Carlson School of Management - BA 3551: Cluster Analysis and Association Rules

A comprehensive collection of vocabulary flashcards covering Association Rule Mining (Support, Confidence, Lift, Apriori Algorithm), Distance Measures, Normalization, Hierarchical and Partitioning Clustering (K-Means), Linkage Methods, and Cluster Evaluation Metrics (WSS and BSS) for BA 3551.

Unsupervised Learning

A category of data mining methods where data is explored to uncover previously unknown patterns without having a clear outcome in mind or a dependent variable to predict.

Association Rule Mining

A technique (also known as Affinity Analysis or Market Basket Analysis) used to discover interesting relationships and co-occurrence patterns among items, events, or variables in transaction datasets.

Itemset

Any unique subset $X$ of items drawn from the universal set $U$ of all items in a given domain, containing no duplicate elements.

Transaction

An instance of an itemset within a dataset representing a single observation or event, such as a specific combination of products bought by a customer or symptoms present in a patient.

Antecedent

The itemset $X$ on the left-hand side (or body) of an association rule $X \rightarrow Y$, representing the condition or 'if' component.

Consequent

The itemset $Y$ on the right-hand side (or head) of an association rule $X \rightarrow Y$, representing the recommended or predicted 'then' component.

Support Percentage of an Association Rule

The fraction of total transactions in a dataset containing all items from both $X$ and $Y$, given by $\frac{\text{Count}(X, Y)}{\text{Total Transactions}}$; this metric is non-directional.

Confidence

A directional metric measuring the estimated conditional probability that a randomly chosen transaction contains itemset $Y$ given that it contains itemset $X$, computed as $\text{Conf}(X \rightarrow Y) = \frac{\sigma(X \rightarrow Y)}{\sigma(X)} = \frac{\text{Count}(X, Y)}{\text{Count}(X)}$.

Lift

A non-directional metric assessing how much more likely two itemsets co-occur than expected by pure chance, calculated as $\text{Lift}(X \rightarrow Y) = \frac{\text{Supp Percentage}(X \rightarrow Y)}{\text{Supp Percentage}(X) \times \text{Supp Percentage}(Y)} = \frac{\text{Conf}(X \rightarrow Y)}{\text{Supp Percentage}(Y)}$.

Frequent Itemset

An itemset whose calculated support percentage is greater than or equal to a user-defined minimum support threshold ($\text{support} \ge \text{minsupp}$).

Apriori Algorithm

A classic algorithm that reduces computational burden using the principle that if an itemset $X$ is not frequent, any larger itemset containing $X$ cannot be frequent.

Intra-similarity

A desirable cluster property specifying that data points assigned to the same cluster should be cohesive and highly similar to one another.

Inter-similarity

A cluster property describing the similarity between different clusters; desirable clustering requires low inter-similarity so clusters are distinctly separated.

Euclidean Distance

The straight-line distance between two $k$-dimensional points $A$ and $B$, given by the formula $d(A, B) = \sqrt{(a_1 - b_1)^2 + \dots + (a_k - b_k)^2}$.

Manhattan Distance

The rectilinear distance between two points calculated as the sum of the absolute differences of their coordinates: $d(A, B) = |a_1 - b_1| + \dots + |a_k - b_k|$.

Matching Distance

A distance metric for binary data defined as the ratio of mismatches to the total number of binary features: $d(A, B) = \frac{N_{01} + N_{10}}{N_{00} + N_{01} + N_{10} + N_{11}} = \frac{N_{01} + N_{10}}{k}$.

Jaccard Distance

A binary distance metric that excludes joint absences ($N_{00}$), defined as the ratio of mismatches to the total number of features present in at least one observation: $d(A, B) = \frac{N_{01} + N_{10}}{N_{01} + N_{10} + N_{11}}$.

Min-Max Normalization

A scaling technique that rescales numerical attributes to a bounded range between $0$ and $1$ using the formula $\text{NewValue} = \frac{X - \min}{\max - \min}$.

Standardization

A data transformation method that centers an attribute around its sample mean and divides by its sample standard deviation: $\text{NewValue} = \frac{X - \text{Sample mean}}{\text{Sample standard deviation}}$.

Hierarchical Clustering

An agglomerative (bottom-up) clustering algorithm that begins with each point as its own single-point cluster and successively merges the nearest pairs until all points belong to a single cluster.

Dendrogram

A tree-structured diagram generated by hierarchical clustering that illustrates the sequence and distance levels of cluster merges, used to determine the optimal number of clusters.

K-Means Clustering

A partitioning-based clustering algorithm where the number of clusters $k$ is chosen ex-ante, and data points are iteratively reassigned to the nearest cluster centroid to minimize within-cluster variance.

Cluster Centroid

The mean coordinate point representing the center of a cluster, calculated by taking the average value for each feature across all data points in that cluster.

Single Linkage

A hierarchical clustering linkage method that measures distance between two clusters as the minimum distance between any single point in one cluster and any single point in the other; sensitive to noise and outliers but handles non-convex shapes.

Complete Linkage

A hierarchical clustering linkage method that defines distance as the maximum distance between any point in one cluster and any point in another; tends to break large clusters into groups of similar diameter.

Average Linkage

A hierarchical clustering linkage method that measures the average pairwise distance between all data points across two clusters, tending to produce spherical clusters less sensitive to outliers than single or complete linkage.

Centroid Linkage

A hierarchical clustering linkage method that defines the distance between two clusters as the distance between their respective cluster centroids.

Ward's Method

A hierarchical clustering linkage method that merges clusters to minimize the increase in the total within-cluster sum of squared errors; robust to outliers and creates dense, spherical clusters.

Within Sum of Squared Errors (WSS)

A cluster cohesion metric calculated by summing the squared Euclidean distances from each data point to its assigned cluster centroid: $\text{WSS} = \sum_{i=1}^j \sum_{x \in C_i} d(x, m_i)^2$.

Between Sum of Squared Errors (BSS)

A cluster separation metric calculated by weighting the squared Euclidean distance from each cluster centroid $m_i$ to the dataset centroid $m^*$ by cluster size $n_i$: $\text{BSS} = \sum_{i=1}^j n_i \cdot d(m_i, m^*)^2$.