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Sign in[Submit an Article](https://write.insightmediagroup.io) [Latest](https://towardsdatascience.com/latest/)[Editor's Picks](https://towardsdatascience.com/tag/editors-pick/)[Newsletter](https://towardsdatascience.com/tag/the-variable/)[ShipAI](https://towardsdatascience.com/shipai/) * * * [Write For TDS](https://towardsdatascience.com/submissions/) [LinkedIn](https://www.linkedin.com/company/towards-data-science/)[X](https://x.com/TDataScience)Toggle Search [Probability](https://towardsdatascience.com/category/probability/) # Text Classification Using Naive Bayes: Theory & A Working Example In this article, I explain how the Naive Bayes works and I implement a multi-class text classification problem step-by-step in Python. [Serafeim Loukas, PhD](https://towardsdatascience.com/author/seralouk/) October 12, 202010 min read ### [Getting Started](https://towardsdatascience.com/tagged/getting-started) ![Figure created by the author.](../images/000.png) Figure created by the author. Learn this step by step with the interactive [Computer Science](https://roadmap.sh/computer-science) and [Machine Learning](https://roadmap.sh/machine-learning) roadmaps. ### Table of contents 1. **Introduction** 2. **The Naive Bayes algorithm** 3. **Dealing with text data** 4. **Working Example in Python (step-by-step guide)** 5. **Bonus: Having fun with the model** 6. **Conclusions** * * * ## 1. Introduction **Naive Bayes** classifiers are a collection of classification algorithms based on **Bayes' Theorem**. It is not a single algorithm but a family of algorithms where all of them share a common principle, i.e. every pair of features being classified is independent of each other. **Naive Bayes** classifiers have been heavily used for **text classification** and **text** **analysis** machine learning **problems**. **Text Analysis** is a major application field for machine learning algorithms. However the raw data, a sequence of symbols (i.e. strings) cannot be fed directly to the algorithms themselves as most of them expect numerical feature vectors with a fixed size rather than the raw text documents with variable length. In this article I explain a) how **Naive Bayes** works**,** b) how we can use **text** **data** and **fit** them into a **model** after transforming them into a more appropriate form. Finally, I **implement** a **multi-class text classification problem step-by-step in Python**. Let's get started !!! * * * * **NEW** : After a great deal of hard work and staying behind the scenes for quite a while, we're excited to now offer our expertise through a platform, the "[**Data Science Hub**](https://www.patreon.com/TheDataScienceHub\))" on Patreon (). This hub is our way of providing you with **bespoke consulting services** and comprehensive **responses to all your inquiries** , ranging from Machine Learning to strategic data analytics planning. * * * ## 2. The Naive Bayes algorithm Naive Bayes classifiers are a collection of classification algorithms based on **Bayes' Theorem**. It is not a single algorithm but a family of algorithms where all of them share a common principle, i.e. every pair of features being classified is independent of each other. The dataset is divided into two parts, namely, **feature matrix** and the **response/target vector**. * The **Feature** **matrix** (X) contains all the vectors(rows) of the dataset in which each vector consists of the value of **dependent features**. The number of features is **d** i.e. **X = (x1,x2,x2, xd).** * The **Response/target** **vector** (y) contains the value of **class/group variable** for **each row of feature matrix.** ### **2.1. The main two assumptions of Naive Bayes** Naive Bayes assumes that **each feature/variable** of the same class makes an: * **independent** * **equal** **contribution to the outcome.** **Side Note:** The assumptions made by Naive Bayes are not generally correct in real-world situations. In-fact, the independence assumption is often not met and this is why it is called "**Naive** " i.e. because it assumes something that might not be true. ### 2.2. The Bayes' Theorem Bayes' Theorem finds the probability of an event occurring given the probability of another event that has already occurred. Bayes' theorem is stated mathematically as follows: ![Figure created by the author.](../images/001.png) Figure created by the author. where: * **A** and **B** are called **events.