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Class: NaiveBayes

Create Naive Bayes classifier object by fitting training data


nb =, class)
nb =, 'param1',val1, 'param2',val2, ...)


fit will be removed in a future release. Use fitcnb instead.


nb =, class) builds a NaiveBayes classifier object nb. training is an N-by-D numeric matrix of training data. Rows of training correspond to observations; columns correspond to features. class is a classing variable for training taking K distinct levels. Each element of class defines which class the corresponding row of training belongs to. training and class must have the same number of rows.

nb =, 'param1',val1, 'param2',val2, ...) specifies one or more of the following name/value pairs:

  • 'Distribution' – a character vector or a 1-by-D cell array of character vectors, specifying which distributions fit uses to model the data. If the value is a , fit models all the features using one type of distribution. fit can also model different features using different types of distributions. If the value is a cell array, its jth element specifies the distribution fit uses for the jth feature. The available types of distributions are:

    'normal' (default)Normal (Gaussian) distribution.
    'kernel'Kernel smoothing density estimate.
    'mvmn'Multivariate multinomial distribution for discrete data. fit assumes each individual feature follows a multinomial model within a class. The parameters for a feature include the probabilities of all possible values that the corresponding feature can take.

    Multinomial distribution for classifying the count-based data such as the bag-of-tokens model. In the bag-of-tokens model, the value of the jth feature is the number of occurrences of the jth token in this observation, so it must be a nonnegative integer. When 'mn' is used, fit considers each observation as multiple trials of a multinomial distribution, and considers each occurrence of a token as one trial. The number of categories (bins) in this multinomial model is the number of distinct tokens, i.e., the number of columns of training.

    If you specify mn, then all features are components of a multinomial distribution. Therefore, you cannot include 'mn' as an element of a cell array of character vectors.

  • 'Prior' – The prior probabilities for the classes, specified as one of the following:

    'empirical' (default)fit estimates the prior probabilities from the relative frequencies of the classes in training.
    'uniform'The prior probabilities are equal for all classes.
    vectorA numeric vector of length K specifying the prior probabilities in the class order of class.
    structureA structure S containing class levels and their prior probabilities. S must have two fields:
    • S.prob: A numeric vector of prior probabilities.

    • S.class: A vector of the same type as class, containing unique class levels indicating the class for the corresponding element of prob. S.class must contain all the K levels in class. It can also contain classes that do not appear in class. This can be useful if training is a subset of a larger training set. fit ignores any classes that appear in S.class but not in class.

    If the prior probabilities don't sum to one, fit will normalize them.

  • 'KSWidth' – The bandwidth of the kernel smoothing window. The default is to select a default bandwidth automatically for each combination of feature and class, using a value that is optimal for a Gaussian distribution. You can specify the value as one of the following:

    scalarWidth for all features in all classes.
    row vector1-by-D vector where the jth element is the bandwidth for the jth feature in all classes.
    column vectorK-by-1 vector where the ith element specifies the bandwidth for all features in the ith class. K represents the number of class levels.
    matrixK-by-D matrix M where M(i,j) specifies the bandwidth for the jth feature in the ith class.
    structureA structure S containing class levels and their bandwidths. S must have two fields:
    • S.width – A numeric array of bandwidths specified as a row vector, or a matrix with D columns.

    • S.class – A vector of the same type as class, containing unique class levels indicating the class for the corresponding row of width.

  • 'KSSupport' – The regions where the density can be applied. It can be 'unbounded' (default), 'positive', a two-element vector as shown below, or a 1-by-D cell array of these values:

    'unbounded' (default)The density can extend over the whole real line.
    'positive'The density is restricted to positive values.
    [L,U]A two-element vector specifying the finite lower bound L and upper bound U for the support of the density.

  • 'KSType' – The type of kernel smoother to use. It can be 'normal' (default), 'box', 'triangle', 'epanechnikov', or a 1-by-D cell array of these values.

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