# How to Perform Principal Component Analysis (PCA) in Python


## Key Takeaways

- PCA is a linear dimensionality reduction technique that transforms high-dimensional biological data into a lower-dimensional space of uncorrelated principal components, ordered by captured variance.
- Proper implementation necessitates feature standardization (e.g., using `StandardScaler`) to prevent variables with larger scales from dominating the analysis, followed by fitting the `sklearn.decomposition.PCA` model.
- Component selection requires evaluating multiple criteria (Kaiser criterion, scree plot, cumulative variance, parallel analysis) and considering the biological interpretability of loadings and scores, not just statistical thresholds.
- Interpretation relies on analyzing score plots for sample clustering and loading plots to identify influential variables, which can reveal biological patterns like gene expression pathways or metabolite profiles.
- PCA is unsuitable for nonlinear relationships; data exhibiting such patterns may require alternative methods like t-SNE or UMAP for effective dimensionality reduction and visualization.
- Reproducibility hinges on meticulous documentation of the entire workflow, including data import, preprocessing choices, PCA parameters, component selection justification, and version control for code and data.

---

## Quick Answer

- Principal component analysis (PCA) reduces high-dimensional biological datasets into a smaller set of uncorrelated variables while preserving the majority of variance, and Python libraries such as scikit-learn provide the core implementation.
- The correct workflow requires standardizing features before decomposition, then selecting components based on explained variance and interpreting loadings and scores to identify biological patterns.
- PCA is a linear dimensionality reduction method, so it cannot capture nonlinear relationships, and results depend heavily on preprocessing choices and data quality.

## Understanding Principal Component Analysis in Biological Research

Principal component analysis is a statistical technique that transforms a dataset with many potentially correlated variables into a smaller number of uncorrelated variables called principal components. Each principal component is a linear combination of the original variables, and the components are ordered so that the first component captures the largest possible variance in the data, the second captures the next largest variance under the constraint of being orthogonal to the first, and so on.

For biology students and researchers, PCA serves as a data exploration and visualization tool that helps identify patterns, clusters, and outliers in complex datasets. Common applications include gene expression analysis, metabolomics profiling, population genetics, and ecological community analysis. The technique is particularly valuable when working with datasets that contain dozens or hundreds of measured variables per sample, where direct visualization is impossible.

The mathematical foundation of PCA involves computing the eigenvectors and eigenvalues of the covariance matrix of the standardized data. The eigenvectors define the directions of maximum variance, and the eigenvalues indicate the amount of variance explained by each principal component. In practice, researchers rarely compute these quantities manually because Python libraries handle the linear algebra efficiently.

PCA is an unsupervised method, meaning it does not use class labels or outcome information during the computation. This property makes it useful for discovering hidden structure in data without prior assumptions about grouping. However, the same property means that PCA cannot be used directly for classification or prediction tasks without additional supervised methods applied to the reduced data.

The output of PCA consists of two main components. The scores represent the coordinates of each sample in the new principal component space, and the loadings represent the contribution of each original variable to each principal component. Together, these outputs allow researchers to visualize sample relationships and identify which variables drive the observed separation.

## Core Principles of PCA Implementation

### Mathematical Basis of Principal Components

The mathematical procedure for PCA begins with a data matrix where rows represent samples and columns represent variables. For biological data, samples might be individual organisms, tissue samples, or experimental replicates, while variables might be gene expression levels, metabolite concentrations, or morphological measurements.

The first step is to center the data by subtracting the mean of each variable. This ensures that the principal components describe variance around the centroid of the data instead of the absolute values. Standardization, which divides each variable by its standard deviation, is also common when variables are measured on different scales. Without standardization, variables with larger numerical ranges would dominate the principal components regardless of their biological importance.

The covariance matrix of the standardized data captures the pairwise relationships between variables. The eigenvectors of this matrix define the principal component directions, and the eigenvalues indicate the amount of variance explained by each direction. The eigenvector with the largest eigenvalue corresponds to the first principal component, and subsequent eigenvectors correspond to components with decreasing eigenvalues.