** * P(A | B) is the probability of event A, given the event B is true (has occured). Event B is also termed as **evidence**. * P(A) is the **priori** of A (the prior independent probability, i.e. probability of event before evidence is seen). * P(B | A) is the probability of B given event A, i.e. probability of event B after evidence A is seen. ### Summary ![Figure created by the author.](../images/002.png) Figure created by the author. ### 2.3. The Naive Bayes Model Given a data matrix **X** and a target vector **y,** we state our problem as: ![Figure created by the author.](../images/003.png) Figure created by the author. where, **y** is **class variable** and **X** is a **dependent feature vector with dimension d i.e. X = (x1,x2,x2, xd),** where **d** is the number of variables/features of the sample. * P(y|X) is the probability of observing the class **y** given the sample **X** with **X = (x1,x2,x2, xd),** where **d** is the number of variables/features of the sample. Now the "naïve" [conditional independence](https://en.wikipedia.org/wiki/Conditional_independence) assumptions come into play: assume that all features in **X** are [mutually independent](https://en.wikipedia.org/wiki/Mutually_independent), conditional on the category **y** : ![Figure created by the author.](../images/004.png) Figure created by the author. Finally, to find the probability of a given **sample** for all possible values of the class variable _**y**_ , we just need to find the output with maximum probability: ![Figure created by the author.](../images/005.png) Figure created by the author. * * * ## 3. Dealing with text data One question that arises at this point is the following: > How are we going to use the raw text data to train the model ? The raw data is a collection of strings ! Text Analysis is a major application field for machine learning algorithms. **However the raw data, a sequence of symbols (i.e. strings) cannot be fed directly to the algorithms themselves as most of them expect numerical feature vectors with a fixed size rather than the raw text documents with variable length.** In order to address this, scikit-learn provides utilities for the most common ways to extract numerical features from text content, namely: * **tokenizing** strings and giving an integer id for each possible token, for instance by using white-spaces and punctuation as token separators. * **counting** the occurrences of tokens in each document. In this scheme, features and samples are defined as follows: * each **individual token occurrence frequency** is treated as a **feature**. * the vector of all the token frequencies for a given **document** is considered a multivariate **sample**. ### "Counting" Example (to really understand this before we move on): text ``` from sklearn.feature_extraction.text import CountVectorizer corpus = [ 'This is the first document.', 'This document is the second document.', 'And this is the third one.', 'Is this the first document?', ] ``` text ``` vectorizer = CountVectorizer() X = vectorizer.fit_transform(corpus) ``` text ``` print(vectorizer.get_feature_names()) ['and', 'document', 'first', 'is', 'one', 'second', 'the', 'third', 'this'] ``` text ``` print(X.toarray()) [[0 1 1 1 0 0 1 0 1] [0 2 0 1 0 1 1 0 1] [1 0 0 1 1 0 1 1 1] [0 1 1 1 0 0 1 0 1]] ``` In the above toy example, we have a collection of strings stored into the variable **corpus.** Using the **text** **transformer** , we can see that we have a specific number of unique strings (vocabulary) in our data. This can be seen by printing the **vectorizer.get_feature_names()** variable**.** We observe that we have **9 unique words**. Next, we printed the transformed data (**X**) and **we observe the following** : * We have 4 rows in X as the number of our text strings (**we have the same number of samples after the transformation**). * **We have the same number of columns** (features/variables) in the transformed data (**X**) f**or all the samples (** this was not the case before that transformation i.e. the individual strings had different lengths). * The values 0,1,2, encode the **frequency** of a **word** that **appeared** in the **initial text data.** **E.g**. The first transformed row is **[0 1 1 1 0 0 1 0 1]** and **** th** e unique vocabulary**i** s ['and', 'document', 'first', 'is', 'one', 'second', 'the', 'third', 'this'],** thus this means that the words "document", "first", "is", "the" and "this" appeared 1 time each in the initial text string (i.e. 