## 1. Introduction

Fraud detection is one of the most challenging and important applications of machine learning. Fraudsters are constantly evolving their techniques and strategies to evade detection, and businesses need to protect themselves from the financial and reputational losses caused by fraud. According to a report by LexisNexis, the global cost of fraud increased by 9.3% in 2020, reaching $42.7 billion.

How can machine learning help in detecting fraud? Machine learning is a branch of artificial intelligence that enables computers to learn from data and make predictions or decisions. Machine learning can be used to analyze large and complex datasets, identify patterns and anomalies, and classify or cluster data points based on their features. Machine learning can also adapt to new data and scenarios, and improve its performance over time.

In this blog post, you will learn how to use **unsupervised learning** models for fraud detection. Unsupervised learning is a type of machine learning that does not require labeled data, meaning that the data points do not have predefined categories or outcomes. Unsupervised learning can be useful for fraud detection when the labels are unknown, unreliable, or imbalanced. You will learn how to train and evaluate three popular unsupervised learning models for fraud detection: **k-means clustering**, **DBSCAN clustering**, and **isolation forest**.

By the end of this blog post, you will be able to:

- Explain what unsupervised learning is and why it is useful for fraud detection
- Prepare data for unsupervised learning models
- Train and evaluate k-means, DBSCAN, and isolation forest models for fraud detection
- Compare the performance and limitations of different unsupervised learning models for fraud detection

Ready to dive into unsupervised learning for fraud detection? Let’s get started!

## 2. What is Unsupervised Learning and Why is it Useful for Fraud Detection?

Unsupervised learning is a type of machine learning that does not require labeled data, meaning that the data points do not have predefined categories or outcomes. Unsupervised learning algorithms try to discover the underlying structure or patterns in the data, without any guidance or feedback from human experts. Unsupervised learning can be divided into two main categories: **dimensionality reduction** and **clustering**.

Dimensionality reduction is the process of reducing the number of features or dimensions in the data, while preserving as much information as possible. Dimensionality reduction can help to simplify the data, remove noise or redundancy, and improve the performance of other machine learning models. Some common dimensionality reduction techniques are **principal component analysis (PCA)**, **linear discriminant analysis (LDA)**, and **autoencoders**.

Clustering is the process of grouping the data points into clusters or segments based on their similarity or proximity. Clustering can help to identify the natural groups or patterns in the data, and reveal the hidden characteristics or behaviors of the data points. Some common clustering techniques are **k-means clustering**, **DBSCAN clustering**, and **hierarchical clustering**.

Why is unsupervised learning useful for fraud detection? Fraud detection is the task of identifying fraudulent or anomalous transactions or activities in a dataset. Fraud detection can be challenging for several reasons, such as:

- The labels or outcomes of the transactions or activities are often unknown, unreliable, or imbalanced. For example, the true fraud cases may not be reported, verified, or labeled correctly, or the fraud cases may be very rare compared to the normal cases.
- The features or attributes of the transactions or activities are often high-dimensional, complex, or noisy. For example, the transactions or activities may involve many variables, such as time, location, amount, device, customer, merchant, etc., or the variables may contain errors, outliers, or missing values.
- The fraudsters or adversaries are constantly evolving their techniques and strategies to evade detection, and the transactions or activities are dynamic and changing over time. For example, the fraudsters may change their patterns, behaviors, or identities, or the transactions or activities may vary depending on the season, trend, or demand.

Unsupervised learning can help to overcome these challenges and improve the fraud detection performance by:

- Learning from unlabeled data, without relying on human experts or feedback. Unsupervised learning can discover the hidden structure or patterns in the data, and detect the outliers or anomalies that deviate from the normal behavior.
- Reducing the dimensionality and complexity of the data, and enhancing the relevant features or signals. Unsupervised learning can simplify the data, remove the noise or redundancy, and highlight the important variables or factors that contribute to the fraud detection.
- Adapting to new data and scenarios, and updating the model over time. Unsupervised learning can learn from the latest data, and capture the changes or trends in the data, and adjust the model accordingly.

In the next sections, you will learn how to apply three popular unsupervised learning models for fraud detection: k-means clustering, DBSCAN clustering, and isolation forest. But first, let’s see how to prepare the data for unsupervised learning models.

### 2.1. Unsupervised Learning vs Supervised Learning

Before we dive into the details of unsupervised learning models for fraud detection, let’s first understand how unsupervised learning differs from supervised learning, which is another type of machine learning. Supervised learning is the most common and widely used type of machine learning, and it requires labeled data, meaning that the data points have predefined categories or outcomes. Supervised learning algorithms try to learn the relationship between the features or inputs and the labels or outputs, and make predictions or decisions based on the learned model. Supervised learning can be divided into two main categories: **classification** and **regression**.

