Multivariate analysis is a statistical technique for understanding relationships among multiple variables, primarily used in data analytics to extract insights and patterns. Key methods include principal component analysis (PCA) for reducing dimensionality while retaining variance, and cluster analysis for grouping similar observations. Techniques like k-means clustering are employed to segment data effectively.

1. Multivariate analysis

2. • Multivariate analysis is a statistical technique used to understand
relationships between multiple variables simultaneously. It is
commonly applied in data analytics to extract insights, identify
patterns, and make informed decisions based on complex data. Here’s
an overview of multivariate analysis methods, their applications, and
how they can be used in data analytics:

3. Principal Component Analysis (PCA):
• Purpose: Reduce dimensionality while retaining most of the variance.
• Use Case: Useful when dealing with high-dimensional datasets, such
as image data or gene expression data.
• Process: It transforms original variables into a new set of uncorrelated
variables (principal components) ordered by the amount of original
variance they explain.

4. Suppose we have a dataset with 5 observations (samples) and 2
variables (X1​and X2​
). The dataset is as follows:

9. Summary of the PCA Result
• The first principal component (PC1text{PC}_1PC1​
) explains most of the variance (1.98
out of a total variance of 2).
• The original 2-dimensional data is reduced to 1 dimension along PC1text{PC}_1PC1​
.
• This process helps to simplify the data while retaining the relationships between the
variables.

10. Cluster Analysis
• Purpose: Group observations into clusters that have similar
characteristics.
• Use Case: Segmentation of customers in marketing, grouping patients
with similar symptoms in healthcare.
• Techniques: K-means, hierarchical clustering, DBSCAN, etc.

11. K-means Clustering

17. Summary of the K-means Clustering Result
• After assigning points to clusters and updating the centroids, the algorithm
iterated until there were no changes in the assignments, indicating
convergence.
• Cluster 1 groups the closer points (1 and 2), while Cluster 2 groups the
remaining points (3, 4, and 5).