Tensor network algorithms for image classification

For many real-world image classification tasks, collecting high-quality labeled image data is challenging. Therefore, a complicated convolutional neural network might not be able to get well trained and traditional machine learning methods would be a better choice. However, traditional vector-based machine learning algorithms cannot achieve a satisfactory performance when dealing with high-dimensional tensorial data. There are mainly two reasons. First, vectorizing tensor data loses useful structural information in the original data, which might be helpful in the classification task. Second, traditional vector-based methods commonly contain a similar number of model parameters as the data size. In this case, when the data dimension is relatively high and the number of training samples is small, an overfitted model would be derived. To address these issues, researchers extend the vector-based classifiers into their tensorial formats, which accept tensorial data as input directly, and at the same time employ much fewer model parameters. In this chapter, two traditional vector-based machine learning algorithms, namely, support vector machine and logistic regression, are generalized to their tensorial counterparts to facilitate the tensor-based classification tasks.