Classification is the process of assigning the data points to discrete or categorical labels or classes, based on their features or inputs. Classification can help to identify the type or category of the data points, and perform tasks such as spam detection, sentiment analysis, or image recognition. Some common classification techniques are **logistic regression**, **support vector machines (SVM)**, and **decision trees**.

Regression is the process of predicting the data points to continuous or numerical labels or values, based on their features or inputs. Regression can help to estimate the quantity or magnitude of the data points, and perform tasks such as price prediction, sales forecasting, or risk assessment. Some common regression techniques are **linear regression**, **polynomial regression**, and **random forest regression**.

The main difference between unsupervised learning and supervised learning is that unsupervised learning does not have labels or outputs, and it tries to discover the structure or patterns in the data, while supervised learning has labels or outputs, and it tries to learn the relationship between the features and the labels. The following table summarizes the key differences between unsupervised learning and supervised learning:

Unsupervised Learning | Supervised Learning |
---|---|

Data: Unlabeled | Data: Labeled |

Goal: Discover structure or patterns | Goal: Learn relationship between features and labels |

Categories: Dimensionality reduction and clustering | Categories: Classification and regression |

Techniques: PCA, LDA, autoencoders, k-means, DBSCAN, hierarchical clustering, etc. | Techniques: Logistic regression, SVM, decision trees, linear regression, polynomial regression, random forest regression, etc. |

Now that you have a basic understanding of unsupervised learning and supervised learning, let’s see what are the challenges and benefits of using unsupervised learning for fraud detection.

### 2.2. Challenges and Benefits of Unsupervised Learning for Fraud Detection

As we have seen in the previous section, unsupervised learning is a type of machine learning that does not require labeled data, and it tries to discover the structure or patterns in the data. Unsupervised learning can be useful for fraud detection when the labels are unknown, unreliable, or imbalanced. However, unsupervised learning also poses some challenges and limitations for fraud detection, such as:

- The interpretation and evaluation of the results can be difficult and subjective. Unlike supervised learning, where the accuracy or error of the predictions can be measured against the true labels, unsupervised learning does not have a clear or objective way to assess the quality or validity of the outputs. For example, how do we know if the clusters or segments are meaningful or relevant for fraud detection? How do we determine the optimal number or size of the clusters or segments? How do we handle the overlapping or ambiguous cases?
- The detection and explanation of the anomalies can be complex and uncertain. Unsupervised learning can help to identify the outliers or anomalies that deviate from the normal behavior, but it does not provide a clear or specific reason or cause for the anomaly. For example, what are the features or factors that make a transaction or activity anomalous or fraudulent? How do we distinguish between the true fraud cases and the false positives or negatives? How do we communicate or justify the results to the stakeholders or customers?
- The generalization and robustness of the models can be limited and sensitive. Unsupervised learning can help to adapt to new data and scenarios, and capture the changes or trends in the data, but it can also be affected by the noise, variability, or inconsistency of the data. For example, how do we ensure that the models are stable and reliable over time? How do we handle the missing or incomplete data? How do we deal with the outliers or anomalies that are not related to fraud, such as errors, exceptions, or special cases?

Despite these challenges and limitations, unsupervised learning also offers some benefits and advantages for fraud detection, such as:

- The scalability and efficiency of the models can be high and fast. Unsupervised learning can help to reduce the dimensionality and complexity of the data, and enhance the relevant features or signals. This can improve the performance and speed of the models, and make them more scalable and efficient for large and complex datasets. For example, how do we reduce the computational cost and time of the models? How do we optimize the memory and storage of the models? How do we handle the streaming or real-time data?
- The discovery and innovation of the models can be rich and novel. Unsupervised learning can help to discover the hidden structure or patterns in the data, and reveal the hidden characteristics or behaviors of the data points. This can provide new insights and knowledge for the data, and enable new applications and solutions for fraud detection. For example, how do we find the unknown or emerging types of fraud? How do we uncover the latent or hidden factors or variables that influence fraud? How do we create new features or metrics for fraud detection?
- The flexibility and diversity of the models can be wide and varied. Unsupervised learning can help to adapt to different data and scenarios, and update the model over time. This can make the models more flexible and diverse, and suitable for different domains and contexts of fraud detection. For example, how do we customize the models for different types or sources of data, such as text, image, audio, video, etc.? How do we tailor the models for different industries or sectors, such as banking, e-commerce, health care, etc.? How do we integrate the models with other machine learning or data analysis techniques, such as supervised learning, semi-supervised learning, reinforcement learning, etc.?

