Similarity metrics are a core component of many information retrieval and machine learning systems. In this work we propose a method capable of learning a similarity metric from data equipped with a binary relation. By considering only the similarity constraints, and initially ignoring the features, we are able to learn target vectors for each instance using one of several appropriately designed loss functions. A regression model can then be constructed that maps novel feature vectors to the same target vector space, resulting in a feature extractor that computes vectors for which a predefined metric is a meaningful measure of similarity. We present results on both multiclass and multi-label classification datasets that demonstrate considerably faster convergence, as well as higher accuracy on the majority of the intrinsic evaluation tasks and all extrinsic evaluation tasks.
There is also an extension of NCA to nonlinear transformations of the input data @cite_16 . This method can be viewed as a probabilistic variant of Siamese networks. The nonlinear transformation models used in the original exposition of this method were stacked Restricted Boltzmann Machines, initialised using unsupervised pretraining and subsequently fine-tuned using the NCA loss function.
@cite_16
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Deep learning has been successfully applied to perform non-linear embedding. In this paper, we present supervised embedding techniques that use a deep network to collapse classes. The network is pre-trained using a stack of RBMs, and finetuned using approaches that try to collapse classes. The finetuning is inspired by ideas from NCA, but it uses a Student t-distribution to model the similarities of data points belonging to the same class in the embedding. We investigate two types of objective functions: deep t-distributed MCML (dt-MCML) and deep t-distributed NCA (dt-NCA). Our experiments on two handwritten digit data sets reveal the strong performance of dt-MCML in supervised parametric data visualization, whereas dt-NCA outperforms alternative techniques when embeddings with more than two or three dimensions are constructed, e.g., to obtain good classification performances. Overall, our results demonstrate the advantage of using a deep architecture and a heavy-tailed t-distribution for measuring pairwise similarities in supervised embedding. Abstract Deep neural networks with several layers have recently become a highly successful and popular research topic in machine learning due to their excellent performance in many benchmark problems and applications. A key idea in deep learning is to learn not only the nonlinear mapping between the inputs and outputs but also the underlying structure of the data (input) vectors. In this chapter, we first consider problems with training deep networks using backpropagation-type algorithms. After this, we consider various structures used in deep learning, including restricted Boltzmann machines, deep belief networks, deep Boltzmann machines, and nonlinear autoencoders. In the latter part of this chapter, we discuss in more detail the recently developed neural autoregressive distribution estimator and its variants. We describe an image compression method, consisting of a nonlinear analysis transformation, a uniform quantizer, and a nonlinear synthesis transformation. The transforms are constructed in three successive stages of convolutional linear filters and nonlinear activation functions. Unlike most convolutional neural networks, the joint nonlinearity is chosen to implement a form of local gain control, inspired by those used to model biological neurons. Using a variant of stochastic gradient descent, we jointly optimize the entire model for rate-distortion performance over a database of training images, introducing a continuous proxy for the discontinuous loss function arising from the quantizer. Under certain conditions, the relaxed loss function may be interpreted as the log likelihood of a generative model, as implemented by a variational autoencoder. Unlike these models, however, the compression model must operate at any given point along the rate-distortion curve, as specified by a trade-off parameter. Across an independent set of test images, we find that the optimized method generally exhibits better rate-distortion performance than the standard JPEG and JPEG 2000 compression methods. More importantly, we observe a dramatic improvement in visual quality for all images at all bit rates, which is supported by objective quality estimates using MS-SSIM. Some of the main challenges in skeleton-based action recognition systems are redundant and noisy pose transformations. Earlier works in skeleton-based action recognition explored different approaches for filtering linear noise transformations, but neglect to address potential nonlinear transformations. In this paper, we present an unsupervised learning approach for estimating nonlinear noise transformations in pose estimates. Our approach starts by decoupling linear and nonlinear noise transformations. While the linear transformations are modelled explicitly the nonlinear transformations are learned from data. Subsequently, we use an autoencoder with L2-norm reconstruction error and show that it indeed does capture nonlinear noise transformations, and recover a denoised pose estimate which in turn improves performance significantly. We validate our approach on a publicly available dataset, NW-UCLA.