Variance explained

Definition

Variance explained refers to the proportion of the total variance in a dataset that is accounted for by a statistical model, such as principal component analysis (PCA). This concept helps in understanding how well the model captures the underlying structure of the data, indicating the effectiveness of the components in representing the original features. The higher the variance explained by the principal components, the more informative and compact the model becomes, ultimately aiding in data reduction and interpretation.

5 Must Know Facts For Your Next Test

1. In PCA, variance explained is often expressed as a percentage, allowing researchers to easily gauge how much information is retained in fewer dimensions.
2. Components are ranked based on their eigenvalues, with the first component explaining the most variance, followed by subsequent components explaining decreasing amounts.
3. The cumulative variance explained can be plotted to help determine how many components are needed to capture a desired level of variance, typically set at 70-90%.
4. Variance explained can also help identify noise in the data; components with very low variance are often discarded as they contribute little useful information.
5. In genomic studies, understanding variance explained is crucial for interpreting genetic variation and its relationship to phenotypic traits.

Review Questions

• How does variance explained enhance the understanding of data structure when using PCA?
  • Variance explained provides insights into how effectively PCA reduces dimensionality while preserving essential information. By quantifying the proportion of total variance captured by each principal component, researchers can assess which components hold significant data patterns. This understanding helps in selecting an appropriate number of components to retain, ensuring that the analysis remains informative without being overly complex.
• Discuss how eigenvalues relate to variance explained and their significance in PCA.
  • Eigenvalues play a critical role in determining variance explained in PCA. Each principal component is associated with an eigenvalue that reflects how much variance it accounts for from the original dataset. Higher eigenvalues indicate that a component explains more variance. Therefore, analyzing eigenvalues allows researchers to prioritize which components to include based on their contribution to explaining the data’s variability.
• Evaluate the implications of high versus low variance explained in the context of genomic data analysis.
  • High variance explained in genomic data analysis indicates that a significant portion of genetic variability is captured by selected components, suggesting robust insights into genetic factors influencing traits or diseases. Conversely, low variance explained may signal inadequate model fit or noise dominance, leading researchers to reconsider their approach. Understanding these implications helps refine analysis strategies and improve interpretations of genetic associations with phenotypes.

Related terms

Principal Component: A linear combination of original variables that captures the maximum variance possible in the data, serving as new axes for representing the data in a reduced dimension.

Eigenvalue: A scalar value that represents the amount of variance captured by its corresponding eigenvector in PCA; higher eigenvalues indicate that more variance is explained by that component.

Dimensionality Reduction:

The process of reducing the number of random variables under consideration, by obtaining a set of principal variables, often utilizing techniques like PCA.