The total variance in the data is the sum of all eigenvalues. The proportion of variance explained by each principal component is calculated by dividing its eigenvalue by the total variance. This proportion is the basis for deciding how many components to retain for downstream analysis.

### Mathematical Relationship Between Loadings and Scores

The loadings matrix contains the coefficients that define each principal component as a linear combination of the original variables. Each loading value represents the correlation between the original variable and the principal component. Variables with large absolute loading values contribute more strongly to that component.

The scores matrix contains the coordinates of each sample in the principal component space. The score for a sample on a given component is calculated by multiplying the sample's standardized variable values by the corresponding loadings and summing the products. This calculation is equivalent to projecting the sample onto the principal component direction.

The relationship between loadings and scores is symmetric. A sample with a high score on a component has variable values that align with the variables that have high loadings on that component. This relationship is the basis for interpreting biological patterns in the PCA plot.

## Practical Workflow for PCA in Python

### Setting Up the Python Environment

The implementation of PCA in Python requires several libraries. The `pandas` library handles data import and manipulation, `numpy` provides numerical operations, `scikit-learn` contains the PCA implementation, and `matplotlib` or `seaborn` generates the visualizations. These libraries are available through the standard Python package managers and are commonly preinstalled in scientific computing distributions.

The core PCA class in scikit-learn is `sklearn.decomposition.PCA`. This class provides methods for fitting the model to data, transforming data into the principal component space, and accessing the explained variance and loadings. The implementation uses singular value decomposition internally, which is numerically stable for most biological datasets.

Before running PCA, the data must be organized in a matrix format where rows are samples and columns are variables. Missing values must be handled before PCA because the algorithm cannot process incomplete data. Common approaches include removing samples or variables with excessive missing values, imputing missing values using mean or median substitution, or using more sophisticated imputation methods.

### Data Preprocessing Steps

Data preprocessing is the most consequential step in the PCA workflow. The choice of preprocessing method can change the results substantially, and researchers should document their decisions carefully.

Standardization is the default preprocessing for PCA when variables are measured on different scales. The `StandardScaler` in scikit-learn centers each variable to zero mean and unit variance. This transformation ensures that each variable contributes equally to the analysis regardless of its original measurement units.

For biological data where variables are already on comparable scales, such as gene expression values that have been normalized, standardization may still be appropriate. The decision depends on whether the researcher wants variables with larger variance to have more influence on the principal components.

Log transformation is often applied to biological data before standardization. Many biological measurements, such as gene expression counts and metabolite concentrations, follow approximately log-normal distributions. Log transformation makes the data more symmetric and reduces the influence of extreme values.

### Implementing PCA with scikit-learn

The implementation of PCA in scikit-learn follows a consistent pattern. First, the data is loaded into a pandas DataFrame with samples as rows and variables as columns. Second, the data is preprocessed using the appropriate scaler. Third, the PCA model is fitted to the scaled data. Fourth, the results are examined and visualized.

The following code structure demonstrates the implementation:

```python
import pandas as pd
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
import matplotlib.pyplot as plt

## Load data
data = pd.read_csv('biological_data.csv', index_col=0)

## Standardize the data
scaler = StandardScaler()
scaled_data = scaler.fit_transform(data)

## Fit PCA
pca = PCA()
scores = pca.fit_transform(scaled_data)

## Examine explained variance
explained_variance = pca.explained_variance_ratio_
```

The `fit_transform` method fits the PCA model to the data and returns the scores in a single step. The `explained_variance_ratio_` attribute contains the proportion of variance explained by each component.

### Choosing the Number of Components

The number of principal components to retain is a critical decision that affects both the interpretation and the downstream analysis. Several criteria are commonly used.

The Kaiser criterion suggests retaining components with eigenvalues greater than one. This criterion is based on the idea that a component should explain at least as much variance as a single standardized variable. The criterion is simple but can be conservative or liberal depending on the number of variables.

The scree plot is a graphical method that plots the eigenvalues against the component number. The researcher looks for an elbow where the eigenvalues level off. Components before the elbow are retained, and components after the elbow are considered to capture noise.

