bayesian

README

Naive Bayesian Classification

Perform naive Bayesian classification into an arbitrary number of classes on sets of strings.

Copyright (c) 2011. Jake Brukhman. (jbrukh@gmail.com). All rights reserved. See the LICENSE file for BSD-style license.

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Background

See code comments for a refresher on naive Bayesian classifiers.

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Installation

Using the go command:

$ go get github.com/jbrukh/bayesian
$ go install !$

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Documentation

See the GoPkgDoc documentation here.

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Features

• Conditional probability and "log-likelihood"-like scoring.
• Underflow detection.
• Simple persistence of classifiers.
• Statistics.

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Example

To use the classifier, first you must create some classes and train it:

import . "bayesian"

const (
    Good Class = "Good"
    Bad Class = "Bad"
)

classifier := NewClassifier(Good, Bad)
goodStuff := []string{"tall", "rich", "handsome"}
badStuff  := []string{"poor", "smelly", "ugly"}
classifier.Learn(goodStuff, Good)
classifier.Learn(badStuff,  Bad)

Then you can ascertain the scores of each class and the most likely class your data belongs to:

scores, likely, _ := classifier.LogScores(
                        []string{"tall", "girl"}
                     )

Magnitude of the score indicates likelihood. Alternatively (but with some risk of float underflow), you can obtain actual probabilities:

probs, likely, _ := classifier.ProbScores(
                        []string{"tall", "girl"}
                     )

Use wisely.

Documentation

Overview

A Naive Bayesian Classifier Jake Brukhman <jbrukh@gmail.com>

BAYESIAN CLASSIFICATION REFRESHER: suppose you have a set of classes (e.g. categories) C := {C_1, ..., C_n}, and a document D consisting of words D := {W_1, ..., W_k}. We wish to ascertain the probability that the document belongs to some class C_j given some set of training data associating documents and classes.

By Bayes' Theorem, we have that

P(C_j|D) = P(D|C_j)*P(C_j)/P(D).

The LHS is the probability that the document belongs to class C_j given the document itself (by which is meant, in practice, the word frequencies occurring in this document), and our program will calculate this probability for each j and spit out the most likely class for this document.

P(C_j) is referred to as the "prior" probability, or the probability that a document belongs to C_j in general, without seeing the document first. P(D|C_j) is the probability of seeing such a document, given that it belongs to C_j. Here, by assuming that words appear independently in documents (this being the "naive" assumption), we can estimate

P(D|C_j) ~= P(W_1|C_j)*...*P(W_k|C_j)

where P(W_i|C_j) is the probability of seeing the given word in a document of the given class. Finally, P(D) can be seen as merely a scaling factor and is not strictly relevant to classificiation, unless you want to normalize the resulting scores and actually see probabilities. In this case, note that

P(D) = SUM_j(P(D|C_j)*P(C_j))

One practical issue with performing these calculations is the possibility of float64 underflow when calculating P(D|C_j), as individual word probabilities can be arbitrarily small, and a document can have an arbitrarily large number of them. A typical method for dealing with this case is to transform the probability to the log domain and perform additions instead of multiplications:

log P(C_j|D) ~ log(P(C_j)) + SUM_i(log P(W_i|C_j))

where i = 1, ..., k. Note that by doing this, we are discarding the scaling factor P(D) and our scores are no longer probabilities; however, the monotonic relationship of the scores is preserved by the log function.

Index

• type Class
• type Classifier
  • func NewClassifier(classes ...Class) (c *Classifier)
  • func NewClassifierFromFile(name string) (c *Classifier, err error)
  • func NewClassifierFromReader(r io.Reader) (c *Classifier, err error)
  • func (c *Classifier) Learn(document []string, which Class)
  • func (c *Classifier) Learned() int
  • func (c *Classifier) LogScores(document []string) (scores []float64, inx int, strict bool)
  • func (c *Classifier) ProbScores(doc []string) (scores []float64, inx int, strict bool)
  • func (c *Classifier) SafeProbScores(doc []string) (scores []float64, inx int, strict bool, err error)
  • func (c *Classifier) Seen() int
  • func (c *Classifier) WordCount() (result []int)
  • func (c *Classifier) WordFrequencies(words []string) (freqMatrix [][]float64)
  • func (c *Classifier) WriteTo(w io.Writer) (err error)
  • func (c *Classifier) WriteToFile(name string) (err error)