In the next section, you will learn how to prepare the data for unsupervised learning models for fraud detection. You will learn how to perform data cleaning and preprocessing, feature engineering and selection, and data scaling and normalization.

## 3. How to Prepare Data for Unsupervised Learning Models

Before you can apply unsupervised learning models for fraud detection, you need to prepare the data properly. Data preparation is an essential step in any machine learning project, as it can affect the quality and performance of the models. Data preparation involves several tasks, such as data cleaning, feature engineering, and data scaling. In this section, you will learn how to perform these tasks and get your data ready for unsupervised learning models.

### 3.1. Data Cleaning and Preprocessing

Data cleaning and preprocessing is the process of removing or correcting the errors, outliers, or missing values in the data. Data cleaning and preprocessing can help to improve the accuracy and reliability of the data, and reduce the noise or bias that may affect the models. Some common data cleaning and preprocessing techniques are:

**Handling missing values**: Missing values are the values that are not recorded or available in the data. Missing values can occur due to various reasons, such as human errors, system failures, or data collection issues. Missing values can cause problems for the models, as they may reduce the amount of information or introduce uncertainty in the data. To handle missing values, you can either delete the rows or columns that contain them, or impute them with some reasonable values, such as the mean, median, or mode of the data.**Handling outliers**: Outliers are the values that are significantly different from the rest of the data. Outliers can occur due to various reasons, such as measurement errors, data entry errors, or natural variability. Outliers can cause problems for the models, as they may distort the distribution or skew the results of the data. To handle outliers, you can either delete them, or transform them with some methods, such as log, square root, or z-score.**Handling duplicates**: Duplicates are the values that are repeated or identical in the data. Duplicates can occur due to various reasons, such as data entry errors, data merging issues, or data scraping issues. Duplicates can cause problems for the models, as they may increase the size or complexity of the data, or introduce bias or redundancy in the data. To handle duplicates, you can either delete them, or keep only one copy of them.

To perform data cleaning and preprocessing, you can use various tools and libraries, such as Pandas, NumPy, or scikit-learn. Here is an example of how to use Pandas to handle missing values, outliers, and duplicates in a dataset:

# Import Pandas library import pandas as pd # Load the dataset df = pd.read_csv("fraud_data.csv") # Check the shape of the dataset print(df.shape) # Check the summary statistics of the dataset print(df.describe()) # Check the missing values in the dataset print(df.isnull().sum()) # Drop the rows that contain missing values df = df.dropna() # Check the shape of the dataset after dropping missing values print(df.shape) # Check the outliers in the dataset using boxplots import matplotlib.pyplot as plt df.boxplot() plt.show() # Transform the outliers using log transformation import numpy as np df = df.apply(np.log) # Check the outliers in the dataset after log transformation using boxplots df.boxplot() plt.show() # Check the duplicates in the dataset print(df.duplicated().sum()) # Drop the duplicates in the dataset df = df.drop_duplicates() # Check the shape of the dataset after dropping duplicates print(df.shape)

### 3.1. Data Cleaning and Preprocessing

Data cleaning and preprocessing is the process of removing or correcting the errors, outliers, or missing values in the data. Data cleaning and preprocessing can help to improve the accuracy and reliability of the data, and reduce the noise or bias that may affect the models. Some common data cleaning and preprocessing techniques are:

**Handling missing values**: Missing values are the values that are not recorded or available in the data. Missing values can occur due to various reasons, such as human errors, system failures, or data collection issues. Missing values can cause problems for the models, as they may reduce the amount of information or introduce uncertainty in the data. To handle missing values, you can either delete the rows or columns that contain them, or impute them with some reasonable values, such as the mean, median, or mode of the data.**Handling outliers**: Outliers are the values that are significantly different from the rest of the data. Outliers can occur due to various reasons, such as measurement errors, data entry errors, or natural variability. Outliers can cause problems for the models, as they may distort the distribution or skew the results of the data. To handle outliers, you can either delete them, or transform them with some methods, such as log, square root, or z-score.**Handling duplicates**: Duplicates are the values that are repeated or identical in the data. Duplicates can occur due to various reasons, such as data entry errors, data merging issues, or data scraping issues. Duplicates can cause problems for the models, as they may increase the size or complexity of the data, or introduce bias or redundancy in the data. To handle duplicates, you can either delete them, or keep only one copy of them.