The cumulative explained variance criterion retains enough components to explain a target proportion of the total variance. A common target is 80 percent, but the appropriate threshold depends on the research question and the downstream analysis requirements.

The parallel analysis method compares the eigenvalues from the actual data with eigenvalues from random data with the same dimensions. Components with eigenvalues greater than the random data eigenvalues are retained. This method is more rigorous but requires additional computation.

## At a Glance

| Step | Action | Key Decision | Common Error |
|------|--------|--------------|--------------|
| Data import | Load data into pandas DataFrame | Confirm samples are rows and variables are columns | Transposing the data matrix |
| Preprocessing | Standardize variables with StandardScaler | Decide whether to log transform first | Skipping standardization when variables have different scales |
| PCA fitting | Use sklearn.decomposition.PCA | Choose the number of components | Using raw data without scaling |
| Component selection | Examine explained variance and scree plot | Set a cumulative variance threshold | Retaining too many or too few components |
| Interpretation | Plot scores and loadings | Identify clusters and influential variables | Overinterpreting patterns that are not statistically supported |

## Data Inputs and Format Requirements

### Acceptable Data Types

PCA accepts continuous numerical data. The data matrix must be complete, meaning that every sample must have a value for every variable. The data can be stored in a CSV file, an Excel spreadsheet, or a pandas DataFrame.

For gene expression data, the typical format is a matrix where rows are genes and columns are samples. This format requires transposition before PCA because PCA expects samples as rows and variables as columns. The `pandas.DataFrame.transpose` method or the `T` attribute can be used for this transformation.

For metabolomics data, the format is similar with rows representing metabolites and columns representing samples. The data may require normalization before PCA to account for differences in sample concentration or instrument sensitivity.

### Handling Categorical Variables

PCA is designed for continuous variables. Categorical variables such as treatment group, sex, or genotype cannot be included directly in the PCA computation. These variables can be used to color or label the samples in the PCA plot after the analysis is complete.

If a categorical variable must be included in the analysis, it must be encoded as dummy variables. However, this approach is generally not recommended because the dummy variables can dominate the principal components and obscure the continuous variable patterns.

### Data Quality Checks

Before running PCA, the data should be checked for quality issues. The first check is for missing values. The second check is for constant variables that have zero variance. Constant variables do not contribute to the analysis and should be removed.

The third check is for highly correlated variables. While PCA handles correlated variables well, extreme correlation can cause numerical instability. The fourth check is for outliers, which can have a disproportionate influence on the principal components.

## Interpreting PCA Results

### Explained Variance and Scree Plots

The explained variance ratio is the primary output for determining how many components to retain. The first component always explains the most variance, and each subsequent component explains less. The cumulative explained variance is the sum of the explained variance ratios up to a given component.

A scree plot is a line plot of the explained variance ratio against the component number. The plot typically shows a steep decline followed by a leveling off. The point where the decline levels off is the elbow, and components before the elbow are considered meaningful.

The explained variance ratio should be reported in the methods section of any publication. The cumulative explained variance for the retained components should also be reported so that readers can assess how much of the original variance is preserved.

### Score Plots and Sample Patterns

The score plot is a scatter plot of the sample scores on two principal components. The plot shows the relationships between samples. Samples that are close together in the plot have similar variable values, and samples that are far apart are different.

The score plot is used to identify clusters of samples that may correspond to biological groups. The clusters can be colored by a categorical variable such as treatment group or genotype to visualize whether the groups separate in the principal component space.

The score plot can also reveal outliers. Samples that are far from the main cluster may be technical outliers or biologically distinct samples. These samples should be investigated before the analysis is finalized.

### Loading Plots and Variable Contributions

The loading plot shows the contribution of each original variable to the principal components. The loading values can be plotted as a bar chart or as a scatter plot with the loadings on the first two components.

Variables with large absolute loading values on a component are the variables that drive the separation of samples along that component. These variables are the most important for interpreting the biological meaning of the component.

The loading plot can be used to identify groups of variables that contribute to the same component. These variables may be functionally related, such as genes in the same pathway or metabolites in the same biochemical pathway.

