MACHINE LEARNING

Answer: (iii) Anomaly Detection

Explanation:

• Anomaly Detection (also called outlier detection) is the ML technique explicitly designed to identify rare items, events or observations which raise suspicions by differing significantly from the majority of the data.
• Clustering groups similar data points; outliers may be found as points not belonging to any cluster, but it is not its primary purpose.
• Classification assigns data to predefined classes; it needs labeled outlier examples which are rarely available.
• Techniques used for Anomaly Detection: Statistical (Z-score, Gaussian), Density-based (LOF, DBSCAN), Distance-based, Isolation Forest, One-Class SVM, Autoencoders.

Hence the most specific answer is (iii) Anomaly Detection. Option (iv) All of the above is not best choice because clustering/classification are not primarily outlier detectors.

Answer: (ii) 1

Explanation:

• Clustering (K-means, hierarchical, DBSCAN) groups data points by similarity in feature space.
• Requires at least 1 feature/variable to compute distance/similarity. With 0 features there is no data to cluster.
• With 1 feature, 1D clustering is valid (e.g., points on a line clustered by value: {1,2,10} → clusters {1,2} and {10} via 1D K-means).
• While typically we use $\ge 2$ features for visualization, minimum mathematically is 1.

Therefore (ii) 1 is correct.

Answer: (i) Null Hypothesis

Explanation:

• Null Hypothesis ($H_0$): A hypothesis which defines the population distribution / assumes no effect, no difference. It is a statement to be tested and possibly rejected. Example: $\mu = \mu_0$, distribution is Normal $N(\mu,\sigma^2)$.
• Alternative Hypothesis ($H_1$ / $H_a$): Complements $H_0$, indicates existence of effect/difference.
• The term statistical hypothesis which completely specifies the population distribution (parameters) is called simple hypothesis; if $H_0$ does that it defines the distribution. In MCQ context, expected answer is Null Hypothesis.

Positive/Negative hypotheses are not standard statistical terms. Hence (i) Null Hypothesis is correct. If question meant simple hypothesis, null hypothesis is the standard example taught as defining population distribution under assumption.

K-means vs K-medoid:

Aspect	K-means (Lloyd)	K-medoid (PAM)
Center	Centroid = mean $\mu_j=\frac1{|C_j|}\sum x$ (not necessarily data point, continuous)	Medoid = actual data point minimizing sum distance to cluster members
Distance	Euclidean (minimizes SSE)	Any metric (Manhattan, arbitrary dissimilarity)
Robustness	Sensitive to outliers (mean shifts)	Robust (medoid not affected by extreme outlier)
Cost function	$J=\sum\sum||x-\mu||^2$	$E=\sum\sum d(x,m_j)$
Complexity	$O(nkdi)$ fast	$O(k(n-k)^2)$ per iteration (PAM) much slower, $CLARA/CLARANS$ for large data
When to use	Continuous, spherical clusters, fast	Categorical/mixed, need representatives from dataset, noisy data

Density-Based Hierarchical Clustering:

Combines density and hierarchy. Unlike flat K-means, builds tree (dendrogram) where clustering reflects density connectivity at different thresholds.

• Core idea: Clusters are dense regions separated by sparse regions. Define $\epsilon$-neighborhood and $minPts$. Point types: core (≥$minPts$ in $\epsilon$), border, noise. Hierarchical variant (e.g., HDBSCAN, OPTICS, DENCLUE hierarchical) varies $\epsilon$/density threshold to create hierarchy.

• OPTICS: Ordering Points To Identify Clustering Structure — computes reachability distance, produces reachability plot, extracts hierarchy without fixing single $\epsilon$.

• HDBSCAN: Converts DBSCAN to hierarchical, builds minimum spanning tree of mutual reachability, condenses, selects stable clusters via persistence $\lambda=1/distance$.

• Hierarchical density dendrogram: Bottom leaves = core points merge at lowest density threshold as $\epsilon$ increases.

Advantages: Finds arbitrary shapes, handles noise, no need to preset $k$, hierarchy reveals clusters at multiple densities.

Steps generic: Estimate density (kernel), build graph where edges if density > threshold, connected components = clusters, vary threshold → hierarchy, prune unstable branches.

K-NN vs K-means:

Aspect	K-NN (K-Nearest Neighbors)	K-means (Clustering)
Type	Supervised, instance-based, lazy classifier/regressor	Unsupervised clustering
Purpose	Predict label $y$ for query using labeled neighbors	Group unlabeled data into $k$ clusters minimizing SSE
Input	Labeled training $(x_i,y_i)$	Unlabeled $x_i$ only, need $k$ preset
Working	For query $x_q$, find $k$ nearest labeled points by distance, majority vote / average: $\hat y = \arg\max_c \sum \mathbb{I}(y_i=c)$	Iteratively assign points to nearest centroid $\mu_j$, recompute $\mu_j=$ mean, repeat until convergence
Training	No model building, stores data	Builds model (centroids)
Prediction cost	$O(n d)$ per query (slow)	$O(k d)$ after training (fast assign)
Output	Single label per query	Cluster id for all points
Choosing $k$	$k$ = neighborhood size via CV (bias-variance)	$k$ = number clusters via elbow/silhouette
Example	Classify email as spam using 5 nearest labeled emails	Segment customers into 3 groups without labels

Common confusion: Both use distance and $k$, but meanings completely different: $k$ in K-NN = neighbors to vote, $k$ in K-means = clusters. K-NN needs labels, K-means does not. K-NN predicts new point, K-means discovers structure.

When to use: Labels available + need classification → K-NN. No labels + need grouping → K-means.