Clustering is a long-standing problem area in data mining. The centroid-based classical approaches to clustering mainly face difficulty in the case of high dimensional inputs such as images. With the advent of deep neural networks, a common approach to this problem is to map the data to some latent space of comparatively lower dimensions and then do the clustering in that space. Network architectures adopted for this are generally autoencoders that reconstruct a given input in the output. To keep the input in some compact form, the encoder in AE's learns to extract useful features that get decoded at the reconstruction end. A well-known centroid-based clustering algorithm is K-means. In the context of deep feature learning, recent works have empirically shown the importance of learning the representations and the cluster centroids together. However, in this aspect of joint learning, recently a continuous variant of K-means has been proposed; where the softmax function is used in place of argmax to learn the clustering and network parameters jointly using stochastic gradient descent (SGD). However, unlike K-means, where the input space stays constant, here the learning of the centroid is done in parallel to the learning of the latent space for every batch of data. Such batch updates disagree with the concept of classical K-means, where the clustering space remains constant as it is the input space itself. To this end, we propose to alternatively learn a clustering-friendly data representation and K-means based cluster centers. Experiments on some benchmark datasets have shown improvements of our approach over the previous approaches.

Deep kernel machines (DKMs) are a recently introduced kernel method with the flexibility of other deep models including deep NNs and deep Gaussian processes. DKMs work purely with kernels, never with features, and are therefore different from other methods ranging from NNs to deep kernel learning and even deep Gaussian processes, which all use features as a fundamental component. Here, we introduce convolutional DKMs, along with an efficient inter-domain inducing point approximation scheme. Further, we develop and experimentally assess a number of model variants, including 9 different types of normalisation designed for the convolutional DKMs, two likelihoods, and two different types of top-layer. The resulting models achieve around 99% test accuracy on MNIST, 92% on CIFAR-10 and 71% on CIFAR-100, despite training in only around 28 GPU hours, 1-2 orders of magnitude faster than full NNGP / NTK / Myrtle kernels, whilst achieving comparable performance.

Deep neural network (DNN) model compression for efficient on-device inference is becoming increasingly important to reduce memory requirements and keep user data on-device. To this end, we propose a novel differentiable k-means clustering layer (DKM) and its application to train-time weight clustering-based DNN model compression. DKM casts k-means clustering as an attention problem and enables joint optimization of the parameters and clustering centroids. Unlike prior works that rely on additional regularizers and parameters, DKM-based compression keeps the original loss function and model architecture fixed. We evaluated DKM-based compression on various DNN models for computer vision and natural language processing (NLP) tasks. Our results demonstrate that DMK delivers superior compression and accuracy trade-off on ImageNet1k and GLUE benchmarks. For example, DKM-based compression can offer 74.5% top-1 ImageNet1k accuracy on ResNet50 DNN model with 3.3MB model size (29.4x model compression factor). For MobileNet-v1, which is a challenging DNN to compress, DKM delivers 62.8% top-1 ImageNet1k accuracy with 0.74 MB model size (22.4x model compression factor). This result is 6.8% higher top-1 accuracy and 33% relatively smaller model size than the current state-of-the-art DNN compression algorithms. Additionally, DKM enables compression of DistilBERT model by 11.8x with minimal (1.1%) accuracy loss on GLUE NLP benchmarks.

Recently, neuro-inspired episodic control (EC) methods have been developed to overcome the data-inefficiency of standard deep reinforcement learning approaches. Using non-/semi-parametric models to estimate the value function, they learn rapidly, retrieving cached values from similar past states. In realistic scenarios, with limited resources and noisy data, maintaining meaningful representations in memory is essential to speed up the learning and avoid catastrophic forgetting. Unfortunately, EC methods have a large space and time complexity. We investigate different solutions to these problems based on prioritising and ranking stored states, as well as online clustering techniques. We also propose a new dynamic online k-means algorithm that is both computationally-efficient and yields significantly better performance at smaller memory sizes; we validate this approach on classic reinforcement learning environments and Atari games.

We study in this paper the problem of jointly clustering and learning representations. As several previous studies have shown, learning representations that are both faithful to the data to be clustered and adapted to the clustering algorithm can lead to better clustering performance, all the more so that the two tasks are performed jointly. We propose here such an approach for $k$-Means clustering based on a continuous reparametrization of the objective function that leads to a truly joint solution. The behavior of our approach is illustrated on various datasets showing its efficacy in learning representations for objects while clustering them.

Inspired by a growing interest in analyzing network data, we study the problem of node classification on graphs, focusing on approaches based on kernel machines. Conventionally, kernel machines are linear classifiers in the implicit feature space. We argue that linear classification in the feature space of kernels commonly used for graphs is often not enough to produce good results. When this is the case, one naturally considers nonlinear classifiers in the feature space. We show that repeating this process produces something we call "deep kernel machines." We provide some examples where deep kernel machines can make a big difference in classification performance, and point out some connections to various recent literature on deep architectures in artificial intelligence and machine learning.

In this paper, we propose a new spectral clustering method, referred to as Spectral Embedded Clustering (SEC), to minimize the normalized cut criterion in spectral clustering as well as control the mismatch between the cluster assignment matrix and the low dimensional embedded representation of the data. SEC is based on the observation that the cluster assignment matrix of high dimensional data can be represented by a low dimensional linear mapping of data. We also discover the connection between SEC and other clustering methods, such as spectral clustering, Clustering with local and global regularization, K-means and Discriminative K-means. The experiments on many real-world data sets show that SEC significantly outperforms the existing spectral clustering methods as well as K-means clustering related methods.