Multi-layered tensor networks for image classification
University of Copenhagen（哥本哈根大学）
Raghavendra Selvan, Silas Ørting, Erik B Dam
备注：
Updated version with exact computation costs. 6 pages. Accepted to the First Workshop on Quantum Tensor Networks in Machine Learning. In conjunction with 34th NeurIPS, 2020. Source code at https://github.com/raghavian/mltn
The recently introduced locally orderless tensor network (LoTeNet) for supervised image classification uses matrix product state (MPS) operations on grids of transformed image patches. The resulting patch representations are combined back together into the image space and aggregated hierarchically using multiple MPS blocks per layer to obtain the final decision rules. In this work, we propose a non-patch based modification to LoTeNet that performs one MPS operation per layer, instead of several patch-level operations. The spatial information in the input images to MPS blocks at each layer is squeezed into the feature dimension, similar to LoTeNet, to maximise retained spatial correlation between pixels when images are flattened into 1D vectors. The proposed multi-layered tensor network (MLTN) is capable of learning linear decision boundaries in high dimensional spaces in a multi-layered setting, which results in a reduction in the computation cost compared to LoTeNet without any degradation in performance.
The interest in machine learning with tensor networks has been growing rapidly in recent years. We show that tensor-based methods developed for learning the governing equations of dynamical systems from data can, in the same way, be used for supervised learning problems and propose two novel approaches for image classification. One is a kernel-based reformulation of the previously introduced MANDy (multidimensional approximation of nonlinear dynamics), the other an alternating ridge regression in the tensor-train format. We apply both methods to the MNIST and fashion MNIST data set and show th…
Sun Yat-Sen University（中山大学）；SYSU-CMU Shunde International Joint Research Institute（中山大学-卡内基梅隆大学顺德国际联合研究院）
Constructing effective representations is a critical but challenging problem in multimedia understanding. The traditional handcraft features often rely on domain knowledge, limiting the performances of exiting methods. This paper discusses a novel computational architecture for general image feature mining, which assembles the primitive filters (i.e. Gabor wavelets) into compositional features in a layer-wise manner. In each layer, we produce a number of base classifiers (i.e. regression stumps) associated with the generated features, and discover informative compositions by using the boosting…
EPHE-PSL University（巴黎高等实践研究大学-巴黎文理研究大学）；Ho Chi Minh University of Technology（胡志明市技术大学）
Face recognition is the important field in machine learning and pattern recognition research area. It has a lot of applications in military, finance, public security, to name a few. In this paper, the combination of the tensor sparse PCA with the nearest-neighbor method (and with the kernel ridge regression method) will be proposed and applied to the face dataset. Experimental results show that the combination of the tensor sparse PCA with any classification system does not always reach the best accuracy performance measures. However, the accuracy of the combination of the sparse PCA method an…
Multi-layered Semantic Representation Network for Multi-label Image Classification
Anhui University of Technology（安徽工业大学）；Australian National University（澳大利亚国立大学）；Hefei Comprehensive National Science Center（合肥综合性国家科学中心）；The Hong Kong Polytechnic University（香港理工大学）
The approximation of nonlinear kernels via linear feature maps has recently gained interest due to their applications in reducing the training and testing time of kernel-based learning algorithms. Current random projection methods avoid the curse of dimensionality by embedding the nonlinear feature space into a low dimensional Euclidean space to create nonlinear kernels. We introduce a Layered Random Projection (LaRP) framework, where we model the linear kernels and nonlinearity separately for increased training efficiency. The proposed LaRP framework was assessed using the MNIST hand-written …
With the increasing adoption of machine learning tools like neural networks across several domains, interesting connections and comparisons to concepts from other domains are coming to light. In this work, we focus on the class of Tensor Networks, which has been a work horse for physicists in the last two decades to analyse quantum many-body systems. Building on the recent interest in tensor networks for machine learning, we extend the Matrix Product State tensor networks (which can be interpreted as linear classifiers operating in exponentially high dimensional spaces) to be useful in medical…
This paper defines a new learning architecture, Layered Self-Organizing Maps (LSOMs), that uses the SOM and supervised-SOM learning algorithms. The architecture is validated with the MNIST database of hand-written digit images. LSOMs are similar to convolutional neural nets (covnets) in the way they sample data, but different in the way they represent features and learn. LSOMs analyze (or generate) image patches with maps of exemplars determined by the SOM learning algorithm rather than feature maps from filter-banks learned via backprop. LSOMs provide an alternative to features derived from c…
