Tensor decomposition techniques such as CANDECOMP/PARAFAC (CP) decomposition have achieved great success across a range of scientific fields. They have been traditionally applied to dense, static data. However, today's datasets are often highly sparse and dynamically changing over time. Traditional decomposition methods such as Alternating Least Squares (ALS) cannot be easily applied to sparse tensors, due to poor efficiency. Furthermore, existing online tensor decomposition methods mostly target dense tensors, and thus also encounter significant scalability issues for sparse data. To address this gap, we propose a new incremental algorithm for tracking the CP decompositions of online sparse tensors on-the-fly. Experiments on nine real-world datasets show that our algorithm is able to produce quality decompositions of comparable quality to the most accurate algorithm, ALS, whilst at the same time achieving speed improvements of up to 250 times and 100 times less memory.

Datasets with significant proportions of noisy (incorrect) class labels present challenges for training accurate Deep Neural Networks (DNNs). We propose a new perspective for understanding DNN generalization for such datasets, by investigating the dimensionality of the deep representation subspace of training samples. We show that from a dimensionality perspective, DNNs exhibit quite distinctive learning styles when trained with clean labels versus when trained with a proportion of noisy labels. Based on this finding, we develop a new dimensionality-driven learning strategy, which monitors the dimensionality of subspaces during training and adapts the loss function accordingly. We empirically demonstrate that our approach is highly tolerant to significant proportions of noisy labels, and can effectively learn low-dimensional local subspaces that capture the data distribution.

CANDECOMP/PARAFAC Decomposition (CPD) is one of the most popular tensor decomposition methods that has been extensively studied and widely applied. In recent years, sparse tensors that contain a huge portion of zeros but a limited number of non-zeros have attracted increasing interest. Existing techniques are not directly applicable to sparse tensors, since they mainly target dense ones and usually have poor efficiency. Additionally, specific issues also arise for sparse tensors, depending on different data sources and applications: the role of zero entries can be different; incorporating constraints like non-negativity and sparseness might be necessary; the ability to learn on-the-fly is a must for dynamic scenarios that new data keeps arriving at high velocity. However, state-of-art algorithms only partially address the above issues. To fill this gap, we propose a general framework for finding the CPD of sparse tensors. Modeling the sparse tensor decomposition problem by a generalized weighted CPD formulation and solving it efficiently, our proposed method is also flexible to handle constraints and dynamic data streams. Through experiments on both synthetic and real-world datasets, for the static case, our method demonstrates significant improvements in terms of effectiveness, efficiency and scalability. Moreover, under the dynamic setting, our method speeds up current technology by hundreds to thousands times, without sacrificing decomposition quality.

Simulation-based training (SBT) is gaining popularity as a low-cost and convenient training technique in a vast range of applications. However, for a SBT platform to be fully utilized as an effective training tool, it is essential that feedback on performance is provided automatically in real-time during training. It is the aim of this paper to develop an efficient and effective feedback generation method for the provision of real-time feedback in SBT. Existing methods either have low effectiveness in improving novice skills or suffer from low efficiency, resulting in their inability to be used in real-time. In this paper, we propose a neural network based method to generate feedback using the adversarial technique. The proposed method utilizes a bounded adversarial update to minimize a L1 regularized loss via back-propagation. We empirically show that the proposed method can be used to generate simple, yet effective feedback. Also, it was observed to have high effectiveness and efficiency when compared to existing methods, thus making it a promising option for real-time feedback generation in SBT.

Tensors are a natural representation for multidimensional data. In recent years, CANDECOMP/PARAFAC (CP) decomposition, one of the most popular tools for analyzing multi-way data, has been extensively studied and widely applied. However, today's datasets are often dynamically changing over time. Tracking the CP decomposition for such dynamic tensors is a crucial but challenging task, due to the large scale of the tensor and the velocity of new data arriving. Traditional techniques, such as Alternating Least Squares (ALS), cannot be directly applied to this problem because of their poor scalability in terms of time and memory. Additionally, existing online approaches have only partially addressed this problem and can only be deployed on third-order tensors. To fill this gap, we propose an efficient online algorithm that can incrementally track the CP decompositions of dynamic tensors with an arbitrary number of dimensions. In terms of effectiveness, our algorithm demonstrates comparable results with the most accurate algorithm, ALS, whilst being computationally much more efficient. Specifically, on small and moderate datasets, our approach is tens to hundreds of times faster than ALS, while for large-scale datasets, the speedup can be more than 3,000 times. Compared to other state-of-the-art online approaches, our method shows not only significantly better decomposition quality, but also better performance in terms of stability, efficiency and scalability.