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12.5 Homework Assignment: Anomaly Detection in Automotive Data

12.5.1 Objective:

Explore anomaly detection techniques using the mtcars dataset to identify unusual observations in automotive specifications. Apply three different statistical methods: linear regression analysis, k-Nearest Neighbors (k-NN), and Random Forest.

12.5.2 Dataset:

The mtcars dataset available in R contains data on 32 automobiles (1973-74 models) with 11 variables such as MPG (miles per gallon), number of cylinders, horsepower, and weight.

12.5.3 Instructions:

Step 1: Setup and Data Loading - Load the necessary R packages. If not installed, install them using the commands from the setup block at the beginning of this chapter. - Load the mtcars dataset and explore its structure using head() and summary() functions.

data(mtcars)
head(mtcars)

mpg	cyl	disp	hp	drat	wt	qsec	vs	am	gear	carb
21	6	160	110	3.9	2.62	16.5	0	1	4	4
21	6	160	110	3.9	2.88	17	0	1	4	4
22.8	4	108	93	3.85	2.32	18.6	1	1	4	1
21.4	6	258	110	3.08	3.21	19.4	1	0	3	1
18.7	8	360	175	3.15	3.44	17	0	0	3	2
18.1	6	225	105	2.76	3.46	20.2	1	0	3	1

Step 2: Data Preparation - Convert categorical variables (if any) to factor variables. In mtcars, convert cyl, vs, am, and gear into factors using the mutate() function from dplyr.

mtcars.df <- mtcars |>
mutate(cyl = as.factor(cyl),
 vs = as.factor(vs),
 am = as.factor(am),
 gear = as.factor(gear)) |>
  dummy_cols(remove_first_dummy = TRUE) |>
  select(-where(is.factor))

row.names(mtcars.df) <- row.names(mtcars)

Step 3: Anomaly Detection using Linear Regression - Fit a linear regression model with MPG as the dependent variable and all other variables as predictors.

lm_model <- lm(mpg ~ ., data = mtcars.df)

• Calculate and inspect residuals. Consider observations with residuals greater than 2 standard deviations from the mean as potential outliers.

# Define threshold as 2 standard deviations from the mean residual
threshold <- 2 * sd(lm_model$residuals)

# Create a dataframe for plotting the residuals and their corresponding fitted values
plot_data <- data.frame(
  Fitted = lm_model$fitted.values,
  Residuals = lm_model$residuals
)

• Create a diagnostic plot to visualize these outliers.

# Generate the plot of residuals versus fitted values
ggplot(plot_data, aes(x = Fitted, y = Residuals)) +
  geom_hline(yintercept = 0, linetype = "dashed", color = "grey") +
  geom_point(aes(color = Residuals > threshold)) +
  scale_color_manual(values = c("black", "red")) +
  labs(title = "Residual vs. Fitted Plot",
       x = "Fitted Values",
       y = "Residuals",
       color = "Threshold Exceeded") +
  theme_minimal()

Step 4: Anomaly Detection using k-NN

• Use the kNNdist function from the dbscan package to calculate the distance to the k-th nearest neighbor. Select k as the square root of the number of observations.

pacman::p_load(caret, dbscan)  # Load necessary libraries
set.seed(123)  # Ensure reproducibility

mtcars.knn <- mtcars.df
k <- floor(sqrt(nrow(mtcars.knn)))  # Determine the number of neighbors
mtcars.knn$distances <- dbscan::kNNdist(x = mtcars.knn, k = k)

• Identify anomalies as observations where the distance is greater than the 95th percentile of all distances.

threshold <- quantile(mtcars.knn$distances, 0.95)
mtcars.knn$IsAnomalous <- mtcars.knn$distances > threshold

• Visualize these anomalies using a plot of anomaly scores.

ggplot(mtcars.knn, aes(x = row.names(mtcars.knn), y = distances, color = IsAnomalous)) +
  geom_point() +
  scale_color_manual(values = c("black", "red")) +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

Step 5: Anomaly Detection using Random Forest - Use the randomForest package to fit a model on the dataset, enabling the proximity option to calculate the proximity matrix.

rf_model <- randomForest(mpg ~ ., data = mtcars, proximity = TRUE)

• Derive anomaly scores from the proximity matrix and flag instances with scores above the 95th percentile as anomalies.

mtcars.rf <- mtcars

mtcars.rf$score <- 1 - apply(rf_model$proximity, 1, mean)
anomaly_threshold <- quantile(mtcars.rf$score, 0.95)
mtcars.rf$IsAnomalous <- mtcars.rf$score > anomaly_threshold

• Visualize these anomalies using a plot of anomaly scores.

pacman::p_load(ggplot2)
ggplot(mtcars.rf, aes(x = row.names(mtcars.rf), y = score)) +
 geom_line() +
 geom_point(aes(color = IsAnomalous), size = 2) +
 scale_color_manual(values = c("black", "red")) +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

Step 6: Analysis and Comparison - Compare the results from the three methods. Identify which observations are consistently flagged as anomalies across the different techniques. - Provide a brief analysis explaining why these observations might be considered anomalies and discuss the potential implications of these anomalies on automotive performance. Highlight any noticeable differences between anomalous and non-anomalous observations.

Step 7: Report Writing - Compile your findings, including the methodology, results, and detailed discussion, into a structured Quarto document. Incorporate plots to visually support your analysis. - Conclude with your reflections on the effectiveness of each anomaly detection method used in this study.

Submission Requirements: - Students are not required to submit their Quarto document (.qmd file). Instead, render your Quarto document to a Microsoft Word format (.docx) and submit this document. - Ensure that the rendered Word document includes all necessary plots and outputs to comprehensively present your analysis.

Chapter 13 introduces spec-driven development — the practice of defining requirements, data specifications, and validation criteria before writing code. Chapter 14 applies this approach to plan and execute a complete analysis of the absenteeism data. Chapter 15 covers dashboards and reporting — the “last mile” where analysis reaches the decision-maker. Chapter 16 builds a complete dashboard using flexdashboard.