'This is the first document.'). **Side note:** This is the counting approach. The [term-frequency transform](https://scikit-learn.org/stable/modules/generated/sklearn.feature_extraction.text.TfidfTransformer.html#sklearn.feature_extraction.text.TfidfTransformer) is nothing more than a transformation of a count matrix into a normalized term-frequency matrix. Hope everything is clear now. If not, read this paragraph as many times as it is needed in order to really grasp the idea and understand this transformation. **It is a fundamental step.** * * * ## 4. Working example in Python Now that you understood how the Naive Bayes and the Text Transformation work, it's time to start coding ! ### Problem Statement As a working example, we will use some **text** **data** and we will build a **Naive** **Bayes** model to **predict** the **categories** of the **texts**. This is a **multi-class (20 classes) text classification problem**. Let's start (I will walk you through). First, we will **load all the necessary libraries** : text ``` import numpy as np, pandas as pd import seaborn as sns import matplotlib.pyplot as plt from sklearn.datasets import fetch_20newsgroups from sklearn.feature_extraction.text import TfidfVectorizer from sklearn.naive_bayes import MultinomialNB from sklearn.pipeline import make_pipeline from sklearn.metrics import confusion_matrix, accuracy_score ``` text ``` sns.set() # use seaborn plotting style ``` Next, **let's load the data** (**training** and **test** sets): text ``` # Load the dataset data = fetch_20newsgroups() ``` text ``` # Get the text categories text_categories = data.target_names ``` text ``` # define the training set train_data = fetch_20newsgroups(subset="train", categories=text_categories) ``` text ``` # define the test set test_data = fetch_20newsgroups(subset="test", categories=text_categories) ``` Let's find out **how many classes** and **samples** we have: text ``` print("We have {} unique classes".format(len(text_categories))) print("We have {} training samples".format(len(train_data.data))) print("We have {} test samples".format(len(test_data.data))) ``` The above prints: text ``` We have 20 unique classes We have 11314 training samples We have 7532 test samples ``` So, this is a **20-class text classification problem** with n_train = **11314** **training** **samples** (text sentences) and n_test = **7532** **test** **samples** (text sentences). Let's visualize the 5th training sample: text ``` # let's have a look as some training data print(test_data.data[5]) ``` As mentioned previously, our data are **texts** (more specifically, **emails**) so you should see something like the following printed out: ![Figure created by the author.](../images/006.png) Figure created by the author. The next step consists of building the **Naive Bayes classifier** and finally **training** the **model.** In our example, we will convert the collection of text documents (train and test sets) into a matrix of token counts (I explained how this works in **Section 3**). > To implement that text transformation we will use the **make_pipeline** function. This will internally transform the text data and then the model will be fitted **using the transformed data**. text ``` # Build the model model = make_pipeline(TfidfVectorizer(), MultinomialNB()) ``` text ``` # Train the model using the training data model.fit(train_data.data, train_data.target) ``` text ``` # Predict the categories of the test data predicted_categories = model.predict(test_data.data) ``` The last line of code **predicts the labels of the test set**. Let's see the predicted categories names: text ``` print(np.array(test_data.target_names)[predicted_categories]) array(['rec.autos', 'sci.crypt', 'alt.atheism', ..., 'rec.sport.baseball', 'comp.sys.ibm.pc.hardware', 'soc.religion.christian'], dtype=' [**Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques...