The recent technological developments in astrophysics have resulted in a dramatic increase in measurement capabilities. As a consequence, astronomical data are frequently acquired as a function of many dimensions such as spatial, spectral, and temporal dimensions. Although the increasing dimensionality of the data can provide valuable information in many applications, extracting information from such data becomes a critical and challenging problem. Subsets of those data are usually only analyzed along one or two dimensions at a time.
A natural way to represent such high dimensional data is higher-order extensions of vectors and matrices, known as tensors, with entries indexed by several variables. Despite the complexities involved in handling and manipulating tensors, tools for tensor analysis can effectively overcome the limitations of traditional processing models. In particular, tensor decomposition techniques have been recently used in several applications in machine learning, including regression, classification, and data preprocessing tasks. Recent developments in deep learning have also introduced an increasing number of deep neural network architectures with significant gains in many problems in astrophysics. Therefore, a deep learning formulation of tensor models is a highly promising research direction. In this way, we could leverage the benefits of both tensor analysis and deep learning techniques in a unified framework, providing a way to analyze high-dimensional data in all dimensions and improving the performance of standard models.
Objectives:
The objectives of this project can be summarized as follows:
- The analysis of high-dimensional astrophysical data in all dimensions simultaneously using tensor-based techniques.
- The development of tensor-based models in the deep learning framework to leverage the benefits of both fields in a unified framework.
- The combination of tensor-based networks with other popular networks to perform two tasks simultaneously.
- The application of the proposed models in problems such as the recovery of missing or corrupted measurements in combination with classification problems in multitemporal data.
Methodology:
To introduce tensor models in the deep learning framework, the unrolling technique will be used, which is a connection of the iterative algorithms with neural networks. The unrolled networks have higher representation power than the iterative algorithms, and they generalize better than generic networks, hence providing an attractive balance. In addition, unrolled networks have fewer parameters and require less training data, so they can be computationally faster. Specifically, in this technique, each iteration of the iterative algorithm will be a layer of the network as it is illustrated in the figure. Concatenating these layers, we can form a deep neural network, and the algorithm parameters are transferred to the network parameters learned from training samples through end-to-end training. Following this technique, we can also combine the proposed tensor networks with other popular networks to perform two tasks simultaneously. Finally, we will apply the tensor networks to process and analyse higher-order astrophysical data.