DM5 - Outlier Detection Flashcards

Question 1

How did Hawkins famously define an outlier?

Accepted Answer

An observation which deviates so much from the other observations as to arouse suspicions that it was generated by a different mechanism.

Question 2

What is the conceptual difference between noise and an outlier?

Accepted Answer

Noise is a random measurement error or variance, whereas an outlier is a valid data point that is highly unusual or rare.

Question 3

What defines a global outlier?

Accepted Answer

A data point that significantly deviates from the entire rest of the dataset.

Question 4

What defines a contextual outlier?

Accepted Answer

A data point that deviates significantly only within a specific context or subset of the data.

Question 5

What defines a collective outlier?

Accepted Answer

A subset of data points that strongly deviates from the entire dataset collectively, even if the individual points do not.

Question 6

How do model-based statistical methods identify outliers?

Accepted Answer

They assume the data follows a specific distribution (like a Gaussian) and flag points with a very low probability of belonging to that model.

Question 7

What is the formula for the Grubbs' test statistic $G$ used to find outliers in univariate data?

Accepted Answer

$G=\frac{\max|x_{i}-\bar{x}|}{s}$

Question 8

How do depth-based outlier detection approaches work?

Accepted Answer

They typically use convex hull algorithms to assign depths, classifying points on the outermost layers (shallowest depth) as outliers.

Question 9

How is a distance-based outlier generally defined?

Accepted Answer

A point $p$ is an outlier if a specific percentage of all other points in the dataset are farther away than a given distance radius $\epsilon$.

Question 10

Why do simple distance-based methods struggle with varying densities?

Accepted Answer

Because they rely on global parameters (like a single radius), making it hard to identify outliers near both dense and sparse clusters simultaneously.

Question 11

Why is Angle-based Outlier Detection (ABOD) particularly useful for high-dimensional data?

Accepted Answer

Because angles between points are far less affected by the curse of dimensionality than Euclidean distances.

Question 12

In ABOD, how do you mathematically distinguish an outlier from an inlier?

Accepted Answer

An outlier is located far from the main cluster, so the angles it forms with other pairs of points have a much smaller variance compared to an inlier.

Question 13

What is the mathematical formulation for the Angle-based Outlier Factor $ABOD(p)$?

Accepted Answer

$ABOD(p)=VAR_{x,y\in\mathcal{D}}\left(\frac{\langle x-p,y-p\rangle}{||x-p||^{2}\cdot||y-p||^{2}}\right)$

Question 14

What is the computational complexity of the standard naïve ABOD algorithm?

Accepted Answer

$\mathcal{O}(n^{3})$

Question 15

What is the core idea behind the Local Outlier Factor (LOF) algorithm?

Accepted Answer

It identifies outliers by comparing the local density of a point to the local densities of its $k$-nearest neighbors.

Question 16

What is the definition of reachability distance $rdist_{k}(p,o)$ in LOF?

Accepted Answer

$rdist_{k}(p,o)=\max\{k	ext{-distance}(o),dist(p,o)\}$

Question 17

In the LOF algorithm, what does a score significantly greater than 1 indicate?

Accepted Answer

It indicates that the point's local density is much lower than its neighbors, meaning it is likely an outlier.

Question 18

How do clustering algorithms like DBSCAN handle outlier detection natively?

Accepted Answer

They classify any data points that do not meet the density requirements to join a cluster as noise or outliers.

Question 19

What is the core principle of an Isolation Forest?

Accepted Answer

It builds random decision trees to isolate points;outliers are easier to separate and thus end up closer to the root of the trees (shorter path lengths).

Question 20

What is the formula for the anomaly score $s(x,n)$ of a point $x$ in an Isolation Forest?

Accepted Answer

$s(x,n)=2^{-\frac{E(h(x))}{c(n)}}$

DM5 - Outlier Detection

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