**](https://amzn.to/3t4YB2d) ## 5. Bonus: Having fun with the model Let's have some fun using the trained model. Let's classify whatever sentence we like 😄 . text ``` # custom function to have fun def my_predictions(my_sentence, model): all_categories_names = np.array(data.target_names) prediction = model.predict([my_sentence]) return all_categories_names[prediction] ``` text ``` my_sentence = "jesus" print(my_predictions(my_sentence, model)) ['soc.religion.christian'] ``` text ``` my_sentence = "Are you an atheist?" print(my_predictions(my_sentence, model)) ['alt.atheism'] ``` We inserted the string "jesus" to the model and it predicted the class "['soc.religion.christian']". Change the "my_sentence" into other stings and **play with the model** 😃 . * * * ## 6. Conclusions We saw that **Naive Bayes is a very powerful algorithm** for **multi-class text classification problems.** _**Side Note**_ : _If you want to know more about the confusion matrix (and the ROC curve) read this:_ > [**ROC Curve Explained using a COVID-19 hypothetical example: Binary & Multi-Class Classification...**](https://towardsdatascience.com/roc-curve-explained-using-a-covid-19-hypothetical-example-binary-multi-class-classification-bab188ea869c) ### Interpreting the confusion matrix From the above **confusion** **matrix** , we can verify that the model is really good. * It is able to correctly predict all 20 classes of the text data (most values are on the diagonal and few are off-the-diagonal). * We also notice that the highest miss-classification (value off-the-diagonal) is **131** (5 lines from the end, last column at the right). The value 131 means that 131 documents that belonged to the "**religion miscellaneous** " category were miss-classified as belonging to the "**religion christian** " category. Interesting thing that these 2 categories are really similar and actually one could characterize these as 2 subgroups of a larger group e.g. "religion" in general. Finally, the **accuracy** on the **test** set is **0.7739** which is quite good for a **20-class text classification problem** 🚀 . **That's all folks! Hope you liked this article.** * * * If you liked and found this article useful, **follow 👣** me to be able to see all my new posts. Questions? Post them as a comment and I will reply as soon as possible. * * * ### My Profile (have a look to find out about my collection of articles): > [**Serafeim Loukas - Towards Data Science**](https://towardsdatascience.com/@seralouk) * * * ## Get in touch with me * **LinkedIn** : * * * ### You may also like: > [**Support Vector Machines (SVM) clearly explained: A python tutorial for classification problems...**](https://towardsdatascience.com/support-vector-machines-svm-clearly-explained-a-python-tutorial-for-classification-problems-29c539f3ad8) > [**K-Means Clustering: How It Works & Finding The Optimum Number Of Clusters In The Data**](https://towardsdatascience.com/k-means-clustering-how-it-works-finding-the-optimum-number-of-clusters-in-the-data-13d18739255c) > [**LSTM Time-Series Forecasting: Predicting Stock Prices Using An LSTM Model**](https://towardsdatascience.com/lstm-time-series-forecasting-predicting-stock-prices-using-an-lstm-model-6223e9644a2f) > [**Time-Series Forecasting: Predicting Stock Prices Using An ARIMA Model**](https://towardsdatascience.com/time-series-forecasting-predicting-stock-prices-using-an-arima-model-2e3b3080bd70) > [**The Best FREE Data Science Resources: FREE Books & Online Courses**](https://medium.com/@seralouk/the-best-free-data-science-resources-free-books-online-courses-9c4a2df194e5) > [**ROC Curve Explained using a COVID-19 hypothetical example: Binary & Multi-Class Classification...**](https://towardsdatascience.com/roc-curve-explained-using-a-covid-19-hypothetical-example-binary-multi-class-classification-bab188ea869c) > [**Support Vector Machines (SVM) clearly explained: A python tutorial for classification problems...**](https://towardsdatascience.com/support-vector-machines-svm-clearly-explained-a-python-tutorial-for-classification-problems-29c539f3ad8) > [**PCA clearly explained - How, when, why to use it and feature importance: A guide in Python**](https://towardsdatascience.com/pca-clearly-explained-how-when-why-to-use-it-and-feature-importance-a-guide-in-python-7c274582c37e) > [**Everything you need to know about Min-Max normalization in Python**](https://towardsdatascience.com/everything-you-need-to-know-about-min-max-normalization-in-python-b79592732b79) > [**How Scikit-Learn's StandardScaler works**](https://towardsdatascience.com/how-and-why-to-standardize-your-data-996926c2c832) ## Register Now to Continue Reading ### Unlock Towards Data Science with a Free Account All articles on Towards Data Science are available to registered users. 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