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PCA (Principal Component Analysis) is one of the top algorithms used for dimensionality reduction. It has applications in data science, data-driven decision-making labs, or even in biology and chemistry and even in economics! But as helpful as PCA is, so many people struggle using it because they get stuck making basic errors that can lead to highly inaccurate conclusions.
As of now, this this article aims to help you get the results you want by discussing some of the most notable blunders along with easy fixes when attempting to perform PCA.
This is one of the most often encountered issues. Skipping the process of either the standardization or normalization of prior data is the most common error related to PCA. PCA has to be performed taking into consideration the scale of variables, because ignoring to do so, will lead to features with larger scales dominating over the principal components even if they are irrelevant.
Also read:Principal Component Analysis (PCA): A Complete Overview
Determining how many principal components to retain after performing PCA can be tricky. Keeping too many components can clutter your results, and keeping too little can result in the loss of key information.
Employ a scree plot or explained variance ratio graph to identify the optimal number of components. The elbow method on a scree plot can be useful for identifying where the explained variance levels off, indicating where components can potentially be cut off without loss of useful information.
Strive to achieve a minimum of 80-90% variance covered with the components kept.
Confusion regarding loadings can lead to flawed conclusions. Some users might be confused about magnitudes of loadings, thinking it reflects importance of the variables when, in fact, it has no bearing on the calculation of loadings.
Concentrate on the shape of the principal components which indicate which variables are most highly associated with each component. Vertices with comparatively higher values of loadings portray amplified influence of that variable on the component.
Keep in mind that direction and signs of loadings are important—similar components with the same/loading sign add together while opposite sign means opposing each other in that component.
PCA checks for the existence of a linear correlation of a data set with its characteristics having a Gaussian distribution. Skewed data that has a significant non-linear relationship is problematic for the results.
For non-linear data, consider applying Kernel PCA or t-SNE that are known to accommodate non-linear relationships.
Make certain that data distribution is closely resembling Gaussian. If not, use log transformation or several techniques such as Independent Component Analysis (ICA).
PCA is not always the method of choice for every dataset that is available. It is believed that the primary and most relevant information will always be along the axes of the highest variance which is not the case in datasets with more intricate patterns.
Analyze your data before applying PCA. In case you think some of the more important relationships are likely to be non-linear or interact in complicated ways, use other dimensionality reduction methods such as t-SNE or auto encoders.
The principal components in PCA are impacted strongly by outliers, which may provide skewed results. This can cause the output to be intricately disfigured if no prior measures are taken.
Outlier detection and handling must precede application of PCA. Outliers can be removed or alternatively, PCA can be made robust to outliers and masked to some degree using robust PCA.
Have recovery measures in place because outliers could heavily skew results, more so with smaller datasets.
Your data should not contain missing values or incorrect data types because it significantly hampers the effectiveness of PCA. Misleading or incomplete results can occur when data is not cleaned before applying PCS.
All variables need to be numerical, a value is expected for each record, and the data type should be consistent.
Make sure categorical variables are either excluded or properly encoded prior to performing PCA.
PCA is a great method to reducing dimensionality and revealing underlying patterns in data sets, but as any statistician technique, claiming its perks come with risks if one is not careful. Moreover, this statement could be overshot with caution, optimal number of components plugged in, precise assumptions made, and data prepossessed meticulously as discussed throughout this paper.
