Q. 1. Consider the market basket transactions. When answering the below questions, . Also, clearly indicate for instance how you came up with the answer for the questions asked below. Show detailed steps/explanation for each of the question below.  (100 points) (a) What is the maximum number of association rules that can be extracted from this data (including rules that have zero support)? (b) What is the maximum size of frequent itemsets that can be extracted (assuming 0)? (c) Write an expression for the maximum number of size-3 itemsets that can be derived from this data set. (d) Find an itemset (of size 2 or larger) that has the largest support. (e) Find a pair of items, a and b, such that the rules   and   have the same confidence. Q. 2. What is Anomaly Detection? Describe in detail the characteristics of the Anomaly Detection Problems. Also, describe in detail the characteristics of Anomaly Detection Methods. (100 points) When referring to other articles, you need to cite using the format given here (either APA or MLA): : Failure of citations will lead to several deduction of points or zero points may be awarded for the answer.

Q. 1.

(a) To determine the maximum number of association rules that can be extracted from the market basket transactions dataset, we need to consider the number of possible combinations of items.

Let’s assume there are n distinct items in the dataset. The number of association rules can be calculated using the formula: 2^n – 1.

The minus one is subtracted because we exclude the empty itemset rule.

So, the maximum number of association rules that can be extracted from the data is 2^n – 1.

(b) To find the maximum size of frequent itemsets that can be extracted, we need to consider all possible subsets of items in the dataset.

Assuming 0 is included, we can calculate the maximum size by raising 2 to the power of n (where n is the number of distinct items) and subtracting 1.

So, the maximum size of frequent itemsets that can be extracted is 2^n – 1.

(c) To express the maximum number of size-3 itemsets that can be derived from the data set, we need to calculate the number of combinations of distinct items taken 3 at a time.

The formula to calculate the number of combinations is nC3 = n! / (3!(n-3)!), where n is the number of distinct items.

So, the expression for the maximum number of size-3 itemsets is n! / (3!(n-3)!).

(d) To find an itemset (of size 2 or larger) that has the largest support, we need to calculate the support for each itemset and identify the one with the highest value.

Support measures the frequency of an itemset in the dataset. It is calculated by dividing the number of transactions containing the itemset by the total number of transactions.

By calculating the support for each itemset and comparing them, we can determine the itemset with the largest support.

(e) To find a pair of items, a and b, such that the rules “a => b” and “b => a” have the same confidence, we need to calculate the confidence for each rule and compare them.

Confidence measures the conditional probability of the consequent item given the antecedent item in an association rule. It is calculated as the support of the itemset containing both items divided by the support of the antecedent item.

By calculating the confidence for each rule “a => b” and “b => a” and comparing them, we can identify the pair of items with the same confidence.

Q. 2.

Anomaly Detection refers to the process of identifying patterns or instances in a dataset that deviate significantly from the norm or expected behavior. It is used to detect unusual or anomalous data points that may indicate potential abnormalities, errors, or fraudulent activities.

Characteristics of Anomaly Detection Problems:

1. Unsupervised Learning: Anomaly detection is typically an unsupervised learning task, as it aims to identify anomalies without the need for labeled data. The algorithms learn from the intrinsic characteristics and patterns of the data to detect anomalies.

2. Low Prevalence: Anomalies are generally rare occurrences compared to the normal data. Therefore, the proportion of anomalies in the dataset is often significantly smaller, making it a challenging problem to detect them accurately.

3. Imbalanced Data: Due to the low prevalence of anomalies, the dataset is usually imbalanced, with a large majority of normal data instances and a small number of anomalous instances. This class imbalance can affect the performance of anomaly detection algorithms, requiring specialized techniques to handle it.

4. Unexpected Patterns: Anomalous instances often exhibit unexpected patterns or behaviors compared to the normal data. These patterns may include outliers, unexpected variations, or specific combinations of features that deviate significantly from the expected patterns.

5. Lack of Prior Knowledge: Anomaly detection problems often occur in scenarios where little or no prior knowledge about the nature of anomalies is available. This requires the algorithms to be able to adapt and learn from the data itself without relying on predefined rules or assumptions.

Characteristics of Anomaly Detection Methods:

1. Statistical Methods: Many anomaly detection techniques rely on statistical models to characterize the normal behavior of the data. These methods use statistical measures such as mean, standard deviation, or probability distributions to determine the likelihood of an instance being anomalous.

2. Machine Learning Approaches: Anomaly detection also leverages machine learning algorithms such as clustering, nearest neighbor, or outlier detection methods. These methods learn from the data to identify patterns or instances that differ significantly from the majority of the data.

3. Domain Knowledge: Some anomaly detection methods may incorporate domain-specific knowledge or expert input to enhance their accuracy and interpretability. This can be particularly useful in detecting anomalies in complex systems or domains with specific constraints.

4. Online and Batch Detection: Anomaly detection methods can be designed for both online and batch detection scenarios. Online methods continuously monitor and detect anomalies in real-time, while batch methods analyze the entire dataset offline to identify anomalies.

5. Evaluation Metrics: Anomaly detection methods are evaluated using various metrics such as precision, recall, F1 score, or area under the Receiver Operating Characteristic (ROC) curve. These metrics assess the algorithm’s ability to correctly identify anomalies while minimizing false positives or false negatives.