Abstract
This work describes a new method to extract image features using tensor decomposition to model data. Given a set of sample images, we extract patches from images, compute the covariance tensor for all patches, decompose with the Tucker model, and obtain the most critical features from a tensor core. To extract features, we factorize the covariance tensor (CovTen) into its core and propose a new interpretation of the resultant tensor structure, which holds relevant features in a block-wise arrangement (also named filters, weights, or kernels). This tensorial representation allows preserving the spatial structure, learning multichannel filters, and establishing linear dependence between dimensions, reducing the dimensional complexity (the curse of dimensionality). Thus, the proposed method generates filters by a single feed-forward step using a few samples per class as low as 1. Besides, in kernel generation, labels are not needed. The obtained features were extensively tested using a convolutional neural network for classification. All tests were conducted under the VGG architecture conventions. The experiments helped us identify the proposed method’s advantages versus traditional convolutional neural networks in inference capacity and kernels initialization. We also performed experiments to select hyperparameters (nonLinearity, max pooling, samples, filter size) according to their performance. The inference capacity results showed an increased classification accuracy around 67% with CIFAR 10, 64% with CIFAR 100, and 98% with MNIST, using 10,100,1000 samples with a single feed-forward training. On the other hand, the initialization experiments showed the feature extraction capability versus available initializers (He random, He uniform, Glorot, random), confirming linear tensor constraints’ usefulness to generate features. Using the method as kernel initializer returns comparable findings with state of the art around 91% with CIFAR 10, 72% with CIFAR 100, and 99% with MNIST.
Highlights
This work introduces a new algorithm based on multilinear algebra for feature extraction, which later is plugged into a Convolutional Neural Network to perform classification
TRAINING SAMPLES NUMBER We noted that the kernels generation with the covariance tensor (CovTen) method achieved a suitable performance with small sub-datasets and a homogeneous number of images per class
The results show that our method is comparable and proportional to conventional kernel initializer methods using the CIFAR 10 dataset, returning an accuracy of around 91%
Summary
This work introduces a new algorithm based on multilinear algebra for feature extraction, which later is plugged into a Convolutional Neural Network to perform classification. On a dataset composed of images with size I1 × I2, feature extraction by eigenfaces [19] leads to subspaces with I1 I2 coefficients and at most the same number of basis vectors Such high dimensional sets are challenging to handle, so feature selection and dimensionality reduction techniques should be considered to represent data using fewer variables. Most recent approaches seek to replace the standard kernel initialization of ConvNet for a PCA-based method and propose a parametric equalization normalization to adjust the scale among the neuron weights [5], [47] This technique uses image samples per class from the training dataset to get more relevant information; in other words, it extracts the principal features in weighted kernels. This work pretends to be a good baseline for future research incorporating this method during the training stage
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