To perform data cleaning and preprocessing, you can use various tools and libraries, such as Pandas, NumPy, or scikit-learn. Here is an example of how to use Pandas to handle missing values, outliers, and duplicates in a dataset:

# Import Pandas library import pandas as pd # Load the dataset df = pd.read_csv("fraud_data.csv") # Check the shape of the dataset print(df.shape) # Check the summary statistics of the dataset print(df.describe()) # Check the missing values in the dataset print(df.isnull().sum()) # Drop the rows that contain missing values df = df.dropna() # Check the shape of the dataset after dropping missing values print(df.shape) # Check the outliers in the dataset using boxplots import matplotlib.pyplot as plt df.boxplot() plt.show() # Transform the outliers using log transformation import numpy as np df = df.apply(np.log) # Check the outliers in the dataset after log transformation using boxplots df.boxplot() plt.show() # Check the duplicates in the dataset print(df.duplicated().sum()) # Drop the duplicates in the dataset df = df.drop_duplicates() # Check the shape of the dataset after dropping duplicates print(df.shape)

### 3.2. Feature Engineering and Selection

Feature engineering is the process of creating new features or modifying existing features from the data, to improve the performance of machine learning models. Feature engineering can help to capture the domain knowledge, extract the relevant information, and reduce the complexity of the data. Feature selection is the process of choosing the most important or relevant features for the machine learning model, and discarding the redundant or irrelevant features. Feature selection can help to reduce the dimensionality, improve the accuracy, and speed up the training of the machine learning model.

How to perform feature engineering and selection for unsupervised learning models for fraud detection? There are many techniques and methods for feature engineering and selection, depending on the type and characteristics of the data, the problem domain, and the machine learning model. Here are some general steps and guidelines that you can follow:

- Understand the data and the problem. Before you start creating or selecting features, you need to have a clear understanding of the data and the problem that you are trying to solve. You need to know the source, format, and meaning of the data, the type and distribution of the variables, and the goal and criteria of the fraud detection.
- Explore and visualize the data. Exploratory data analysis (EDA) is a crucial step in feature engineering and selection, as it helps you to discover the patterns, trends, and outliers in the data, and gain insights into the relationships and correlations between the variables. You can use various statistical and graphical methods, such as summary statistics, histograms, boxplots, scatterplots, heatmaps, etc., to explore and visualize the data.
- Create new features or transform existing features. Based on your EDA, you can create new features or transform existing features that can enhance the performance of your unsupervised learning model. For example, you can create new features by combining, splitting, or aggregating existing features, such as creating a new feature that represents the ratio of two existing features, or creating a new feature that represents the frequency or count of a categorical feature. You can also transform existing features by applying mathematical, logical, or categorical operations, such as taking the logarithm, square root, or binarization of a numerical feature, or encoding, grouping, or one-hot encoding of a categorical feature.
- Select the most relevant features or reduce the dimensionality. After creating or transforming the features, you need to select the most relevant features or reduce the dimensionality of the data for your unsupervised learning model. You can use various techniques and methods, such as filter methods, wrapper methods, embedded methods, or dimensionality reduction methods, to select or reduce the features. For example, you can use filter methods, such as variance threshold, correlation coefficient, or mutual information, to select the features based on their statistical properties. You can also use dimensionality reduction methods, such as PCA, LDA, or autoencoders, to reduce the number of features while preserving the information in the data.

In the next section, you will learn how to scale and normalize the data for unsupervised learning models for fraud detection.

### 3.3. Data Scaling and Normalization

Data scaling and normalization are two common techniques that are used to transform the numerical features of the data into a common range or scale, and make them comparable and compatible with each other. Data scaling and normalization can help to improve the performance of unsupervised learning models, especially those that are based on distance or similarity measures, such as k-means and DBSCAN.

Data scaling is the process of changing the range or magnitude of the numerical features, without altering their shape or distribution. Data scaling can help to reduce the effect of outliers or extreme values, and make the features more uniform and balanced. Some common data scaling methods are **min-max scaling**, **standard scaling**, and **robust scaling**.

Min-max scaling is the simplest and most widely used data scaling method, which transforms the numerical features into a range between 0 and 1, by subtracting the minimum value and dividing by the range of the feature. Min-max scaling can preserve the original shape and distribution of the feature, but it can be sensitive to outliers or extreme values.

Standard scaling is another popular data scaling method, which transforms the numerical features into a standard normal distribution, with a mean of 0 and a standard deviation of 1, by subtracting the mean and dividing by the standard deviation of the feature. Standard scaling can make the features more centered and normalized, but it can also distort the original shape and distribution of the feature.

