The primary requirement is to use a clustering algorithm that does not need the number of clusters to be specified in advance. DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a density-based algorithm that groups together points that are closely packed, marking as outliers points that lie alone in low-density regions. A key advantage of DBSCAN is that it automatically determines the number of clusters based on the data's density and connectivity, making it ideal for scenarios where the cluster count is unknown.

B. k-nearest neighbors: This is a supervised learning algorithm for classification and regression, not an unsupervised clustering method.

C. k-means: This is a popular clustering algorithm, but it explicitly requires the user to pre-specify the number of clusters ('k') as an input parameter.

D. Logistic regression: This is a supervised classification algorithm used to predict a categorical dependent variable; it does not perform clustering.

1. Ester

M.

Kriegel

H. P.

Sander

J.

& Xu

X. (1996). A density-based algorithm for discovering clusters in large spatial databases with noise. In Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (KDD'96). AAAI Press

pp. 226–231. The paper introduces DBSCAN and states in its abstract

"The proposed algorithm DBSCAN is designed to discover the clusters and the noise in a spatial database... it does not require the number of clusters as input."

2. Scikit-learn Developers. (2023). 2.3. Clustering - 2.3.7. DBSCAN. Scikit-learn 1.3.2 documentation. In the overview of the algorithm

the documentation notes

"In contrast to k-means

DBSCAN does not require the number of clusters to be specified in advance."

3. Leskovec

J.

Rajaraman

A.

& Ullman

J. D. (2020). Mining of Massive Datasets. Cambridge University Press. In Chapter 7

"Clustering

" Section 7.4

the authors describe DBSCAN as a method that can find non-spherical clusters and does not require the number of clusters to be known beforehand

contrasting it with methods like k-means. DOI: https://doi.org/10.1017/9781108684160