Is PCA reversible?

Big Data ML Enginee at BT. I will show how PCA transformation is not reversible (i.e. getting original data back from Principal component is not possible because some information is lost in the process of dimensionality reduction).

Can dimensionality reduction be reversed?

2 Answers. No, dimensionality reduction is not reversible in general. It loses information.

Does PCA create new variables?

PCA creates the new variables by transforming the original (mean-centered) observations (records) in a dataset to a new set of variables (dimensions) using the eigenvectors and eigenvalues calculated from a covariance matrix of your original variables.

How is reconstruction error calculated in PCA?

1. What I usually use as the measure of reconstruction error (in the context of PCA, but also other methods) is the coefficient of determination R2 and the Root Mean Squared Error (or normalised RMSE).
2. The R2 of the ith variable can be computed as:
3. R2i=1−∑nj=1(Xj,i−fj,i)2∑nj=1X2j,i.

What is PCA reconstruction?

PCA is one of the basic techniques for reducing data with multiple dimensions to some much smaller subset that nevertheless represents or condenses the information we have in a useful way. In a PCA approach, we transform the data in order to find the “best” set of underlying components.

How do you find the reconstruction error?

One way to calculate the reconstruction error from a given vector is to compute the euclidean distance between it and its representation. In K-means, each vector is represented by its nearest center.

Which of the following strategies can used for reducing the dimensionality of data?

The various methods used for dimensionality reduction include: Principal Component Analysis (PCA) Linear Discriminant Analysis (LDA) Generalized Discriminant Analysis (GDA)

How do you calculate reconstruction error?

What are two ways in which one can formulate PCA?

The λ ∈ C is called the Eigenvalue of A. The Principal Component Analysis(PCA) problem can be formulated in two ways: Maximum Variance Formulation and Minimum Error Formulation.