多光谱神经网络：深度学习的谱方法

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本文主要探讨了"Learning Deep and Wide: A Spectral Method for Learning Deep Networks"这一主题，它关注的是如何在深度学习领域中有效利用多光谱神经网络（MSNN）来提升模型性能。作者Ling Shao、Di Wu和Xuelong Li三位专家提出了一个多列深度神经网络（Multi-column Deep Neural Networks, MDNNs）的学习框架，其核心是通过谱方法（Spectral Method）来整合和优化不同深度层的特征表示。在当前的计算机视觉任务中，构建能够从高维传感器数据中提取高级别特征的智能系统至关重要。MSNN的设计目标在于解决深度网络中的学习瓶颈，特别是当训练数据有限时，如何提高模型的泛化能力和鲁棒性。通过在倒数第二层（即penultimate hierarchical discriminative manifolds）嵌入低维度表示，MSNN巧妙地利用了不同深度层的互补性。每个视图（column）的数据分布被假设是平滑的，这有助于在较少标记数据的情况下增强模型的稳健性。该论文的关键贡献包括： 1. **多光谱神经网络**：设计了一种结构，允许深度网络的不同列（spectra）协同工作，以捕捉输入数据的不同角度和特征组合，从而提供更丰富的表示。 2. **谱方法应用**：使用谱理论和矩阵分解技术，将复杂的多列网络映射到一个紧凑且低维度的表示空间，这样可以更好地控制和理解模型内部的复杂性。 3. **优化输出与泛化**：实验结果表明，通过谱嵌入，多列深度网络能够在探索最优输出方面超越单个深度网络，显著降低错误率，尤其是在训练数据稀缺的情况下。 4. **术语索引**：关键词包括深度网络、多光谱嵌入和表示学习，这些都是本文研究的核心概念和技术细节。总结来说，这篇论文提出了一种创新的方法，通过结合深度和宽度（深度网络的多列结构），利用谱方法有效地处理高维数据，从而在深度学习领域取得了重要的进步。这种方法对于提高计算机视觉任务中的性能，尤其是在数据稀缺的情况下，具有实际应用价值。

IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 25, NO. 12, DECEMBER 2014 2303

Learning Deep and Wide: A Spectral Method

for Learning Deep Networks

Ling Shao, Senior Member, IEEE, Di Wu, and Xuelong Li, Fellow, IEEE

Abstract—Building intelligent systems that are capable of extracting

high-level representations from high-dimensional sensory data lies at

the core of solving many computer vision-related tasks. We propose

the multispectral neural networks (MSNN) to learn features from

multicolumn deep neural networks and embed the penultimate hier-

archical discriminative manifolds into a compact representation. The

low-dimensional embedding explores the complementary property of

different views wherein the distribution of each view is sufﬁciently smooth

and hence achieves robustness, given few labeled training data. Our

experiments show that spectrally embedding several deep neural net-

works can explore the optimum output from the multicolumn networks

and consistently decrease the error rate compared with a single deep

network.

Index Terms—Deep networks, multispectral embedding,

representation learning.

I. I

NTRODUCTION

Recent publications suggest that unsupervised pretraining

of deep, hierarchical neural networks improves supervised

pattern classiﬁcation [1]–[4]. Learning machines that are able

to automatically build feature extractors instead of hand-crafting

them is a wide research area in pattern recognition. The main

beneﬁt of these models is their high generation since they can

automatically learn to extract salient patterns directly from the raw

input, without any use of prior knowledge. Recent advancement

and applications using learned features have yielded excellent

results in several tasks, e.g., object recognition and video sequence

classiﬁcation. Krizhevsky et al. [5] train a large, deep convolutional

neural network (CNN) to classify 1000 different classes;

Baccouche et al. [6] learn a sparse shift-invariant representation of

the local salient information using a spatio-temporal convolutional

Manuscript received July 21, 2013; accepted February 22, 2014. Date of

publication March 11, 2014; date of current version November 17, 2014.

This work was supported in part by the National Basic Research Program of

China (973 Program) under Grant 2012CB316400, in part by the University

of Shefﬁeld, in part by the China Scholarship Council, in part by the National

Natural Science Foundation of China under Grant 61125106, and in part by

the Shaanxi Key Innovation Team of Science and Technology under Grant

2012KCT-04.

L. Shao is with the College of Electronic and Information Engineer-

ing, Nanjing University of Information Science and Technology, Nanjing

210044, China, and also with the Department of Electronic and Electri-

cal Engineering, University of Shefﬁeld, Shefﬁeld S1 3JD, U.K. (e-mail:

ling.shao@shefﬁeld.ac.uk).

D. Wu is with the Department of Electronic and Electrical Engineering, Uni-

versity of Shefﬁeld, Shefﬁeld S1 3JD, U.K. (e-mail: stevenwudi@gmail.com).

X. Li is with the Center for Optical Imagery Analysis and Learning, State

Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics

and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China

(e-mail: xuelong_li@opt.ac.cn).

Color versions of one or more of the ﬁgures in this paper are available

online at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TNNLS.2014.2308519

sparse autoencoder, without any use of prior knowledge, and classify

each sequence by a long short-term memory recurrent neural

network [7]. Meanwhile, various architectures and techniques have

been proposed to enhance the learning capacity: a multiresolution

deep belief network (DBN) [8] combines a Laplacian pyramid

with deep learning to learn coarse structures from low-resolution

images, leading to a better generative model; multicolumn deep

neural networks proposed by Cire¸san et al. [9]–[11] use GPUs to

train several deep neural columns and average the output of each

individual network under the condition that given enough labeled

data, their networks do not need additional heuristics, such as

unsupervised pretraining or carefully prewired synapses.

Inspired by microcolumns of neurons in the cerebral cortex, several

deep neural columns are trained and become experts to unfold

their potential when they are wide. Conventional multicolumn deep

neural networks average the output of the prediction under the

condition that there are enough labeled training data and an individual

neural network is close to the global optimum. However, simple

output averaging may not achieve the model’s optimum if only few

labeled data are provided. As indicated in [9], several deep neural

columns are trained to become experts to unfold their potential

when they are wide. However, if the labeled training instances are

few, i.e., ﬁne-tuning information is scarce, the deep networks can

suffer from overﬁtting. Such a setting is pervasive in real-world

applications, such as the gender prediction (Section IV-C), where

the randomized, controlled experiments may be costly, unethical, and

intrusive.

In this brief, we show how combining several deep network

columns as a basic building block into the multicolumn deep nets and

embedding the spectral relationships can further enhance robustness

and hence decrease the error rate. We deﬁne the wide deep net

as the juxtaposition of multiple randomly initialized nonconvex

deep nets, and refer to our proposed architecture as multispectral

neural networks (MSNN). The multicolumn procedure can be easily

implemented in a parallelized, multithreaded fashion that requires no

signiﬁcant extra training time for MSNN. Our architecture does this

by combining several techniques in a novel way.

1) Through encouraging the neural networks to learn deep models

reusing intermediate features to extract more abstract repre-

sentations that are more correlated with the underlying causes

generating the data, we utilize the penultimate layer of the

hierarchy as our intermediate feature space in contrast to the

paradigm that outputs the top predictor layer (also known as

softmax output layer). Such nets can be DBNs or CNNs with

fully connected penultimate layers.

2) Our architecture renders the networks to learn wide horizontally

to explore the feature space admitting stochasticity of the deep

nets, rendering a mixture-of-experts style ﬁeld. Unlike the

conventional multicommittee systems that extract the trivial 1-

D winner-take-all regions, that is, the top part of the hierarchy

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