ML Interview Q Series: How could clustering methods be used to detect unusual data points in a dataset?

Comprehensive Explanation

One of the most intuitive ways to detect outliers with clustering is to organize the data into homogeneous groups first and then single out data points that do not fit well with the rest of their respective clusters. The key rationale is that a cluster contains observations that share similar characteristics. If a particular data point has a large distance from its cluster center (or belongs to a very small cluster in density-based algorithms), it can be flagged as an anomaly.

Clustering-based outlier detection often involves these steps: run a clustering algorithm, compute a measure (such as the distance to centroid or the size of the cluster), and declare points that exceed a certain threshold as outliers. Methods such as K-means or DBSCAN are commonly applied.

K-means Clustering Approach for Outlier Detection

K-means is a distance-based algorithm that partitions data into K clusters. Each cluster has a centroid that serves as a representative “center.” After performing K-means, each data point is assigned to the cluster whose centroid is the closest to it. A potential approach to outlier detection is to measure the distance from each point to its assigned centroid. Points that have a significantly larger distance compared to the overall distribution of distances within that cluster are outliers.

Below is the centroid formula for cluster j. This is often considered a core formula because it describes how the central representative of a cluster is computed. The centroid is the mean of all points in that cluster.

Here, mu_j is the centroid of cluster j. The set C_j contains all data points assigned to cluster j. The size of that set is denoted lvert C_j rvert. For each data point x in cluster j, we sum its feature values and then divide by the total number of points in that cluster. Once we compute this centroid, we can gauge a point’s “outlier-ness” by calculating its distance from mu_j. If the distance for a point is substantially higher than the rest of the distances, it is classified as an outlier.

In many practical scenarios, a threshold is determined either by examining the empirical distribution of distances or by using statistical heuristics. One might compute, for instance, the median distance within each cluster and then define a cutoff based on median absolute deviation or standard deviation.

DBSCAN Approach for Outlier Detection

DBSCAN is another clustering algorithm that does not require specifying the number of clusters beforehand. It also automatically flags data points that do not belong to any dense region, labeling them as outliers. DBSCAN works by grouping points that are in high-density regions and separating out low-density regions. Points that do not lie in any high-density region are labeled as noise or outliers. This is a natural outcome of the algorithm’s definition, so no additional threshold is needed to detect outliers beyond the required parameters eps (neighborhood radius) and min_samples (minimum number of points needed for a cluster).

DBSCAN is often favored for outlier detection when the data has complex shapes because it can discover arbitrarily shaped clusters. However, choosing eps and min_samples can be tricky. If eps is too large, clusters might merge incorrectly and outliers become part of big clusters; if eps is too small, many normal data points may be labeled outliers.

Using Clustering in Practical Settings

Clustering-based outlier detection can be useful when the data is not overly high-dimensional and where cluster structures are expected. For instance, in a credit card transaction dataset, normal transactions might form dense clusters, whereas fraudulent transactions may be scattered or lie farther from cluster centers. Once clustering is performed, those distant points are flagged and examined further by investigators.

However, real-world datasets can be noisy and have complex distributions. K-means can be sensitive to initialization and outliers themselves (since outliers can drag centroids in their direction). DBSCAN requires good hyperparameter choices, which may not be trivial. Thus, domain knowledge and experimentation are critical for refining these methods.

Below is a short Python snippet to illustrate how one might use K-means for outlier detection:

import numpy as np
from sklearn.cluster import KMeans

# Sample data generation
np.random.seed(42)
data = np.random.randn(100, 2)
outliers = np.array([[10, 10], [12, 8], [15, 14]])
data_with_outliers = np.vstack([data, outliers])

# K-means clustering
kmeans = KMeans(n_clusters=3, random_state=42)
labels = kmeans.fit_predict(data_with_outliers)
centers = kmeans.cluster_centers_

# Calculate distances from each point to its cluster centroid
distances = []
for idx, point in enumerate(data_with_outliers):
    centroid = centers[labels[idx]]
    dist = np.linalg.norm(point - centroid)
    distances.append(dist)

# Define an outlier threshold (e.g., 2 standard deviations above mean distance)
distances = np.array(distances)
threshold = np.mean(distances) + 2 * np.std(distances)

outlier_indices = np.where(distances > threshold)[0]
print("Indices of detected outliers:", outlier_indices)
print("Detected outliers:", data_with_outliers[outlier_indices])

In this example, the code clusters the data, computes distances from each point to its centroid, and then labels those points that exceed a chosen threshold as outliers.

