Papers › Hybrid Orthogonal Projection and Estimation (HOPE): A New Framework to Probe and Learn...

Hybrid Orthogonal Projection and Estimation (HOPE): A New Framework to Probe and Learn Neural Networks

3 Feb 2015arXiv:1502.00702archive 2025-07-28

Shiliang Zhang, Hui Jiang

In this paper, we propose a novel model for high-dimensional data, called the Hybrid Orthogonal Projection and Estimation (HOPE) model, which combines a linear orthogonal projection and a finite mixture model under a unified generative modeling framework. The HOPE model itself can be learned unsupervised from unlabelled data based on the maximum likelihood estimation as well as discriminatively from labelled data. More interestingly, we have shown the proposed HOPE models are closely related to neural networks (NNs) in a sense that each hidden layer can be reformulated as a HOPE model. As a result, the HOPE framework can be used as a novel tool to probe why and how NNs work, more importantly, to learn NNs in either supervised or unsupervised ways. In this work, we have investigated the HOPE framework to learn NNs for several standard tasks, including image recognition on MNIST and speech recognition on TIMIT. Experimental results have shown that the HOPE framework yields significant performance gains over the current state-of-the-art methods in various types of NN learning problems, including unsupervised feature learning, supervised or semi-supervised learning.

PaperPDF

Code

No code repository is listed for this paper in the archive or in Syntology's graph.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Tasks

Image ClassificationSpeech Recognitionspeech-recognition

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Image Classification MNIST HOPE Percentage error 0.4 #27 of 81 Archive leaderboard report

Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections