space ) Mathematically, the joint representation is expressed as: xm = f(x1, . . . , xn) (1) Neural networks To construct a multimodal representation using neural networks each modality starts with several individual neural layers fol lowed by a hidden layer that projects the modalities into a joint space.The joint multimodal representation is then be passed through multiple hidden layers itself or used directly for prediction.(usually be trained end to end) advantages: neural network based joint rep resentations comes from their often superior performance and the ability to pre-train the representations in an unsu pervised manner. The performance gain is, however, depen dent on the amount of data available for training. disadvantages: model not being able to handle missing data naturally deep networks are often diffificult to train Probabilistic graphical models advantages: generative nature, which allows for an easy way to deal with missing data ( even if a whole modality is missing, the model has a natural way to cope) generate samples of one modality in the presence of the other one, or both modalities from the representation s the representation can be trained in an unsupervised manner enabling the use of unlabeled data disadvantages: the diffificulty of training them( high computational cost, and the need to use approximate variational training methods ) Sequential Representation(varying length sequences) 略 3.2 Coordinated Representations ( learn separate representations for each modality but coordinate them through a constraint ) While coordinated representation is as follows: f ( x 1 ) ∼ g ( x 2 ) (2) Similarity models( minimize the distance between modal ities in the coordinated space ) structured coordinated space( Structured coordinated spaces are commonly used in cross-modal hashing ) Hashing enforces certain constraints on the resulting multimodal space: 1) it has to be an N -dimensionalHamming space — a binary representation with controllable number of bits; 2) the same object from different modalities has to have a similar hash code; 3) the space has to be similarity-preserving. 4 T RANSLATION Given an entity in one modality the task is to generate the same entity in a different modality. 4.1 Example-based Retrieval-based models ( directly use the retrieved translation without modifying it ) Combination-based models ( rely on more complex rules to create translations based on a number of retrieved instances ) 4.2 Generative approaches Grammar-based models Encoder-decoder models Continuous generation models 5 A LIGNMENT 5.1 Explicit alignment Unsupervised Supervised 5.2 Implicit alignment Graphical models Neural networks
6 F USION 6.1 Model-agnostic approaches 6.2 Model-based approaches Multiple kernel learning (MKL) Graphical models Neural Networks 7 C O - LEARNING 7.1 Parallel data Co-training Transfer learning 7.2 Non-parallel data Transfer learning Conceptual grounding Zero shot learning 7.3 Hybrid data



