Cumulative explained variance

Definition

Cumulative explained variance refers to the total amount of variance in a dataset that is accounted for by a set of principal components in Principal Component Analysis (PCA). It gives insights into how much information each component contributes to the overall dataset and helps in deciding how many components to retain for analysis, balancing data reduction with information preservation.

5 Must Know Facts For Your Next Test

1. Cumulative explained variance is often expressed as a percentage, showing the proportion of total variance captured by the selected principal components.
2. In PCA, a common practice is to retain components that together explain at least 70-90% of the cumulative variance, balancing data reduction and information retention.
3. Cumulative explained variance helps visualize how many principal components are necessary to adequately represent the data without losing significant information.
4. The first principal component usually accounts for the most variance, with subsequent components contributing less, which is reflected in the cumulative explained variance.
5. Analyzing cumulative explained variance can guide decisions on dimensionality reduction methods and feature selection in data preprocessing stages.

Review Questions

• How does cumulative explained variance assist in determining the number of principal components to retain in PCA?
  • Cumulative explained variance provides a clear metric for evaluating how much of the total dataset's variance is represented by a certain number of principal components. By calculating this value, one can identify the point at which adding more components yields diminishing returns regarding additional explained variance. Typically, a threshold is set (like 70-90%) to guide the decision on how many components to keep while ensuring meaningful data representation.
• Discuss the relationship between eigenvalues and cumulative explained variance in the context of PCA.
  • Eigenvalues are fundamental in calculating cumulative explained variance since each eigenvalue corresponds to a principal component and indicates how much variance that component captures from the data. When you sum these eigenvalues up to a certain number of components, you derive the cumulative explained variance. This relationship highlights which components contribute significantly to understanding the dataset's structure and helps decide which components to retain based on their eigenvalues.
• Evaluate the implications of using cumulative explained variance for dimensionality reduction in real-world datasets.
  • Using cumulative explained variance for dimensionality reduction has significant implications in real-world datasets, as it helps maintain a balance between reducing complexity and retaining essential information. By selecting an optimal number of principal components based on this metric, analysts can improve computational efficiency and model performance while minimizing loss of important data characteristics. This process is crucial in fields such as finance, healthcare, and machine learning, where interpretability and accuracy are paramount in decision-making processes.

Related terms

Principal Component Analysis (PCA): A statistical technique used to reduce the dimensionality of a dataset while preserving as much variance as possible, by transforming original variables into a new set of uncorrelated variables called principal components.

Eigenvalues: Scalar values that indicate the amount of variance captured by each principal component in PCA; higher eigenvalues correspond to components that explain more variance.

Scree Plot: A graphical representation used to determine the number of principal components to retain, where the eigenvalues are plotted against the component numbers, often showing an 'elbow' point.