Statistics: fitcknn

### Function Reference: `fitcknn`

statistics: obj = fitcknn (X, Y)
statistics: obj = fitcknn (…, name, value)

Fit a k-Nearest Neighbor classification model.

`obj = fitcknn (X, Y)` returns a k-Nearest Neighbor classification model, obj, with X being the predictor data, and Y the class labels of observations in X.

- `X` must be a N×P numeric matrix of input data where rows correspond to observations and columns correspond to features or variables. X will be used to train the kNN model.
- `Y` is N×1 matrix or cell matrix containing the class labels of corresponding predictor data in X. Y can contain any type of categorical data. Y must have same numbers of Rows as X.

`obj = fitcknn (…, name, value)` returns a k-Nearest Neighbor classification model with additional options specified by `Name-Value` pair arguments listed below.

| Name | Value
--- | --- | ---
`"PredictorNames"` |  | A cell array of character vectors specifying the predictor variable names. The variable names are assumed to be in the same order as they appear in the training data X.
`"ResponseName"` |  | A character vector specifying the name of the response variable.
`"ClassNames"` |  | A cell array of character vectors specifying the names of the classes in the training data Y.
`"BreakTies"` |  | Tie-breaking algorithm used by predict when multiple classes have the same smallest cost. By default, ties occur when multiple classes have the same number of nearest points among the k nearest neighbors. The available options are specified by the following character arrays:

| `"smallest"` | This is the default and it favors the class with the smallest index among the tied groups, i.e. the one that appears first in the training labelled data.
| `"nearest"` | This favors the class with the nearest neighbor among the tied groups, i.e. the class with the closest member point according to the distance metric used.
| `"nearest"` | This randomly picks one class among the tied groups.

`"BucketSize"` |  | The maximum number of data points in the leaf node of the Kd-tree and it must be a positive integer. By default, it is 50. This argument is meaningful only when the selected search method is `"kdtree"`.
`"Cost"` |  | A N×R numeric matrix containing misclassification cost for the corresponding instances in X where R is the number of unique categories in Y. If an instance is correctly classified into its category the cost is calculated to be 1, If not then 0. cost matrix can be altered use `obj.cost = somecost`. default value `cost = ones(rows(X),numel(unique(Y)))`.
`"Prior"` |  | A numeric vector specifying the prior probabilities for each class. The order of the elements in `Prior` corresponds to the order of the classes in `ClassNames`.
`"NumNeighbors"` |  | A positive integer value specifying the number of nearest neighbors to be found in the kNN search. By default, it is 1.
`"Exponent"` |  | A positive scalar (usually an integer) specifying the Minkowski distance exponent. This argument is only valid when the selected distance metric is `"minkowski"`. By default it is 2.
`"Scale"` |  | A nonnegative numeric vector specifying the scale parameters for the standardized Euclidean distance. The vector length must be equal to the number of columns in X. This argument is only valid when the selected distance metric is `"seuclidean"`, in which case each coordinate of X is scaled by the corresponding element of `"scale"`, as is each query point in Y. By default, the scale parameter is the standard deviation of each coordinate in X. If a variable in X is constant, i.e. zero variance, this value is forced to 1 to avoid division by zero. This is the equivalent of this variable not being standardized.
`"Cov"` |  | A square matrix with the same number of columns as X specifying the covariance matrix for computing the mahalanobis distance. This must be a positive definite matrix matching. This argument is only valid when the selected distance metric is `"mahalanobis"`.
`"Distance"` |  | is the distance metric used by `knnsearch` as specified below:

| `"euclidean"` | Euclidean distance.
| `"seuclidean"` | standardized Euclidean distance. Each coordinate difference between the rows in X and the query matrix Y is scaled by dividing by the corresponding element of the standard deviation computed from X. To specify a different scaling, use the `"Scale"` name-value argument.
| `"cityblock"` | City block distance.
| `"chebychev"` | Chebychev distance (maximum coordinate difference).
| `"minkowski"` | Minkowski distance. The default exponent is 2. To specify a different exponent, use the `"P"` name-value argument.
| `"mahalanobis"` | Mahalanobis distance, computed using a positive definite covariance matrix. To change the value of the covariance matrix, use the `"Cov"` name-value argument.
| `"cosine"` | Cosine distance.
| `"correlation"` | One minus the sample linear correlation between observations (treated as sequences of values).
| `"spearman"` | One minus the sample Spearman’s rank correlation between observations (treated as sequences of values).
| `"hamming"` | Hamming distance, which is the percentage of coordinates that differ.
| `"jaccard"` | One minus the Jaccard coefficient, which is the percentage of nonzero coordinates that differ.
| @distfun | Custom distance function handle. A distance function of the form `function D2 = distfun (XI, YI)`, where XI is a 1×P vector containing a single observation in P-dimensional space, YI is an N×P matrix containing an arbitrary number of observations in the same P-dimensional space, and D2 is an N×P vector of distances, where `(D2k)` is the distance between observations XI and `(YIk,:)`.

`"DistanceWeight"` |  | A distance weighting function, specified either as a function handle, which accepts a matrix of nonnegative distances and returns a matrix the same size containing nonnegative distance weights, or one of the following values: `"equal"`, which corresponds to no weighting; `"inverse"`, which corresponds to a weight equal to 1/distance; `"squaredinverse"`, which corresponds to a weight equal to 1/distance^2.
`"IncludeTies"` |  | A boolean flag to indicate if the returned values should contain the indices that have same distance as the K^th neighbor. When `false`, `knnsearch` chooses the observation with the smallest index among the observations that have the same distance from a query point. When `true`, `knnsearch` includes all nearest neighbors whose distances are equal to the K^th smallest distance in the output arguments. To specify K, use the `"K"` name-value pair argument.
`"NSMethod"` |  | is the nearest neighbor search method used by `knnsearch` as specified below.

| `"kdtree"` | Creates and uses a Kd-tree to find nearest neighbors. `"kdtree"` is the default value when the number of columns in X is less than or equal to 10, X is not sparse, and the distance metric is `"euclidean"`, `"cityblock"`, `"manhattan"`, `"chebychev"`, or `"minkowski"`. Otherwise, the default value is `"exhaustive"`. This argument is only valid when the distance metric is one of the four aforementioned metrics.
| `"exhaustive"` | Uses the exhaustive search algorithm by computing the distance values from all the points in X to each point in Y.

See also: ClassificationKNN, knnsearch, rangesearch, pdist2

Source Code: fitcknn