## Visualization Techniques for PCA

### Score Scatter Plots

The most common PCA visualization is the score scatter plot. The plot shows the first principal component on the x-axis and the second principal component on the y-axis. Each point represents a sample, and the points can be colored by a categorical variable.

The plot should include axis labels that indicate the component number and the percentage of variance explained. The plot should also include a legend when samples are colored by a categorical variable.

The score plot can be extended to three dimensions by plotting the first three principal components. This visualization can reveal patterns that are not visible in two dimensions, but it is harder to interpret.

### Biplots

A biplot combines the score plot and the loading plot in a single figure. The scores are plotted as points, and the loadings are plotted as arrows. The arrows indicate the direction of the variables in the principal component space.

The biplot is useful for interpreting the relationship between samples and variables. Samples that are in the direction of an arrow have high values for that variable. The length of the arrow indicates the strength of the variable's contribution to the components.

The biplot can become cluttered when there are many variables. In this case, only the variables with the largest loadings should be plotted.

### Explained Variance Bar Plots

The explained variance bar plot shows the explained variance ratio for each component as a bar. The plot is useful for visualizing the relative importance of each component. The plot can be combined with the cumulative explained variance line.

The bar plot is a simple and effective way to communicate the variance structure of the data. The plot should be included in the methods section of a publication to justify the number of components retained.

## Common Failure Patterns in PCA Implementation

### Failure to Standardize Data

The most common error in PCA implementation is the failure to standardize the data. When variables are measured on different scales, the variables with larger numerical values dominate the principal components. This can lead to components that reflect the measurement scale instead of the biological variation.

The solution is to always standardize the data before PCA unless there is a specific reason not to. The standardization should be documented in the methods section.

### Using Raw Count Data Without Transformation

Biological count data such as gene expression counts are often highly skewed. The PCA of raw count data can be dominated by a few highly expressed genes. The log transformation is often applied to count data before PCA to reduce the influence of the extreme values.

The choice of transformation should be based on the data distribution. The transformation should be documented in the methods section.

### Overinterpreting the Components

The principal components are mathematical constructs that maximize variance. They do not necessarily correspond to biological processes. The interpretation of the components should be based on the loadings and the biological context.

The components should not be interpreted as causal factors. The PCA does not establish a causal relationship between the variables and the biological outcome.

### Ignoring Outliers

Outliers can have a disproportionate influence on the principal components. The outliers should be identified and investigated before the final analysis. The outliers may be technical errors that should be removed, or they may be biologically distinct samples that should be analyzed separately.

The decision to remove outliers should be documented in the methods section.

## Records and Measurements for Reproducibility

### Documenting the Analysis Workflow

The reproducibility of the PCA analysis requires documentation of the entire workflow. The documentation should include the data source, the preprocessing steps, the PCA parameters, and the visualization choices.

The documentation should be stored with the data and the code. The documentation should be written in a way that another researcher can follow the analysis.

### Version Control for Code and Data

The code and the data should be under version control. The version control system tracks changes to the code and the data over time. The version control system allows the researcher to reproduce the analysis at any point in time.

The version control system should be used for the analysis code and the data files. The version control system should be documented in the methods section.

### Data Management and Sharing

The data management and sharing policy of the National Institutes of Health requires that the data be shared in a way that is consistent with the scientific integrity. The data should be shared in a public repository that is appropriate for the data type. The data should be shared in a format that is accessible to other researchers.

The data sharing should be planned at the beginning of the research project. The data management plan should describe the data, the sharing, and the preservation. The data management plan should be updated as the research progresses.

## Quality Controls and Validation

### Cross-Validation of the PCA Model

The PCA model is an unsupervised model, so the cross-validation is not used in the same way as in supervised learning. However, the stability of the PCA can be assessed by running the analysis on a subset of the data and comparing the results.

The stability of the loadings can be assessed by running the PCA on a bootstrap sample of the data. The loadings from the bootstrap samples can be compared to the loadings from the full data. The stable loadings are the ones that are consistent across the bootstrap samples.

