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Machine learning can be applied to categorize text by training a machine learning model with a dataset of labeled examples. The process involves the following steps:

1. Data Preparation: The first step in categorizing text using machine learning is to collect or create a dataset of text examples that are labeled with the appropriate categories.

2. Feature Extraction: The next step is to extract relevant features from the text, which could include word frequency, word length, part-of-speech tags, or other linguistic features.

3. Model Selection: Once the features are extracted, a suitable machine learning model must be selected. Popular models for categorizing text include Naive Bayes, Support Vector Machines (SVM), and Decision Trees.

4. Training: After selecting a model, the dataset is split into training and testing sets. The model is trained on the training set and then tested and evaluated on the testing set.

5. Optimization: If the model does not perform well enough, hyperparameters such as the learning rate or regularization can be adjusted to improve the model's performance.

6. Prediction: Once the model is optimized, it can be used to categorize new text examples.

7. Refinement: The model's performance should be monitored and refined over time as new data and categories become available.