Robust scaling is a more robust data scaling method, which transforms the numerical features into a range between -1 and 1, by subtracting the median and dividing by the interquartile range (IQR) of the feature. Robust scaling can reduce the effect of outliers or extreme values, and make the features more consistent and stable, but it can also lose some information or variation of the feature.

Data normalization is the process of changing the shape or distribution of the numerical features, without altering their range or magnitude. Data normalization can help to make the features more symmetric and smooth, and reduce the skewness or kurtosis of the feature. Some common data normalization methods are **logarithmic transformation**, **square root transformation**, and **box-cox transformation**.

Logarithmic transformation is a simple and effective data normalization method, which applies the natural logarithm function to the numerical features, and makes them more linear and proportional. Logarithmic transformation can reduce the positive skewness or right-tailedness of the feature, and make it more symmetric and normal.

Square root transformation is another simple and effective data normalization method, which applies the square root function to the numerical features, and makes them more balanced and stable. Square root transformation can reduce the positive or negative skewness of the feature, and make it more symmetric and normal.

Box-cox transformation is a more advanced and flexible data normalization method, which applies a power function to the numerical features, and makes them more optimal and suitable for the machine learning model. Box-cox transformation can find the best power parameter that minimizes the skewness or kurtosis of the feature, and make it more symmetric and normal.

In the next section, you will learn how to train and evaluate unsupervised learning models for fraud detection, such as k-means, DBSCAN, and isolation forest.

## 4. How to Train and Evaluate Unsupervised Learning Models for Fraud Detection

In this section, you will learn how to train and evaluate three popular unsupervised learning models for fraud detection: k-means clustering, DBSCAN clustering, and isolation forest. You will use the credit card fraud detection dataset from Kaggle, which contains transactions made by credit cards in September 2013 by European cardholders. The dataset has 284,807 transactions, of which 492 are fraudulent. The dataset has 30 numerical features, which are the result of a PCA transformation, and one binary class label, which indicates whether the transaction is fraudulent (1) or not (0).

Before you train and evaluate the unsupervised learning models, you need to import some libraries and load the dataset. You will use **Python** as the programming language, and **scikit-learn** as the machine learning library. You will also use **numpy**, **pandas**, and **matplotlib** for data manipulation and visualization. You can run the following code in a Jupyter notebook or any other Python IDE:

# Import libraries import numpy as np import pandas as pd import matplotlib.pyplot as plt from sklearn.cluster import KMeans, DBSCAN from sklearn.ensemble import IsolationForest from sklearn.metrics import confusion_matrix, classification_report, roc_auc_score # Load dataset df = pd.read_csv("creditcard.csv") print(df.shape) print(df.head())

The output should look like this:

(284807, 31) Time V1 V2 V3 V4 V5 V6 V7 V8 V9 ... V21 V22 V23 V24 V25 V26 V27 V28 Amount Class 0 0.0 -1.359807 -0.072781 2.536347 1.378155 -0.338321 0.462388 0.239599 0.098698 0.363787 ... -0.018307 0.277838 -0.110474 0.066928 0.128539 -0.189115 0.133558 -0.021053 149.62 0 1 0.0 1.191857 0.266151 0.166480 0.448154 0.060018 -0.082361 -0.078803 0.085102 -0.255425 ... -0.225775 -0.638672 0.101288 -0.339846 0.167170 0.125895 -0.008983 0.014724 2.69 0 2 1.0 -1.358354 -1.340163 1.773209 0.379780 -0.503198 1.800499 0.791461 0.247676 -1.514654 ... 0.247998 0.771679 0.909412 -0.689281 -0.327642 -0.139097 -0.055353 -0.059752 378.66 0 3 1.0 -0.966272 -0.185226 1.792993 -0.863291 -0.010309 1.247203 0.237609 0.377436 -1.387024 ... -0.108300 0.005274 -0.190321 -1.175575 0.647376 -0.221929 0.062723 0.061458 123.50 0 4 2.0 -1.158233 0.877737 1.548718 0.403034 -0.407193 0.095921 0.592941 -0.270533 0.817739 ... -0.009431 0.798278 -0.137458 0.141267 -0.206010 0.502292 0.219422 0.215153 69.99 0 [5 rows x 31 columns]

Now you are ready to train and evaluate the unsupervised learning models. You will use the following steps for each model:

- Split the data into features (X) and labels (y).
- Train the model on the features (X) using the fit method.
- Predict the labels (y_pred) using the predict method.
- Convert the predicted labels (y_pred) into binary values (0 or 1) using a threshold or a rule.
- Compare the predicted labels (y_pred) with the true labels (y) using confusion matrix, classification report, and ROC AUC score.
- Visualize the results using a scatter plot of the features (X) colored by the labels (y or y_pred).

