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--- projects:current:start [2015/02/11 01:40] – hj
+++ projects:current:start [2015/02/11 01:51] (current) – hj
@@ Line 2: / Line 2: @@
-===== Current Projects =====
+===== Hybrid Orthogonal Projection & Estimation (HOPE) =====
-  - **Hybrid Orthogonal Projection & Estimation (HOPE)**
+{{:projects:current:one-nn-layer.png?0x220 |NN hidden layer}}{{ :projects:current:one-hope-layer.png?0x220| HOPE}}
+Each hidden layer in neural networks can be formulated as one HOPE model[1]
-{{:projects:current:one-nn-layer.png?0x200 |NN hidden layer}}{{ :projects:current:one-hope-layer.png?0x200| HOPE}}
-Each hidden layer in neural networks can be formulated as one HOPE model
 \\
+  * The HOPE model combines a linear orthogonal projection and a mixture model under a unied generative modelling framework;
+  * The HOPE model can be used as a novel tool to probe why and how NNs work;
+  * The HOPE model provides several new learning algorithms to learn NNs either supervisedly or unsupervisedly.
 \\
-In this paper, we propose a universal model for high-dimensional data, called the Hybrid
+**Reference:**
-Orthogonal Projection and Estimation (HOPE) model, which combines a linear orthogonal projection
+\\
-and a nite mixture model under a unied generative modelling framework. The HOPE
+[1] //Shiliang Zhang and Hui Jiang//, "Hybrid Orthogonal Projection and Estimation (HOPE): A New Framework to Probe and Learn Neural Networks," [[http://arxiv.org/abs/1502.00702|arXiv:1502.00702]].
-model itself can be learned unsupervisedly from un-labelled data based on the maximum likelihood
-estimation as well as trained discriminatively from labelled data. More interestingly, we
+**Software:**
-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
+The matlab codes to reproduce the MNIST results in [1] can be downloaded here.
-can be used as a novel tool to probe why and how NNs work, more importantly, it also
-provides several new learning algorithms to learn NNs either supervisedly or unsupervisedly. In
-this work, we have investigated the HOPE framework in learning NNs for several standard tasks,
-including image recognition on MNIST and speech recognition on TIMIT. Experimental results
-show that the HOPE framework yields signicant performance gains over the current stateof-
-the-art methods in various types of NN learning problems, including unsupervised feature
-learning, supervised or semi-supervised learning.