What are the Advantages of Using Clustering for Outlier Detection?

Clustering inherently groups similar items together. By measuring how far an item strays from the group, it offers an intuitive metric for whether an item is normal or abnormal. This can make the concept easy to explain to stakeholders. Additionally, if you use a density-based method like DBSCAN, you can detect both arbitrarily shaped clusters and outliers naturally, without manual thresholding.

What Are Some Potential Drawbacks or Pitfalls?

Clustering-based approaches assume that “normal” data forms groups in some sense, which might not always be the case. K-means can be heavily influenced by outliers themselves, causing centroid distortion. High-dimensional data poses the problem of distance metrics becoming less meaningful, often referred to as the curse of dimensionality. DBSCAN requires careful parameter tuning, and it may fail if eps is poorly chosen or if the data distribution lacks distinct density regions.

How Do You Handle Parameters Such as the Number of Clusters for K-means or eps for DBSCAN?

For K-means, the number of clusters is typically decided by domain knowledge, the elbow method, or other heuristic measures (e.g., the silhouette coefficient). It can be challenging to tune K properly if there is no prior knowledge about the structure of the data.

For DBSCAN, eps and min_samples need to be chosen based on data distribution. A common technique is to plot the k-distance graph (such as the distance to the kth nearest neighbor) and look for a jump or “elbow” to guide the selection of eps. Nevertheless, this can still be subjective. Domain insight is again very helpful.

How Can You Avoid the Influence of Outliers When Finding Clusters?

Robust clustering variants such as K-medoids can be used. Instead of computing a mean as a cluster center, K-medoids chooses an actual data point (a “medoid”) to represent the cluster, reducing sensitivity to outliers. There are also robust loss functions or trimming outliers in each iteration for centroid-based clustering. For instance, in an advanced approach, points that exceed a distance threshold might be temporarily removed when recomputing centroids to prevent them from unduly skewing the centers.

How Would You Validate That the Outliers Detected Are Truly Abnormal?

External validation relies on labeled data or domain knowledge. If you have true labels for anomalies, a precision-recall metric or an F1-score can be calculated. In unsupervised contexts, validation often involves manual inspection, contextual reasoning, or business domain experts confirming whether flagged points are truly anomalies. Sometimes, a small test set with known anomalies is used to estimate performance.

Below are additional follow-up questions

How would you handle streaming or real-time data in clustering-based outlier detection?

In a real-time environment, data arrives continuously and must be processed on-the-fly without re-running a full clustering from scratch each time. Traditional clustering algorithms like K-means are typically batch processes that assume all data is available beforehand.

To manage streaming data, one might use incremental or online variants of clustering algorithms that update cluster centers whenever new data points arrive. For instance, online K-means adjusts centroids incrementally, lowering the computational cost. Since outlier detection relies on distances to centroids, these distances can be updated each time a new data point is classified into a cluster.

However, sliding windows or forgetting mechanisms may be required if the data distribution changes over time. A fixed window of recent data ensures that historical points do not dominate the centroids when a concept drift occurs. This approach might risk losing long-term context, so the window size should be carefully selected based on domain requirements. Domain experts can also help interpret whether older patterns remain relevant.

Edge cases include scenarios in which streaming data has intermittent bursts of anomalies. If the window is too large, anomalies could blend into a larger set of normal data and go undetected. Conversely, if the window is too small, spurious noise may appear to be outliers, leading to false positives. Balancing these considerations is essential for effective real-time detection.

How do you scale clustering-based outlier detection to extremely large datasets?

When datasets grow large, running standard clustering algorithms like K-means can become computationally expensive (both in time and memory). One common solution is to use approximate or mini-batch techniques. Mini-batch K-means, for example, processes the data in small batches. This lowers memory usage and can drastically speed up convergence, albeit with a slight reduction in accuracy.

Another strategy involves distributed computing frameworks such as Apache Spark or Hadoop. These platforms partition data across multiple nodes and perform clustering in parallel. For DBSCAN, parallel or approximate versions exist (e.g., HDBSCAN or variant algorithms that use indexing structures like KD-trees or R-trees for neighborhood searches). Still, DBSCAN can become challenging to scale if eps is small and the data is very dense, since nearest neighbor lookups may be expensive.

For extremely large datasets, sampling can be a practical solution. One might cluster a representative subset and then extend assignments to the rest of the data. As for outlier detection, you would check how new points fit into or deviate from the clustering structure derived from the sampled subset. This approach requires careful sampling to preserve the global structure. If the data is highly imbalanced or has rare but important minority clusters, random sampling might overlook them, so stratified or density-preserving sampling methods should be considered.

How does clustering-based outlier detection compare to other methods like Isolation Forest or One-Class SVM?

Clustering-based outlier detection relies on finding natural groupings in the data and then measuring deviation from these groups. Isolation Forest and One-Class SVM are specialized anomaly detection algorithms that do not necessarily assume explicit clusters in the data.

Isolation Forest works by repeatedly partitioning the data. Points that are easier to isolate in fewer partitions are flagged as anomalies. This approach tends to work well with high-dimensional data and can be computationally efficient. One-Class SVM tries to separate normal data points from the origin in feature space, effectively learning a boundary around them, and flags points that fall outside as anomalies.

One advantage of clustering-based methods is interpretability in terms of distance to a centroid or density region, which can be straightforward to explain to stakeholders. On the other hand, specialized algorithms like Isolation Forest or One-Class SVM can sometimes offer better performance, especially when there is no clear cluster structure or the data is high-dimensional. Clustering-based approaches may fail if the data does not naturally form coherent clusters. In such a case, advanced anomaly-specific algorithms might detect outliers more reliably.

How do you proceed when the dataset has both categorical and numerical features?

Many standard clustering algorithms (like K-means) assume a continuous vector space with a Euclidean distance metric. This can be problematic if there are categorical variables. One typical solution is to transform categorical variables into numerical form, for example via one-hot encoding. However, one-hot encoding can inflate dimensionality, and Euclidean distances in that space might not capture the underlying similarity well.

Alternately, specialized distance metrics or clustering algorithms can handle mixed data. Algorithms like K-Prototypes combine the ideas of K-means (for numerical attributes) and K-modes (for categorical attributes) to better cluster mixed data types. You would choose a suitable distance measure (e.g., Gower distance) that accounts for both categorical and numeric differences.

Once clusters are identified, outlier detection can again rely on “distance” to a cluster prototype, but that distance must make sense for mixed data types. Proper scaling or weighting of numerical versus categorical features is critical, and domain knowledge often guides whether certain attributes are more influential than others in measuring outlier-ness.

What happens if the data shows overlapping clusters or if no distinct clusters are apparent?

In many real-world situations, clusters might overlap or have very slight separations, making them difficult to distinguish with standard methods like K-means. This can lead to ambiguous assignments in which outlier detection becomes uncertain, as a point near an overlapping region might appear equidistant to multiple clusters.

Density-based approaches like DBSCAN or HDBSCAN can sometimes handle such overlaps by identifying dense regions that may partially overlap or degrade gradually in density. However, if the data truly has no well-defined structure—e.g., it forms a continuous manifold—clustering might label the entire dataset as a single large cluster, making outlier detection challenging. In such a scenario, alternative methods, possibly manifold-based or advanced density estimations, might be more appropriate. Another strategy is to rely on local density measures such as Local Outlier Factor (LOF) which focuses on the density of a point’s neighborhood relative to other points’ neighborhoods, rather than global clustering boundaries.

How do you handle interpretability in clustering-based outlier detection?

Interpretability can be a major concern when presenting outlier detection results. Stakeholders may ask why a certain point is flagged as an outlier. For centroid-based methods, interpretability is relatively straightforward: you can compute the distance to the centroid and compare it with a threshold. Visualizing data (when feasible in 2D or 3D) alongside cluster boundaries can offer additional clarity.

In density-based methods like DBSCAN, you could explain that a point is flagged as noise because it does not lie in a high-density region. One can calculate how many neighbors are within eps distance and show that it falls below min_samples. The interpretability advantage here is that the notion of “dense region” can be understood as “sufficient points grouped closely together.”

Nevertheless, if the data is high-dimensional, intuitive visualizations are less practical. In such cases, partial dependency plots or dimension reduction techniques (e.g., t-SNE or UMAP) might help provide a qualitative view of why certain points are singled out. However, dimension reduction is itself a transformation that can distort distances, so interpretations must be done carefully.

How do you handle missing or incomplete data when clustering for outlier detection?

When some features have missing values, clustering algorithms like K-means cannot directly operate on those instances unless the missing values are imputed or otherwise handled. Imputation can be done via simple strategies like mean or median substitution for numerical features, or via more sophisticated methods such as iterative imputation. If the fraction of missing data is large, imputation might introduce bias.

Alternatively, one could use algorithms that natively handle missing data, though they tend to be less common. Another approach is to segment the data into subsets based on completeness and cluster them separately, although that might lead to fragmented clusters. For anomaly detection, missing data itself might be an indicator of outlier-ness—some points could be missing key features in a way that suggests abnormal behavior. In that sense, you have to be careful not to “over-impute” anomalies into looking normal.

Additionally, if the fraction of missingness for certain variables is high, it might be wise to re-evaluate which features are truly essential. Domain experts might confirm whether discarding a heavily incomplete feature is more valuable than attempting to patch it with approximations that could lead to spurious cluster assignments.

How might you combine semi-supervised techniques with clustering for outlier detection?

If partial labels are available—say, a small percentage of data is labeled as normal or anomalous—you can use these labels to refine a clustering-based approach. Semi-supervised clustering might place known normal points in a specific cluster or guide the creation of clusters that minimize overlap with known anomalies.

One strategy is to run a baseline clustering algorithm first, then label the known normal data points. The cluster that predominantly contains labeled normal data is assumed to represent normal behavior, and distant points or those in other clusters might be potential anomalies. Conversely, if you have a few labeled anomalies, you can ensure they remain distant from or do not belong to a known normal cluster. Another variant is to train a supervised model only on the small set of anomalies and the cluster-labeled normal data, thus combining unsupervised and supervised signals.

Edge cases include scenarios where the limited labels are noisy or not representative of all types of anomalies. In that case, semisupervised methods can lead to underdetection of new anomalous types or an overemphasis on labeling points similar to the few known anomalies.

How do you handle concept drift or changes in data distribution over time with clustering-based outlier detection?

Concept drift occurs when the statistical properties of the target variable or feature distributions shift over time. In a streaming environment, the previously learned clusters may no longer represent current data well. As a result, a large proportion of normal data might be flagged as outliers simply because the clusters became outdated.

An adaptive strategy is to regularly update the clustering model. One practical solution is to use a rolling window approach, where older data is removed, and new data is introduced for clustering. Incremental clustering algorithms can keep updating cluster assignments. If the data drift is abrupt, you might need a mechanism to reinitialize the clustering model altogether. Alternatively, you might maintain a small set of candidate models, each trained on a different segment of data, and switch based on performance metrics.

A key subtlety is distinguishing between true anomalies and shifts in normal behavior. For instance, in an e-commerce system, a sudden seasonal shift in buying patterns might appear anomalous if the model does not adapt. Proper domain awareness, combined with real-time feedback loops, is often required to detect real anomalies vs. legitimate drifts in the underlying distribution.