Types

type Class

type Class string

Class defines a set of classes that the classifier will filter: C = {C_1, ..., C_n}. You should define your classes as a set of constants, for example as follows:

const (
    Good Class = "Good"
    Bad Class = "Bad
)

Class values should be unique.

type Classifier

type Classifier struct {
	Classes []Class `json:"classes"`
	// contains filtered or unexported fields
}

Classifier implements the Naive Bayesian Classifier.

func NewClassifier

func NewClassifier(classes ...Class) (c *Classifier)

NewClassifier returns a new classifier. The classes the provided should be at least 2 in number and unique, or this method will panic.

func NewClassifierFromFile

func NewClassifierFromFile(name string) (c *Classifier, err error)

NewClassifierFromFile loads an existing classifier from file. The classifier was previously saved with a call to c.WriteToFile(string).

func NewClassifierFromReader

func NewClassifierFromReader(r io.Reader) (c *Classifier, err error)

This actually does the deserializing of a Gob encoded classifier

func (*Classifier) Learn

func (c *Classifier) Learn(document []string, which Class)

Learn will accept new training documents for supervised learning.

func (*Classifier) Learned

func (c *Classifier) Learned() int

Learned returns the number of documents ever learned in the lifetime of this classifier.

func (*Classifier) LogScores

func (c *Classifier) LogScores(document []string) (scores []float64, inx int, strict bool)

LogScores produces "log-likelihood"-like scores that can be used to classify documents into classes.

The value of the score is proportional to the likelihood, as determined by the classifier, that the given document belongs to the given class. This is true even when scores returned are negative, which they will be (since we are taking logs of probabilities).

The index j of the score corresponds to the class given by c.Classes[j].

Additionally returned are "inx" and "strict" values. The inx corresponds to the maximum score in the array. If more than one of the scores holds the maximum values, then strict is false.

Unlike c.Probabilities(), this function is not prone to floating point underflow and is relatively safe to use.

func (*Classifier) ProbScores

func (c *Classifier) ProbScores(doc []string) (scores []float64, inx int, strict bool)

ProbScores works the same as LogScores, but delivers actual probabilities as discussed above. Note that float64 underflow is possible if the word list contains too many words that have probabilities very close to 0.

Notes on underflow: underflow is going to occur when you're trying to assess large numbers of words that you have never seen before. Depending on the application, this may or may not be a concern. Consider using SafeProbScores() instead.

func (*Classifier) SafeProbScores

func (c *Classifier) SafeProbScores(doc []string) (scores []float64, inx int, strict bool, err error)

SafeProbScores works the same as ProbScores, but is able to detect underflow in those cases where underflow results in the reverse classification. If an underflow is detected, this method panics, allowing the user to recover as necessary. Note that underflow, under certain rare circumstances, may still result in incorrect probabilities being returned, but this method guarantees that all panic-less invokations are properly classified.

Underflow detection is more costly because it also has to make additional log score calculations.

func (*Classifier) Seen

func (c *Classifier) Seen() int

Seen returns the number of documents ever classified in the lifetime of this classifier.

func (*Classifier) WordCount

func (c *Classifier) WordCount() (result []int)

WordCount returns the number of words counted for each class in the lifetime of the classifier.

func (*Classifier) WordFrequencies

func (c *Classifier) WordFrequencies(words []string) (freqMatrix [][]float64)

WordFrequencies returns a matrix of word frequencies that currently exist in the classifier for each class state for the given input words. In other words, if you obtain the frequencies

freqs := c.WordFrequencies(/* [j]string */)

then the expression freq[i][j] represents the frequency of the j-th word within the i-th class.

func (*Classifier) WriteTo

func (c *Classifier) WriteTo(w io.Writer) (err error)

Serialize this classifier to GOB and write to Writer

func (*Classifier) WriteToFile

func (c *Classifier) WriteToFile(name string) (err error)

Serialize this classifier to a file.