### Checking the Assumptions of PCA

PCA has several assumptions that should be checked before the analysis. The first assumption is that the data is linear. The second assumption is that the data is continuous. The third assumption is that the data is complete.

The linearity assumption can be checked by examining the relationship between the variables. The linearity assumption is violated when the relationship between the variables is nonlinear. The nonlinearity can be addressed by using a nonlinear dimensionality reduction method.

### The Influence of Outliers

The outliers can be identified by the score plot. The outliers can be identified by the distance from the center of the data. The outliers can be identified by the leverage of the sample.

The influence of the outliers can be assessed by running the PCA with and without the outliers. The results are compared to determine the influence of the outliers. The outliers should be removed if they have a large influence on the results.

## Limitations of PCA in Biological Research

### Linearity Assumption

PCA is a linear method. The principal components are linear combinations of the original variables. The linearity assumption is violated when the biological relationship between the variables is nonlinear.

The nonlinearity can be addressed by using a nonlinear dimensionality reduction method such as t-SNE or UMAP. The nonlinear methods can capture the nonlinear relationships, but they are more difficult to interpret.

### Sensitivity to Scaling

The PCA is sensitive to the scaling of the variables. The standardization of the variables is a critical step. The choice of the scaling method can change the results.

The scaling method should be chosen based on the data. The scaling method should be documented in the analysis.

### The Interpretation of the Components

The principal components are mathematical constructs. The components do not have a biological meaning unless the researcher interprets them. The interpretation of the components is based on the loadings and the biological context.

The interpretation of the components is subjective. The interpretation should be based on the data and the biological knowledge. The interpretation should be documented in the analysis.

### The Number of Components

The number of components to retain is a decision that affects the downstream analysis. The decision is based on the explained variance and the research question. The decision should be documented in the analysis.

The number of components can be too small, which loses important information. The number of components can be too large, which includes noise. The number of components should be chosen to balance the information and the noise.

## Professional Escalation Criteria

### When to Seek Statistical Consultation

The PCA analysis should be escalated to a statistician when the data is complex or when the interpretation is uncertain. The statistician can provide guidance on the preprocessing, the number of components, and the interpretation.

The statistician should be consulted when the data has a complex structure, such as a hierarchical or longitudinal structure. The statistician should be consulted when the data has a large number of variables relative to the number of samples.

### When to Use Alternative Methods

The PCA should be replaced with an alternative method when the data is nonlinear. The alternative methods include t-SNE, UMAP, and kernel PCA. The alternative methods should be used when the PCA does not reveal the biological patterns.

The PCA should be replaced with a supervised method when the research question is about the prediction of an outcome. The supervised methods include partial least squares and linear discriminant analysis.

### When to Report the Results

The PCA results should be reported in the methods section of a publication. The results should be reported with the explained variance, the loadings, and the scores. The results should be reported in a way that allows the reader to reproduce the analysis.

The PCA results should be reported in the results section of a publication. The results should be reported with the score plot and the loading plot. The results should be reported with the interpretation of the components.

## Decision Framework for Component Retention in Biological PCA

Selecting the number of principal components to retain is the most consequential decision in the PCA workflow, yet it is often made without a structured evaluation of the downstream consequences. A practical decision framework helps you move beyond a single threshold and align component retention with the specific biological question, the sample size, and the intended use of the reduced data.

### Define the Analytical Purpose Before Selecting Components

The number of components you retain should depend on what you plan to do with them. Three common purposes require different retention strategies.

For data visualization, you typically need only the first two or three components. The goal is to project samples into a space that can be plotted and inspected for clusters, gradients, or outliers. Retaining additional components does not improve the visualization and can distract from the dominant patterns.

For downstream statistical modeling, such as regression, clustering, or classification, you need to balance information preservation against noise reduction. Retaining too few components discards biologically relevant variation, while retaining too many introduces noise that can degrade model performance. The optimal number depends on the signal-to-noise ratio in your data and the sample size.

