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### Deep Context-Aware Novelty Detection

A common assumption of novelty detection is that the distribution of both "normal" and "novel" data are static. However, this is often not the case in scenarios where data evolves over time, or when the definition of normal and novel depends on contextual information, leading to changes in these distributions. This can lead to significant difficulties when attempting to train a model on datasets where the distribution of normal data in one scenario is similar to that of novel data in another scenario. In this paper we propose a context-aware approach to novelty detection for deep autoencoders. We create a semi-supervised network architecture which utilises auxiliary labels in order to reveal contextual information and allows the model to adapt to a variety of normal and novel scenarios. We evaluate our approach on both synthetic image data and real world audio data displaying these characteristics.

### Any Variational Autoencoder Can Do Arbitrary Conditioning

Arbitrary conditioning is an important problem in unsupervised learning, where we seek to model the conditional densities $p(\mathbf{x}_u \mid \mathbf{x}_o)$ that underly some data, for all possible non-intersecting subsets $o, u \subset \{1, \dots , d\}$. However, the vast majority of density estimation only focuses on modeling the joint distribution $p(\mathbf{x})$, in which important conditional dependencies between features are opaque. We propose a simple and general framework, coined Posterior Matching, that enables any Variational Autoencoder (VAE) to perform arbitrary conditioning, without modification to the VAE itself. Posterior Matching applies to the numerous existing VAE-based approaches to joint density estimation, thereby circumventing the specialized models required by previous approaches to arbitrary conditioning. We find that Posterior Matching achieves performance that is comparable or superior to current state-of-the-art methods for a variety of tasks.

### Training Autoencoders in Sparse Domain

Autoencoders (AE) are essential in learning representation of large data (like images) for dimensionality reduction. Images are converted to sparse domain using transforms like Fast Fourier Transform (FFT) or Discrete Cosine Transform (DCT) where information that requires encoding is minimal. By optimally selecting the feature-rich frequencies, we are able to learn the latent vectors more robustly. We successfully show enhanced performance of autoencoders in sparse domain for images.

### Deep Spectral Clustering using Dual Autoencoder Network

The clustering methods have recently absorbed even-increasing attention in learning and vision. Deep clustering combines embedding and clustering together to obtain optimal embedding subspace for clustering, which can be more effective compared with conventional clustering methods. In this paper, we propose a joint learning framework for discriminative embedding and spectral clustering. We first devise a dual autoencoder network, which enforces the reconstruction constraint for the latent representations and their noisy versions, to embed the inputs into a latent space for clustering. As such the learned latent representations can be more robust to noise. Then the mutual information estimation is utilized to provide more discriminative information from the inputs. Furthermore, a deep spectral clustering method is applied to embed the latent representations into the eigenspace and subsequently clusters them, which can fully exploit the relationship between inputs to achieve optimal clustering results. Experimental results on benchmark datasets show that our method can significantly outperform state-of-the-art clustering approaches.