Differentiate between the evaluation of supervised and unsupervised machine learning methods with the help of suitable equations

Supervised and unsupervised machine learning methods are evaluated differently due to their inherent differences in learning approach.

1. Supervised Learning Evaluation: In supervised learning, we have a target variable or outcome that we want to predict or classify. Therefore, we can evaluate the performance of a supervised learning model based on how well it predicts this target variable.

Common evaluation metrics for supervised learning include:

• Accuracy: This is the proportion of correct predictions made by the model. It's calculated as (True Positives + True Negatives) / Total Observations.

• Precision: This is the proportion of positive identifications that were actually correct. It's calculated as True Positives / (True Positives + False Positives).

• Recall: This is the proportion of actual positives that were identified correctly. It's calculated as True Positives / (True Positives + False Negatives).

• F1 Score: This is the harmonic mean of Precision and Recall and gives a better measure of the incorrectly classified cases than the Accuracy Metric. It's calculated as 2*(Recall * Precision) / (Recall + Precision).

2. Unsupervised Learning Evaluation: In unsupervised learning, we don't have a target variable to predict or classify. Instead, we're trying to identify patterns or structures within the data. Therefore, evaluation of unsupervised learning models is more subjective and can be more challenging.

Common evaluation methods for unsupervised learning include:

• Silhouette Score: This is a measure of how similar an object is to its own cluster compared to other clusters. The silhouette ranges from -1 to 1, where a high value indicates that the object is well matched to its own cluster and poorly matched to neighboring clusters.

• Davies-Bouldin Index: This index signifies the average 'similarity' between clusters, where the similarity is a measure that compares the distance between clusters with the size of the clusters themselves. The lower the Davies-Bouldin index, the better.

• Rand Index: This measures the similarity of the two assignments, ignoring permutations and with chance normalization. A Rand index of 1 indicates that the two data clusterings are identical.

Remember, the choice of evaluation metric largely depends on the specific task and the business context.