For biological interpretation, you need to examine the loadings on each component and determine whether they correspond to coherent biological processes. Components that load heavily on known functional groups, such as genes in the same pathway or metabolites in the same biochemical route, are more likely to represent real biological signal. Components that load on a single sample or a small group of unrelated variables are more likely to represent technical artifacts.

### Use Multiple Criteria and Compare Their Agreement

No single criterion is universally reliable for biological data. The Kaiser criterion, the scree plot, and the cumulative explained variance threshold each have known limitations, and they often disagree. A practical approach is to compute several criteria and examine where they converge.

The Kaiser criterion retains components with eigenvalues greater than one. This criterion is based on the variance of a single standardized variable, so it is appropriate when you have standardized the data. However, it tends to retain too many components when the number of variables is large relative to the number of samples, a common situation in genomics and metabolomics.

The scree plot identifies the elbow where the explained variance levels off. This method is subjective because the elbow is not always clear, and different observers may identify different points. The elbow is more reliable when the sample size is large and the variance structure is distinct.

The cumulative explained variance criterion retains enough components to reach a target proportion, commonly 80 percent. This criterion is straightforward but can be misleading when the data has many variables with small individual contributions. In such cases, reaching 80 percent may require retaining dozens of components that each explain less than one percent of the variance.

Parallel analysis compares the eigenvalues from the actual data with eigenvalues from random data of the same dimensions. Components with eigenvalues greater than the 95th percentile of the random eigenvalues are retained. This method is more rigorous than the other criteria because it accounts for the expected distribution of eigenvalues under the null hypothesis of no structure. The method requires generating random data, which is straightforward in Python using `numpy.random`.

A practical workflow is to compute all four criteria and record the results in a table. If the criteria agree, the decision is straightforward. If they disagree, the disagreement itself is informative and should be investigated. The disagreement often indicates that the data has a weak or ambiguous structure, and the decision should be guided by the research question instead of by a single number.

### Account for the Sample Size and Variable Count

The ratio of samples to variables has a strong influence on the reliability of PCA results. When the number of variables exceeds the number of samples, the covariance matrix is singular and the eigenvalues are not uniquely determined. The PCA implementation in scikit-learn uses singular value decomposition, which handles this situation numerically, but the results are less stable.

For biological data with many variables and few samples, the loadings are less reliable and the components are more likely to reflect noise. A practical rule is to examine the stability of the loadings by running the PCA on bootstrap samples of the data. The bootstrap procedure resamples the samples with replacement, fits the PCA on each resampled dataset, and records the loadings. Variables with stable loadings across the bootstrap samples are more likely to represent real signal.

The bootstrap procedure is computationally feasible for datasets with hundreds of samples and thousands of variables. The procedure can be implemented with a loop in Python, and the results can be summarized as the standard deviation of each loading across the bootstrap samples. The loadings with small standard deviations are the stable ones.

### Record the Decision and the Justification

The component retention decision should be recorded in the analysis documentation. The record should include the criteria that were computed, the values for each criterion, and the final decision. The record should also include the justification for the decision, which should reference the research question and the downstream analysis.

The record should be stored with the code and the data. The record should be written in a way that another researcher can follow the decision process. The record should be included in the methods section of any publication that reports the PCA results.

### Common Failure Patterns in Component Selection

The most common failure pattern is retaining too many components. This pattern occurs when the researcher uses the cumulative explained variance criterion with a high threshold, such as 95 percent, on a dataset with many variables. The result is a large number of components that each explain a small amount of variance and that are difficult to interpret.

The second common failure pattern is retaining too few components. This pattern occurs when the researcher uses the Kaiser criterion on a dataset with few variables. The result is a small number of components that may not capture the full biological variation.

The third common failure pattern is ignoring the stability of the components. The components are computed from a single dataset, and the loadings may change substantially if the dataset is slightly modified. The stability should be assessed with bootstrap or a similar procedure before the components are interpreted.

### Professional Escalation Criteria for Component Selection

The component selection decision should be escalated to a statistician when the criteria disagree substantially and the research question depends on the number of components. The statistician can provide guidance on the appropriate method for the data structure and the research question.