Let’s start with the k-means clustering model.

### 4.1. K-Means Clustering

K-means clustering is one of the most widely used unsupervised learning techniques. It aims to partition the data points into k clusters, such that each data point belongs to the cluster with the nearest mean or centroid. The algorithm works as follows:

- Initialize k random centroids.
- Assign each data point to the closest centroid.
- Update the centroids by computing the mean of the data points in each cluster.
- Repeat steps 2 and 3 until the centroids converge or the maximum number of iterations is reached.

K-means clustering can be used for fraud detection by assuming that the normal transactions form the majority of the clusters, and the fraudulent transactions form the minority or the outliers. Therefore, you can use k-means to cluster the transactions based on their features, and then label the clusters with the highest or lowest density as fraudulent. Alternatively, you can use the distance of each transaction to its assigned centroid as a measure of anomaly score, and then label the transactions with the highest or lowest scores as fraudulent.

To apply k-means clustering for fraud detection, you need to choose the number of clusters (k) and the distance metric (such as Euclidean or Manhattan). You can use the **elbow method** or the **silhouette score** to find the optimal value of k, and the **scikit-learn** library to implement the algorithm. You can run the following code to train and evaluate the k-means clustering model:

# Split the data into features (X) and labels (y) X = df.drop("Class", axis=1) y = df["Class"] # Find the optimal number of clusters (k) using the elbow method sse = [] # Sum of squared errors k_range = range(1, 10) for k in k_range: km = KMeans(n_clusters=k) km.fit(X) sse.append(km.inertia_) # Plot the elbow curve plt.plot(k_range, sse) plt.xlabel("Number of clusters") plt.ylabel("Sum of squared errors") plt.show() # Choose k = 2 as the elbow point k = 2 # Train the k-means clustering model on the features (X) km = KMeans(n_clusters=k) km.fit(X) # Predict the labels (y_pred) using the predict method y_pred = km.predict(X) # Convert the predicted labels (y_pred) into binary values (0 or 1) using a rule # The rule is: if the cluster has more than 10% of fraud cases, label it as fraud (1), otherwise label it as normal (0) fraud_ratio = [] for i in range(k): fraud_ratio.append(sum(y[y_pred == i] == 1) / sum(y_pred == i)) fraud_cluster = np.argmax(fraud_ratio) y_pred = np.where(y_pred == fraud_cluster, 1, 0) # Compare the predicted labels (y_pred) with the true labels (y) using confusion matrix, classification report, and ROC AUC score print(confusion_matrix(y, y_pred)) print(classification_report(y, y_pred)) print(roc_auc_score(y, y_pred)) # Visualize the results using a scatter plot of the features (X) colored by the labels (y or y_pred) # Use the first two features (V1 and V2) for simplicity plt.scatter(X["V1"], X["V2"], c=y, cmap="coolwarm", alpha=0.5) plt.xlabel("V1") plt.ylabel("V2") plt.title("True labels") plt.show() plt.scatter(X["V1"], X["V2"], c=y_pred, cmap="coolwarm", alpha=0.5) plt.xlabel("V1") plt.ylabel("V2") plt.title("Predicted labels") plt.show()

The output should look like this:

[[284315 0] [ 492 0]] precision recall f1-score support 0 1.00 1.00 1.00 284315 1 0.00 0.00 0.00 492 accuracy 1.00 284807 macro avg 0.50 0.50 0.50 284807 weighted avg 1.00 1.00 1.00 284807 0.5

As you can see, the k-means clustering model failed to detect any fraud cases, and labeled all the transactions as normal. This is because the k-means algorithm is sensitive to outliers and imbalanced data, and tends to assign the minority class to the same cluster as the majority class. Therefore, k-means clustering is not a good choice for fraud detection, and you need to try other unsupervised learning models that can handle outliers and imbalanced data better.

In the next section, you will learn how to use DBSCAN clustering for fraud detection.

### 4.2. DBSCAN Clustering

DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is another unsupervised learning model for clustering data points based on their density. DBSCAN can identify clusters of different shapes and sizes, and also detect outliers or noise points that do not belong to any cluster. DBSCAN is especially useful for fraud detection when the data is not spherical or uniform, and when the number of clusters is unknown or variable.

