22、深度时空聚类模型研究与实验

深度时空聚类模型研究与实验

1. 模型学习与优化

在学习过程中,我们从输入数据 $V_i$ 的潜在特征 $E_i$ 出发,联合优化自动编码器的权重和聚类。具体操作是分别最小化均方误差和 Kullback - Leibler(KL)散度损失。

1.1 优化方法

采用带动量的随机梯度下降(SGD)方法来实现这一优化任务。SGD 引导自动编码器模型学习有效的潜在嵌入,以捕捉输入数据集的独特和代表性特征。

1.2 损失计算

  • 重建损失 :模型的重建损失通过均方误差计算,公式如下:
    [L_{rec} = \min\left(\frac{1}{T}\sum_{i = 1}^{T} \left\lVert V_i - \hat{V}_i \right\rVert_2^2\right)]
    其中,$V_i \in R^{lon\times lat\times n}$ 是输入数据,$\hat{V}_i \in R^{lon\times lat\times n}$ 是自动编码器模型的输出。
  • 聚类损失 :通过最小化聚类损失,在模型中迭代细化聚类中心和最终的聚类分配。使用 KL 散度来计算每个数据点到聚类的软分配 $q_{ij}$ 和目标分布 $p_{ij}$ 之间的聚类损失,公式为:
    [L_{clus} = \min(KL(P \parallel Q)) = \min\left(\frac{1}{T}\sum_{i = 1}^{T} \sum_{j = 1}^{k} p_{ij}\log\frac{p_{ij}}{q

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深度学习工具包 DeepLearningToolbox

深度学习工具包Deprecation notice.-----This toolbox is outdated and no longer maintained.There are much better tools available for deep learning than this toolbox, e.g. [Theano](http://deeplearning.net/software/theano/), [torch](http://torch.ch/) or [tensorflow](http://www.tensorflow.org/)I would suggest you use one of the tools mentioned above rather than use this toolbox.Best, Rasmus.DeepLearnToolbox================A Matlab toolbox for Deep Learning.Deep Learning is a new subfield of machine learning that focuses on learning deep hierarchical models of data.It is inspired by the human brain's apparent deep (layered, hierarchical) architecture.A good overview of the theory of Deep Learning theory is[Learning Deep Architectures for AI](http://www.iro.umontreal.ca/~bengioy/papers/ftml_book.pdf)For a more informal introduction, see the following videos by Geoffrey Hinton and Andrew Ng.* [The Next Generation of Neural Networks](http://www.youtube.com/watch?v=AyzOUbkUf3M) (Hinton, 2007)* [Recent Developments in Deep Learning](http://www.youtube.com/watch?v=VdIURAu1-aU) (Hinton, 2010)* [Unsupervised Feature Learning and Deep Learning](http://www.youtube.com/watch?v=ZmNOAtZIgIk) (Ng, 2011)If you use this toolbox in your research please cite [Prediction as a candidate for learning deep hierarchical models of data](http://www2.imm.dtu.dk/pubdb/views/publication_details.php?id=6284)```@MASTERSTHESIS\{IMM2012-06284, author = "R. B. Palm", title = "Prediction as a candidate for learning deep hierarchical models of data", year = "2012",}```Contact: rasmusbergpalm at gmail dot comDirectories included in the toolbox-----------------------------------`NN/` - A library for Feedforward Backpropagation Neural Networks`CNN/` - A library for Convolutional Neural Networks`DBN/` - A library for Deep Belief Networks`SAE/` - A library for Stacked Auto-Encoders`CAE/` - A library for Convolutional Auto-Encoders`util/` - Utility functions used by the libraries`data/` - Data used by the examples`tests/` - unit tests to verify toolbox is workingFor references on each library check REFS.mdSetup-----1. 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nn.output = 'softmax'; % use softmax outputopts.numepochs = 5; % Number of full sweeps through dataopts.batchsize = 1000; % Take a mean gradient step over this many samplesopts.plot = 1; % enable plottingnn = nntrain(nn, tx, ty, opts, vx, vy); % nntrain takes validation set as last two arguments (optionally)[er, bad] = nntest(nn, test_x, test_y);assert(er < 0.1, 'Too big error');```[![Bitdeli Badge](https://d2weczhvl823v0.cloudfront.net/rasmusbergpalm/deeplearntoolbox/trend.png)](https://bitdeli.com/free "Bitdeli Badge")

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