ID column is necessary if ranks are to be calculated train_set <- iris[1:147,-c(5)] #remove Species categorical variable test_set <- iris[148:150,!names(iris) %in% c("Species","ID")] #test set does not contain predicted variables or ID column fit <- knn(train_set=train_set,test_set=test_set, k=5, comparison_measure="squared_euclidean", return_ranked_neighbors=4, id="ID") kable(fit$test_set_scores)
neighbor1 neighbor2 neighbor3 neighbor4
148 111 112 117 146
149 137 116 111 141
150 128 139 102 143

### Logical features

The package supports logical features, to be used with an appropriate similarity measure. This example demonstrates predicting a categorical target and ranking neighbors for the HouseVotes84 dataset (from the mlbench package). The features may be logical consisting of {TRUE, FALSE} or numeric vectors consisting of {0,1}, but not factors. In this example, the factor features are converted to numeric vectors.

library(mlbench)

# change all {yes,no} factors to {0,1}
feature_names <- names(dat)[!names(dat) %in% c("Class","ID")]
for (n in feature_names) {
levels(dat[,n])[levels(dat[,n])=="n"] <- 0
levels(dat[,n])[levels(dat[,n])=="y"] <- 1
}

# change factors to numeric
for (n in feature_names) {dat[,n] <- as.numeric(levels(dat[,n]))[dat[,n]]}

dat$ID <- c(1:nrow(dat)) #an ID column is necessary if ranks are to be calculated train_set <- dat[1:225,] test_set <- dat[226:232,!names(dat) %in% c("Class","ID")] #test set does not contain predicted variables or ID column fit <- knn(train_set=train_set,test_set=test_set, k=7, categorical_target = "Class", comparison_measure="jaccard", return_ranked_neighbors=3, id="ID") kable(fit$test_set_scores)
categorical_target neighbor1 neighbor2 neighbor3
422 democrat 209 109 149
423 democrat 114 148 106
424 democrat 114 96 112
427 democrat 5 47 91
428 republican 70 156 155
431 republican 115 117 152
432 democrat 57 130 135

### Categorical features

Categorical features are not directly supported: categorical numeric features are assumed to be continuous, and if comparison_measure is a similarity measure, only logical features are allowed. However, categorical features may be transformed into the required form with one-hot encoding (for example, using the dummies package).

The algorithm will not work for a dataset with a mix of categorical and continuous features as-is: all features must be either logical, or continuous.

### Comparison measures

Distance measures are used for vectors with continuous elements. Similarity measures are used for logical vectors. The comparison measures used in neighbr are based on those defined in the PMML standard.

Functions in neighbr can be used to calculate distances or similarities between vectors directly:

distance(c(1,2,3),c(2,3,4),"squared_euclidean")
#> [1] 3
similarity(c(0,1,0,0),c(1,1,1,0),"simple_matching")
#> [1] 0.5

The next two sections show the formulas used in measure calculation.

#### Distance

For two vectors $$x$$ and $$y$$ of length $$n$$, distances are calculated as follows:

• Euclidean: $$(\sum_{i=0}^{n}(x_i - y_i)^2)^{1/2}$$

• Squared euclidean: $$\sum_{i=0}^{n}(x_i - y_i)^2$$

#### Similarity

For two vectors $$x$$ and $$y$$ of length $$n$$, let:

• $${a_{11}}$$ = number of times where $$x_i=1$$ and $$y_i=1$$
• $${a_{10}}$$ = number of times where $$x_i=1$$ and $$y_i=0$$
• $${a_{01}}$$ = number of times where $$x_i=0$$ and $$y_i=1$$
• $${a_{00}}$$ = number of times where $$x_i=0$$ and $$y_i=0$$

Then, similarities are calculated as follows:

• Simple matching: $$(a_{11} + a_{00}) / (a_{11} + a_{10} + a_{01} + a_{00})$$

• Jaccard: $$(a_{11}) / (a_{11} + a_{10} + a_{01})$$

• Tanimoto: $$(a_{11} + a_{00}) / (a_{11} + 2 * (a_{10} + a_{01}) + a_{00})$$

### Ties

When two (or more) training instances are the same distance from a test instance, a tie occurs. In this case, the training example that appears first in train_set will be first in the list of nearest neighbors. If ranked neighbors are being output, that training example will be assigned the lower rank.

For categorical targets, a tie occurs when two (or more) training instances have the same class (regardless of distance or similarity), and no single class has the highest frequency of occurrence in a majority vote among k neighbors. In this case, the tie breaking procedure follows the PMML specification:

In case of a tie, the category with the largest number of cases in the training data is the winner. If multiple categories are tied on the largest number of cases in the training data, then the category with the smallest data value (in lexical order) among the tied categories is the winner.

### Missing data

The package does not directly support missing data. Various imputation techniques may be used (e.g., average for continuous features), or rows with N/A may be deleted, before being passed to knn().

### Neighbr and PMML

This package was developed following the KNN specification in the PMML (Predictive Model Markup Language) standard. The models produced by neighbr can be converted to PMML (using the pmml R package).

Some parts of the package are only used for conversion to PMML. For example, the function_name field returned by knn() corresponds to a field required by PMML.