This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and compression quality. Regardless of tensor order, MPS compresses tensors to matrices of moderate dimension which can be used for classification. Mainly based on a successive sequence of singular value decompositions (SVD), MPS is quite simple to implement and arrives at the global optimal matrix, bypassing local alternating optimization, which is not only computa…
Southeast University（东南大学）；INSERM（法国国家健康与医学研究院）；Université de Rennes 1（雷恩第一大学）
The recently proposed principal component analysis network (PCANet) has been proved high performance for visual content classification. In this letter, we develop a tensorial extension of PCANet, namely, multilinear principal analysis component network (MPCANet), for tensor object classification. Compared to PCANet, the proposed MPCANet uses the spatial structure and the relationship between each dimension of tensor objects much more efficiently. Experiments were conducted on different visual content datasets including UCF sports action video sequences database and UCF11 database. The experime…
Tiny object classification problem exists in many machine learning applications like medical imaging or remote sensing, where the object of interest usually occupies a small region of the whole image. It is challenging to design an efficient machine learning model with respect to tiny object of interest. Current neural network structures are unable to deal with tiny object efficiently because they are mainly developed for images featured by large scale objects. However, in quantum physics, there is a great theoretical foundation guiding us to analyze the target function for image classificatio…
Technische Universität Kaiserslautern（凯泽斯劳滕工业大学）；DFKI Kaiserslautern（德国人工智能研究中心凯泽斯劳滕分部）
We present a novel global representation of 3D shapes, suitable for the application of 2D CNNs. We represent 3D shapes as multi-layered height-maps (MLH) where at each grid location, we store multiple instances of height maps, thereby representing 3D shape detail that is hidden behind several layers of occlusion. We provide a novel view merging method for combining view dependent information (Eg. MLH descriptors) from multiple views. Because of the ability of using 2D CNNs, our method is highly memory efficient in terms of input resolution compared to the voxel based input. Together with MLH d…
Southeast University（东南大学）；INSERM（法国国家健康与医学研究院）；Université de Rennes 1（雷恩第一大学）
This paper proposes a multilinear discriminant analysis network (MLDANet) for the recognition of multidimensional objects, known as tensor objects. The MLDANet is a variation of linear discriminant analysis network (LDANet) and principal component analysis network (PCANet), both of which are the recently proposed deep learning algorithms. The MLDANet consists of three parts: 1) The encoder learned by MLDA from tensor data. 2) Features maps ob-tained from decoder. 3) The use of binary hashing and histogram for feature pooling. A learning algorithm for MLDANet is described. Evaluations on UCF11 …
National University of Defense Technology（国防科技大学）；University of Trento（特伦托大学）
This paper presents a tensor alignment (TA) based domain adaptation method for hyperspectral image (HSI) classification. To be specific, HSIs in both domains are first segmented into superpixels and tensors of both domains are constructed to include neighboring samples from single superpixel. Then we consider the subspace invariance between two domains as projection matrices and original tensors are projected as core tensors with lower dimensions into the invariant tensor subspace by applying Tucker decomposition. To preserve geometric information in original tensors, we employ a manifold regu…
Univ. Lille, CNRS, Centrale Lille, UMR 9189 – CRIStAL – Centre de Recherche en Informatique, Signal et Automatique de Lille（里尔大学、法国国家科学研究中心、里尔中央理工学院（里尔信息、信号与自动化研究中心））；IMT Lille Douai（法国里尔-杜埃高等矿业与电信学院）
Spiking neural networks (SNNs) are good candidates to produce ultra-energy-efficient hardware. However, the performance of these models is currently behind traditional methods. Introducing multi-layered SNNs is a promising way to reduce this gap. We propose in this paper a new threshold adaptation system which uses a timestamp objective at which neurons should fire. We show that our method leads to state-of-the-art classification rates on the MNIST dataset (98.60%) and the Faces/Motorbikes dataset (99.46%) with an unsupervised SNN followed by a linear SVM. We also investigate the sparsity leve…
Inspired by the ConvNets with structured hidden representations, we propose a Tensor-based Neural Network, TCNN. Different from ConvNets, TCNNs are composed of structured neurons rather than scalar neurons, and the basic operation is neuron tensor transformation. Unlike other structured ConvNets, where the part-whole relationships are modeled explicitly, the relationships are learned implicitly in TCNNs. Also, the structured neurons in TCNNs are high-rank tensors rather than vectors or matrices. We compare TCNNs with current popular ConvNets, including ResNets, MobileNets, EfficientNets, RegNe…
Deep learning (DL) has been widely investigated in a vast majority of applications in electroencephalography (EEG)-based brain-computer interfaces (BCIs), especially for motor imagery (MI) classification in the past five years. The mainstream DL methodology for the MI-EEG classification exploits the temporospatial patterns of EEG signals using convolutional neural networks (CNNs), which have remarkably succeeded in visual images. However, since the statistical characteristics of visual images depart radically from EEG signals, a natural question arises whether an alternative network architectu…
