An important thing to realize here is that the principal components are less interpretable and don’t have any real meaning since they are constructed as linear combinations of the initial variables.Geometrically speaking, principal components represent the directions of the data that explain a maximal...
We noted the meaning of the axes of variation whenever apparent (red). The right column had the same axes of variations as the middle one. Full size image Some authors consider higher PCs informative and advise considering these PCs alongside the first two. In our case, however, these PCs ...
Even if each low-level feature may not convey a meaningful description by itself, combining lots of them with lots of data makes it possible to derive meaningful meaning using machine learning models. PCA is one method to achieve this goal. 2.2 Linear projection and dot product The main idea...
PCA presents limitations when it comes to interpretability. Since we’re transforming the data, features lose their original meaning. This could be problematic in cases where interpretability of the data is important. However, in the feature selection example we mentioned earlier, there are cases whe...
The sign of the variables in the matrix tells us whether combinations are correlated: Positive (the variables are correlated and increase or decrease at the same time) Negative (the variables are not correlated, meaning that one decreases while the other increases) ...
without changing the meaning. Because '1' and '0' are only an abstract representation of two categories, they cannot be taken interpreted as numerical data. Furthermore, the measurement error of binary data is discrete in nature. Binary measurement error occurs when a category is assigned to th...
and after the first components the seed principal components converge to zero. We can use this to our advantage (in the future), because we have reduced the dimensionality of the problem to ~3 as opposed to 7. Meaning, we found there are only 3 (useful) principal components to the seeds...
Statistics and Machine Learning Toolbox Copy CodeCopy Command Find the principal components for one data set and apply the PCA to another data set. This procedure is useful when you have a training data set and a test data set for a machine learning model. For example, you can preprocess ...
There has been no mathematically precise meaning for the term "out- lier" [24]. Thus multiple methods have been attempted to define or quantify this term, such as alternating minimiza- tion [14], random sampling techniques [9, 17], multivariate trimming [11], and...
In scRNA-seq, dropout occurs randomly, meaning any transcript has an equal chance of being missed. Although dropout is more likely with lower gene expression, even highly expressed genes might not be detected in all cells. We expect that the remaining gene expression data will still have enough...