Today introduces a common classification method based on probability in machine learning: Naive Bayes. Unlike hard decision methods such as KNN or decision trees, which output only 0 or 1, Naive Bayes provides a probability for each class, with values ranging between 0 and 1. This makes it particularly effective in tasks like text classification and spam detection.
Naive Bayes is based on Bayes' theorem, which allows us to calculate the probability of an event given prior knowledge. In a two-class problem, where we have classes câ‚ and câ‚‚, and a sample x (such as an email), we want to determine whether x belongs to câ‚ or câ‚‚. This can be expressed using posterior probability:
$$ P(c|x) = \frac{P(x|c)P(c)}{P(x)} $$
Here, $ P(c|x) $ is the probability that the sample belongs to class c, given the input x. The key assumption in Naive Bayes is that the features are conditionally independent given the class, which simplifies the computation significantly.
To illustrate how Naive Bayes works, let's walk through an example of text categorization. We start by creating a dataset of labeled text samples. For instance, we might have a list of emails, some marked as spam (class 1) and others as non-spam (class 0). Each email is represented as a list of words.
Next, we create a vocabulary list that includes all unique words from the dataset. This helps in converting each email into a numerical vector, which can then be used for training the model. There are different ways to represent the words: one approach is to count whether a word appears at all (binary representation), while another counts the frequency of each word.
Once the data is prepared, we train the Naive Bayes classifier. During training, we compute the probabilities of each word appearing in each class. To avoid zero probabilities, we apply Laplace smoothing, which adds a small constant to the counts. Finally, we convert the probabilities to log space to prevent underflow due to repeated multiplications.
After training, we can classify new emails by computing the likelihood of the test vector belonging to each class and selecting the class with the highest probability.
Below is a simple test case using a sample text. The code parses the text, creates a vocabulary, converts the text into a feature vector, and applies the trained model to predict the class.
This process demonstrates the power and simplicity of Naive Bayes in handling text-based classification tasks efficiently and effectively.
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