Co-occurrence Data is a common and important information source in many areas, such as the word co-occurrence in the sentences, friends co-occurrence in social networks and products co-occurrence in commercial transaction data, etc, which contains rich correlation and clustering information about the items. In this paper, we study co-occurrence data using a general energy-based probabilistic model, and we analyze three different categories of energy-based model, namely, the @math , @math and @math models, which are able to capture different levels of dependency in the co-occurrence data. We also discuss how several typical existing models are related to these three types of energy models, including the Fully Visible Boltzmann Machine (FVBM) ( @math ), Matrix Factorization ( @math ), Log-BiLinear (LBL) models ( @math ), and the Restricted Boltzmann Machine (RBM) model ( @math ). Then, we propose a Deep Embedding Model (DEM) (an @math model) from the energy model in a manner. Furthermore, motivated by the observation that the partition function in the energy model is intractable and the fact that the major objective of modeling the co-occurrence data is to predict using the conditional probability, we apply the method to learn DEM. In consequence, the developed model and its learning method naturally avoid the above difficulties and can be easily used to compute the conditional probability in prediction. Interestingly, our method is equivalent to learning a special structured deep neural network using back-propagation and a special sampling strategy, which makes it scalable on large-scale datasets. Finally, in the experiments, we show that the DEM can achieve comparable or better results than state-of-the-art methods on datasets across several application domains.
DEM is also closely related to the autoencoder @cite_12 models, which contains two components: encoder and decoder. The encoder maps the input data to hidden states, while the decoder reconstructs the input data from the hidden states. There are also some studies to connect denoising auto encoder to generative learning @cite_22 @cite_17 @cite_15 . Indeed, DEM could be also viewed as an special case of denoising autoencoder. In encoder phase, the input data is corrupted by randomly dropping one element, and is then fed into the encoder function to generate the hierarchical latent embedding vectors. Then, in the decoding phase, the missing items are reconstructed from latent vectors afterwards.
@cite_15 @cite_22 @cite_12 @cite_17
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Denoising auto-encoders (DAEs) have been successfully used to learn new representations for a wide range of machine learning tasks. During training, DAEs make many passes over the training dataset and reconstruct it from partial corruption generated from a pre-specified corrupting distribution. This process learns robust representation, though at the expense of requiring many training epochs, in which the data is explicitly corrupted. In this paper we present the marginalized Denoising Auto-encoder (mDAE), which (approximately) marginalizes out the corruption during training. Effectively, the mDAE takes into account infinitely many corrupted copies of the training data in every epoch, and therefore is able to match or outperform the DAE with much fewer training epochs. We analyze our proposed algorithm and show that it can be understood as a classic auto-encoder with a special form of regularization. In empirical evaluations we show that it attains 1-2 order-of-magnitude speedup in training time over other competing approaches. The problem of cross-modal retrieval, e.g., using a text query to search for images and vice-versa, is considered in this paper. A novel model involving correspondence autoencoder (Corr-AE) is proposed here for solving this problem. The model is constructed by correlating hidden representations of two uni-modal autoencoders. A novel optimal objective, which minimizes a linear combination of representation learning errors for each modality and correlation learning error between hidden representations of two modalities, is used to train the model as a whole. Minimization of correlation learning error forces the model to learn hidden representations with only common information in different modalities, while minimization of representation learning error makes hidden representations are good enough to reconstruct input of each modality. A parameter @math is used to balance the representation learning error and the correlation learning error. Based on two different multi-modal autoencoders, Corr-AE is extended to other two correspondence models, here we called Corr-Cross-AE and Corr-Full-AE. The proposed models are evaluated on three publicly available data sets from real scenes. We demonstrate that the three correspondence autoencoders perform significantly better than three canonical correlation analysis based models and two popular multi-modal deep models on cross-modal retrieval tasks. A novel variational autoencoder is developed to model images, as well as associated labels or captions. The Deep Generative Deconvolutional Network (DGDN) is used as a decoder of the latent image features, and a deep Convolutional Neural Network (CNN) is used as an image encoder; the CNN is used to approximate a distribution for the latent DGDN features code. The latent code is also linked to generative models for labels (Bayesian support vector machine) or captions (recurrent neural network). When predicting a label caption for a new image at test, averaging is performed across the distribution of latent codes; this is computationally efficient as a consequence of the learned CNN-based encoder. Since the framework is capable of modeling the image in the presence absence of associated labels captions, a new semi-supervised setting is manifested for CNN learning with images; the framework even allows unsupervised CNN learning, based on images alone. A novel variational autoencoder is developed to model images, as well as associated labels or captions. The Deep Generative Deconvolutional Network (DGDN) is used as a decoder of the latent image features, and a deep Convolutional Neural Network (CNN) is used as an image encoder; the CNN is used to approximate a distribution for the latent DGDN features code. The latent code is also linked to generative models for labels (Bayesian support vector machine) or captions (recurrent neural network). When predicting a label caption for a new image at test, averaging is performed across the distribution of latent codes; this is computationally efficient as a consequence of the learned CNN-based encoder. Since the framework is capable of modeling the image in the presence absence of associated labels captions, a new semi-supervised setting is manifested for CNN learning with images; the framework even allows unsupervised CNN learning, based on images alone.