The decision should also be escalated when the data has a complex structure, such as a hierarchical or longitudinal design. The standard PCA does not account for the structure, and the component selection may be affected by the structure. The statistician can recommend a method that accounts for the structure.

The decision should be escalated when the number of variables is much larger than the number of samples. The PCA results are less reliable in this situation, and the statistician can recommend a regularized or sparse method.

### A Structured Decision Workflow

The following workflow provides a practical structure for the component selection decision.

First, compute the explained variance ratio for all components and record the values. Second, compute the Kaiser criterion by counting the components with eigenvalues greater than one. Third, generate the scree plot and record the elbow location. Fourth, compute the cumulative explained variance for the 80 percent threshold and record the number of components. Fifth, run the parallel analysis and record the number of components that exceed the random data eigenvalues. Sixth, compare the four criteria and record the agreement or disagreement. Seventh, examine the loadings on the candidate components and assess the biological coherence. Eighth, make the decision based on the research question and the downstream analysis. Ninth, record the decision and the justification in the analysis documentation.

This workflow is practical because it does not require specialized software and can be implemented with the standard Python libraries. The workflow is also transparent because the decision is based on a record of the criteria and the justification.

## Records and Measurements for Component Selection

The component selection decision should be recorded in a table that includes the criterion, the value, and the decision. The table should be stored with the analysis code and the data. The table should be included in the methods section of a publication.

The record should also include the stability assessment. The stability assessment should include the bootstrap results and the standard deviations of the loadings. The record should include the number of bootstrap samples and the random seed used for the bootstrap.

The record should include the version of the Python libraries that were used for the analysis. The version information is important for reproducibility because the PCA implementation can change between versions.

The record should include the data preprocessing steps that were applied before the PCA. The preprocessing steps include the standardization, the transformation, and the handling of missing values. The preprocessing steps should be recorded in the order that they were applied.

## Quality Controls for Component Selection

The component selection should be validated by examining the stability of the results. The stability can be assessed by running the PCA on a subset of the data and comparing the results to the full data. The subset can be a random sample of the samples or a random sample of the variables.

The stability can also be assessed by running the PCA with different preprocessing choices. The preprocessing choices include the standardization method, the transformation, and the handling of outliers. The results are compared to determine the influence of the preprocessing choices.

The component selection should be validated by examining the biological coherence of the components. The loadings on each component should be examined for the biological relationship. The components that load on unrelated variables should be examined for the technical artifacts.

## Professional Escalation Criteria for the Selection

The component selection should be escalated to a statistician when the criteria disagree and the research question depends on the exact number of components. The statistician can provide guidance on the appropriate method for the data.

The component selection should be escalated when the data has a complex structure. The complex structure includes the hierarchical, the longitudinal, and the repeated measures. The standard PCA does not account for the structure, and the component selection may be biased.

The component selection should be escalated when the number of variables is much larger than the number of samples. The PCA is less reliable in this situation, and the statistician can recommend a regularized approach.

The component selection should be escalated when the interpretation of the components is uncertain. The statistician can provide guidance on the interpretation and the validation of the components.

## Frequently Asked Questions

### What is the difference between PCA and factor analysis?

PCA and factor analysis are both dimensionality reduction methods, but they have different goals. PCA aims to explain the total variance in the data, while factor analysis aims to explain the covariance between the variables. PCA is a data transformation method, while factor analysis is a latent variable model.

### How do I choose the number of principal components?

The number of components is chosen based on the explained variance, the scree plot, and the research question. The cumulative explained variance is a common criterion, with a threshold of 80 percent being a common choice. The scree plot is a visual criterion that looks for an elbow point.

### What is the difference between loadings and scores?

The loadings are the coefficients that define the principal components as linear combinations of the original variables. The scores are the coordinates of the samples in the principal component space. The loadings are used to interpret the variables, and the scores are used to interpret the samples.

### Can I use PCA on data with missing values?

PCA cannot be used on data with missing values. The missing values must be handled before the analysis. The missing values can be imputed, or the samples or variables with missing values can be removed. The imputation method should be documented.