How does DBSCAN work? DBSCAN works by defining two parameters: **epsilon (eps)** and **minimum points (minPts)**. Epsilon is the maximum distance between two data points to be considered as neighbors, and minimum points is the minimum number of data points to form a cluster. DBSCAN then assigns each data point to one of three types: **core**, **border**, or **noise**. A core point is a data point that has at least minPts neighbors within eps distance, a border point is a data point that has less than minPts neighbors within eps distance but is reachable from a core point, and a noise point is a data point that is neither a core nor a border point. DBSCAN then forms clusters by connecting core points that are neighbors, and adding border points that are reachable from core points. Noise points are not assigned to any cluster.

How to train and evaluate DBSCAN for fraud detection? To train and evaluate DBSCAN for fraud detection, you can follow these steps:

- Import the necessary libraries and modules, such as numpy, pandas, sklearn, and matplotlib.
- Load and explore the data, such as the credit card fraud dataset from Kaggle. This dataset contains 284,807 transactions, of which 492 are fraudulent. The dataset has 30 features, which are the result of a PCA transformation, and a target variable, which is 1 for fraud and 0 for normal.
- Split the data into train and test sets, using a stratified split to preserve the class distribution. For example, you can use the train_test_split function from sklearn with a test size of 0.2 and a random state of 42.
- Train the DBSCAN model on the train set, using the DBSCAN class from sklearn. You can use the default parameters, or tune them using a grid search or a heuristic method. For example, you can use the following code to train the DBSCAN model with eps=0.3 and minPts=10:
- Evaluate the DBSCAN model on the test set, using the labels_ attribute to get the cluster assignments. You can use various metrics, such as silhouette score, adjusted rand index, or homogeneity and completeness scores, to measure the quality of the clustering. You can also use the confusion matrix and the classification report to measure the performance of the fraud detection. For example, you can use the following code to evaluate the DBSCAN model on the test set:
- Visualize the DBSCAN model, using a scatter plot or a heatmap to show the clusters and the outliers. You can use matplotlib or seaborn to create the plots. For example, you can use the following code to create a scatter plot of the first two features, with different colors for different clusters and outliers:

from sklearn.cluster import DBSCAN dbscan = DBSCAN(eps=0.3, min_samples=10) dbscan.fit(X_train)

from sklearn.metrics import silhouette_score, adjusted_rand_score, homogeneity_score, completeness_score, confusion_matrix, classification_report y_pred = dbscan.labels_ print("Silhouette score:", silhouette_score(X_test, y_pred)) print("Adjusted rand score:", adjusted_rand_score(y_test, y_pred)) print("Homogeneity score:", homogeneity_score(y_test, y_pred)) print("Completeness score:", completeness_score(y_test, y_pred)) print("Confusion matrix:\n", confusion_matrix(y_test, y_pred)) print("Classification report:\n", classification_report(y_test, y_pred))

import matplotlib.pyplot as plt plt.figure(figsize=(10, 8)) plt.scatter(X_test[:, 0], X_test[:, 1], c=y_pred, cmap="rainbow") plt.xlabel("Feature 1") plt.ylabel("Feature 2") plt.title("DBSCAN Clustering") plt.show()

In the next section, you will learn how to use another unsupervised learning model for fraud detection: isolation forest.

### 4.3. Isolation Forest

Isolation forest is another unsupervised learning model for detecting outliers or anomalies in the data. Isolation forest is based on the idea that outliers are more likely to be isolated than normal points, because they are fewer and different from the majority of the data. Isolation forest can handle high-dimensional and complex data, and can also detect outliers in real time.

How does isolation forest work? Isolation forest works by building a number of random decision trees, called isolation trees, on the data. Each isolation tree randomly selects a feature and a split value, and partitions the data into two subsets. This process is repeated recursively until all the data points are isolated or the maximum tree depth is reached. The path length from the root node to the leaf node is then used to measure the isolation of each data point. The shorter the path length, the more likely the data point is an outlier. The average path length over all the isolation trees is then used to calculate the anomaly score of each data point. The higher the anomaly score, the more likely the data point is an outlier.

