Clustering of trend data using joinpoint regression models.

Area of Science:

• Statistics
• Data Mining
• Computational Statistics

Background:

• Clustering two-dimensional data with piecewise linear mean functions presents challenges in identifying common characteristics.
• Existing methods may not effectively handle segmented regression models with shared features across clusters.

Purpose of the Study:

• To develop and validate a robust method for clustering two-dimensional data with piecewise linear mean functions.
• To identify clusters exhibiting common characteristics, such as identical slopes, using segmented line regression models.

Main Methods:

• Employs a restricted least squares method to fit segmented line regression models with common features.
• Estimates the maximum number of segments using permutation tests and the Bayes Information Criterion (BIC).
• Determines the optimal number of clusters using the Bayes Information Criterion (BIC).

Main Results:

• Proposes a measure for minimum detectable distance to enhance clustering algorithm effectiveness.
• Simulation results demonstrate the properties and effectiveness of the proposed clustering methods.
• Proves the consistency of cluster grouping estimation for a given number of clusters.

Conclusions:

• The proposed method effectively clusters two-dimensional data with piecewise linear mean functions.
• The approach is applicable to both ordered and unordered independent variables, with a focus on cancer trend analysis.
• The method provides a reliable framework for identifying clusters with shared statistical properties.