### How do I interpret the PCA plot?

The PCA plot is a scatter plot of the scores on two principal components. The samples that are close together are similar, and the samples that are far apart are different. The plot can be colored by a categorical variable to visualize the biological groups.

### What is the difference between PCA and t-SNE?

PCA is a linear method that preserves the global structure of the data. The t-SNE is a nonlinear method that preserves the local structure of the data. The PCA is faster and more interpretable, while the t-SNE is better at capturing the nonlinear relationships.

### How do I report the PCA results in a publication?

The PCA results should be reported in the methods section with the preprocessing, the number of components, and the explained variance. The results should be reported in the results section with the score plot and the loading plot. The interpretation of the components should be reported.

### What is the role of the standardization in PCA?

The standardization is the process of centering the data to zero mean and unit variance. The standardization is required when the variables are measured on different scales. The standardization ensures that each variable contributes equally to the analysis.

## Using the Evidence

| Source | Best use in this topic | Important limitation |
|---|---|---|
| [Research Methods Resources](https://www.ncbi.nlm.nih.gov/books) | official guidance | Check the linked page for current local requirements |
| [EQUATOR Network](https://www.equator-network.org/) | official guidance | Check the linked page for current local requirements |
| [Core Practices](https://publicationethics.org/core-practices) | official guidance | Check the linked page for current local requirements |

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- [Proteomics Data Analysis Workflow: From Raw Spectra to Biological Insights](/knowledge/bioinformatics/proteomics-data-analysis-workflow-from-raw-spectra-to-biological-insights)
- [Spatial Omics Data Analysis: From Image Processing to Biological Interpretation](/knowledge/bioinformatics/spatial-omics-data-analysis-from-image-processing-to-biological-interpretation)
- [Gene Set Enrichment Analysis in R: A Practical Tutorial for Interpreting Omics Data](/knowledge/bioinformatics/gene-set-enrichment-analysis-in-r-a-practical-tutorial-for-interpreting-omics-data)

## Related Clinical & Scientific Guides

* [A Practical Guide to Detecting Antimicrobial Resistance Genes in Shotgun Metagenomic Data](/knowledge/bioinformatics/a-practical-guide-to-detecting-antimicrobial-resistance-genes-in-shotgun-metagenomic-data)
* [Computational Immunology: Modeling the Immune System](/knowledge/bioinformatics/computational-immunology-modeling-the-immune-system)
* [How to Set Hard Filters for Germline Variant Calling: A Practical Guide to GATK Best Practices](/knowledge/bioinformatics/how-to-set-hard-filters-for-germline-variant-calling-a-practical-guide-to-gatk-best-practices)


## References and Further Reading

- [Research Methods Resources](https://www.ncbi.nlm.nih.gov/books). National Library of Medicine.
- [EQUATOR Network](https://www.equator-network.org/). EQUATOR Network.
- [Core Practices](https://publicationethics.org/core-practices). Committee on Publication Ethics.
- [NIH Grants and Funding](https://grants.nih.gov/). National Institutes of Health.
- [ORCID for Researchers](https://info.orcid.org/researchers). ORCID.
- [Data Management and Sharing Policy](https://sharing.nih.gov/data-management-and-sharing-policy). National Institutes of Health.
- [NCBI Data Resources](https://www.ncbi.nlm.nih.gov/). National Center for Biotechnology Information.
- [EMBL-EBI Training](https://www.ebi.ac.uk/training). European Bioinformatics Institute.
- [Combining Serum PVT1 Exon 4A and Exon 9 with Serum Prostate-Specific Antigen Shows Potential for Improving Identification and Risk Stratification of Prostate Cancer.](https://doi.org/10.2147/cmar.s604901). 2026.
- [Validity of the PAWPER XL-MAC Scale in Turkish Children: A Prospective Validation Study](https://doi.org/10.21203/rs.3.rs-9923787/v1). 2026.
- [Demystifying machine learning approaches in digital bone imaging using microCT and HRpQCT.](https://doi.org/10.1016/j.bonr.2026.101911). 2026.

> This article is educational and does not replace validated analysis plans, institutional policy, clinical interpretation, or specialist review.