A restorable autoencoder as a method for dimensionality reduction

In this paper, we propose a restorable autoencoder model as a non-linear method for reducing dimensionality. While non-linear methods can reduce the dimensionality of data more effectively than linear methods, they are, in general, not able to restore the original data from the dimensionality-reduced result. This is because non-linear methods provide a non-linear relationship between the original data and their dimensionality-reduced result. With the advantages of both linear and non-linear methods, the proposed model not only maintains an effective dimensionality reduction but also provides an observation-wise linear relationship with which the original data can be restored from the dimensionality-reduced result. We assessed the effectiveness of the proposed model and compared it with the linear method of principal component analysis and the non-linear methods of typical autoencoders using MNIST and Fashion-MNIST data sets. We demonstrated that the proposed model was more effective than or comparable to the compared methods in terms of the loss function and the reconstruction of input images. We also showed that the lower-dimensional projection obtained by the proposed model produced better or comparable classification results than that by the compared methods.