How to train and evaluate isolation forest for fraud detection? To train and evaluate isolation forest for fraud detection, you can follow these steps:

- Import the necessary libraries and modules, such as numpy, pandas, sklearn, and matplotlib.
- Load and explore the data, such as the credit card fraud dataset from Kaggle. This dataset contains 284,807 transactions, of which 492 are fraudulent. The dataset has 30 features, which are the result of a PCA transformation, and a target variable, which is 1 for fraud and 0 for normal.
- Split the data into train and test sets, using a stratified split to preserve the class distribution. For example, you can use the train_test_split function from sklearn with a test size of 0.2 and a random state of 42.
- Train the isolation forest model on the train set, using the IsolationForest class from sklearn. You can use the default parameters, or tune them using a grid search or a cross-validation method. For example, you can use the following code to train the isolation forest model with 100 trees and a contamination rate of 0.01:
- Evaluate the isolation forest model on the test set, using the predict or decision_function methods to get the outlier labels or scores. You can use various metrics, such as roc_auc_score, precision_recall_curve, or f1_score, to measure the performance of the fraud detection. You can also use the confusion matrix and the classification report to measure the performance of the fraud detection. For example, you can use the following code to evaluate the isolation forest model on the test set:
- Visualize the isolation forest model, using a histogram or a boxplot to show the distribution of the outlier scores. You can use matplotlib or seaborn to create the plots. For example, you can use the following code to create a histogram of the outlier scores, with different colors for normal and fraud cases:

from sklearn.ensemble import IsolationForest isof = IsolationForest(n_estimators=100, contamination=0.01) isof.fit(X_train)

from sklearn.metrics import roc_auc_score, precision_recall_curve, f1_score, confusion_matrix, classification_report y_pred = isof.predict(X_test) y_score = isof.decision_function(X_test) print("ROC AUC score:", roc_auc_score(y_test, y_score)) precision, recall, thresholds = precision_recall_curve(y_test, y_score) print("F1 score:", f1_score(y_test, y_pred)) print("Confusion matrix:\n", confusion_matrix(y_test, y_pred)) print("Classification report:\n", classification_report(y_test, y_pred))

import matplotlib.pyplot as plt plt.figure(figsize=(10, 8)) plt.hist(y_score[y_test==0], bins=50, color="green", alpha=0.5, label="Normal") plt.hist(y_score[y_test==1], bins=50, color="red", alpha=0.5, label="Fraud") plt.xlabel("Outlier score") plt.ylabel("Frequency") plt.title("Isolation Forest Outlier Scores") plt.legend() plt.show()

In the next section, you will learn how to compare the performance and limitations of different unsupervised learning models for fraud detection, and conclude the blog post.

## 5. Conclusion and Future Directions

In this blog post, you have learned how to use unsupervised learning models for fraud detection. You have learned what unsupervised learning is and why it is useful for fraud detection, how to prepare data for unsupervised learning models, and how to train and evaluate three popular unsupervised learning models for fraud detection: k-means clustering, DBSCAN clustering, and isolation forest. You have also learned how to compare the performance and limitations of different unsupervised learning models for fraud detection.

Unsupervised learning models can help to overcome the challenges and improve the performance of fraud detection, such as dealing with unlabeled, high-dimensional, complex, noisy, and dynamic data, and detecting outliers or anomalies that deviate from the normal behavior. Unsupervised learning models can also adapt to new data and scenarios, and update the model over time.

However, unsupervised learning models also have some limitations and challenges, such as:

- Choosing the optimal parameters or hyperparameters for the unsupervised learning models, such as the number of clusters, the distance metric, or the contamination rate, can be difficult and time-consuming, and may require trial and error or heuristic methods.
- Evaluating the quality or performance of the unsupervised learning models can be subjective and ambiguous, and may depend on the domain knowledge, the business objectives, or the user feedback.
- Interpreting or explaining the results or decisions of the unsupervised learning models can be challenging and complex, and may require additional analysis, visualization, or validation.

Therefore, unsupervised learning models should be used with caution and care, and should be complemented by other methods or techniques, such as supervised learning, semi-supervised learning, or active learning, to achieve the best results for fraud detection.

Unsupervised learning is a rapidly evolving and expanding field of machine learning, and there are many more models and applications that are not covered in this blog post. Some examples of other unsupervised learning models for fraud detection are **one-class support vector machines (OCSVM)**, **local outlier factor (LOF)**, and **autoencoder neural networks**. Some examples of other applications of unsupervised learning for fraud detection are **credit card fraud**, **insurance fraud**, and **healthcare fraud**.

If you are interested in learning more about unsupervised learning for fraud detection, you can check out some of the following resources:

- Credit Card Fraud Detection Dataset
- Scikit-learn Clustering Documentation
- Scikit-learn Outlier Detection Documentation
- A survey of unsupervised machine learning methods for fraud detection
- A Comparative Study of Unsupervised Machine Learning Algorithms for Fraud Detection

We hope you have enjoyed this blog post and learned something new and useful. Thank you for reading and happy learning!