Autoencoders for Efficient Data Representation: An Empirical Study of Nonlinear Dimensionality Reduction and Low-Rate Image Reconstruction

This study examines autoencoders as finite-dimensional nonlinear transforms for two signal-representation tasks: two-dimensional feature extraction from MNIST images and low-dimensional reconstruction of CIFAR-10 images. Two different autoencoders are used in the research, which respectively process the images in these two tasks, and convert the original input into a fixed-dimensional code for use. The first is a fully connected autoencoder, which converts each image in MNIST that has a total of 784 dimensions into a code with only two dimensions; the second is a convolutional autoencoder, which converts each image in CIFAR-10 with a size of 32×32×3 into a 128-dimensional code. Two sets of clear quantitative data in the initial results obtained. The first set is the accuracy rate of 5-nearest neighbor classification (5-NN): when the representation generated by the autoencoder is used for classification, the accuracy rate reaches 70.93%, while when the representation generated by the PCA method is used for classification, the accuracy rate is only 42.60%. The second set is the reconstruction effect indicators of CIFAR-10 images. The peak signal-to-noise ratio (PSNR) after reconstruction is 24.04dB, and the structural similarity (SSIM) is 0. 8084.To avoid overstating these preliminary observations, the study distinguishes latent dimensionality reduction from coded storage rate, defines all reconstruction measures, and specifies the repeated-run, uncertainty, convergence, and matched-rate baseline analyses required for a reproducible empirical validation. The work does not claim a numerical-solver stability theorem or a deployable image codec unless the prescribed quantization and rate–distortion experiments are completed.