Now that we've transformed our text into numerical feature vectors using techniques like TF-IDF and N-grams, we can leverage standard machine learning algorithms for classification. The core idea remains the same as in other machine learning domains: we train a model on labeled data (text documents paired with their categories) to learn patterns that allow it to predict the category for new, unseen documents.

Fortunately, the feature representations we've created (like sparse TF-IDF matrices) are compatible with many well-established classification algorithms. While numerous classifiers exist, a few have proven particularly effective or serve as excellent starting points for text classification tasks due to their characteristics when dealing with high-dimensional and sparse data typical of text. Let's review some of these foundational algorithms.

Naive Bayes Classifiers

Naive Bayes classifiers are a family of simple probabilistic algorithms based on applying Bayes' theorem with a strong ("naive") independence assumption between the features. Despite this simplification, they often perform surprisingly well for text classification, especially as a baseline.

The core idea is to calculate the probability of a document belonging to a certain class given its features. According to Bayes' theorem:

P(\text{class}|\text{document}) = \frac{P(\text{document}|\text{class}) \times P(\text{class})}{P(\text{document})}

The "naive" part comes from assuming that the features (e.g., the presence or count of words) are conditionally independent given the class:

P(\text{word}_1, \text{word}_2, ..., \text{word}_n|\text{class}) \approx P(\text{word}_1|\text{class}) \times P(\text{word}_2|\text{class}) \times ... \times P(\text{word}_n|\text{class})

This assumption simplifies the calculation significantly. For text, common variants include:

Multinomial Naive Bayes: Typically used with word counts or TF-IDF values. It models the probability of observing a specific count for each word in a document belonging to a particular class.
Bernoulli Naive Bayes: Used with binary features (e.g., word presence or absence). It models the probability of a word appearing or not appearing in a document of a given class.

Strengths for Text:

Computationally efficient and fast to train, even with high-dimensional feature spaces (many unique words).
Requires relatively small amounts of training data to estimate parameters.
Often provides a solid performance baseline.

Weaknesses for Text:

The conditional independence assumption rarely holds true for language (word order and context matter).
Can be sensitive to how features are represented (counts vs. TF-IDF vs. binary).

Support Vector Machines (SVM)

Support Vector Machines operate differently. Instead of probabilities, they aim to find the optimal hyperplane (a boundary) that best separates data points belonging to different classes in the high-dimensional feature space. The "optimal" hyperplane is the one that maximizes the margin, which is the distance between the hyperplane and the nearest data points (support vectors) from each class.

For text data represented as high-dimensional vectors (e.g., TF-IDF), SVMs are often highly effective. While SVMs can use various kernel functions (like polynomial or Radial Basis Function, RBF) to map data into even higher dimensions to find non-linear separations, linear kernels are frequently sufficient and computationally efficient for text classification. A linear kernel means the decision boundary is a straight line (in 2D), a flat plane (in 3D), or a hyperplane (in higher dimensions).

Strengths for Text:

Effective in high-dimensional spaces, common with text features.
Performs well even when the number of dimensions is greater than the number of samples.
Memory efficient as it only uses a subset of training points (support vectors) for the decision function.
Versatile through different kernel functions (though linear often works well for text).

Weaknesses for Text:

Can be computationally intensive to train, especially with very large datasets.
Less inherently interpretable compared to Naive Bayes or Logistic Regression; understanding why a prediction was made is harder.
Performance can be sensitive to the choice of the regularization parameter (C) and kernel parameters.

Logistic Regression

Despite its name, Logistic Regression is a widely used algorithm for binary classification tasks (it can be extended to multi-class problems, often using a one-vs-rest approach). It models the probability that an input belongs to a particular class using the logistic (sigmoid) function.

The model learns weights for each feature, similar to linear regression. The weighted sum of features is then passed through the sigmoid function, which squashes the output to a value between 0 and 1, interpretable as a probability.

P(y=1|X) = \sigma(w_0 + w_1 x_1 + w_2 x_2 + ... + w_n x_n)

Where $X = (x_1, ..., x_n)$ are the input features (e.g., TF-IDF values), $w_i$ are the learned weights, and $\sigma$ is the sigmoid function:

\sigma(z) = \frac{1}{1 + e^{-z}}

For text classification, Logistic Regression is a strong baseline. Because text features are often high-dimensional and sparse, regularization (like L1 or L2) is almost always applied. Regularization adds a penalty term to the loss function based on the magnitude of the learned weights, which helps prevent overfitting and can improve generalization. L2 regularization encourages smaller weights, while L1 regularization can lead to sparse weights (setting some feature weights exactly to zero), effectively performing feature selection.

Strengths for Text:

Provides probabilistic outputs, which can be useful for ranking or setting confidence thresholds.
The learned weights can offer some level of interpretability regarding feature importance (especially with appropriate scaling and regularization).
Efficient to train and performs well on sparse data like text features.
Regularization techniques (L1, L2) are readily available and effective.

Weaknesses for Text:

Assumes a linear relationship between features and the log-odds of the outcome. May not capture complex, non-linear patterns as effectively as kernelized SVMs or more complex models.
Can be sensitive to multicollinearity among features, although regularization helps mitigate this.

This review provides a foundation for understanding the types of algorithms commonly applied to text classification. Each has its advantages and disadvantages, and the best choice often depends on the specific dataset, the nature of the features, computational resources, and the need for interpretability. In the upcoming sections, we'll discuss how to practically apply these models, evaluate their performance rigorously, and tune them for optimal results.