Compositional Hierarchical Tensor Factorization: Representing Hierarchical Intrinsic and Extrinsic Causal Factors
Visual objects are composed of a recursive hierarchy of perceptual wholes and parts, whose properties, such as shape, reflectance, and color, constitute a hierarchy of intrinsic causal factors of object appearance. However, object appearance is the compositional consequence of both an object's intrinsic and extrinsic causal factors, where the extrinsic causal factors are related to illumination, and imaging conditions. Therefore, this paper proposes a unified tensor model of wholes and parts, and introduces a compositional hierarchical tensor factorization that disentangles the hierarchical causal structure of object image formation, and subsumes multilinear block tensor decomposition as a special case. The resulting object representation is an interpretable combinatorial choice of wholes' and parts' representations that renders object recognition robust to occlusion and reduces training data requirements. We demonstrate ourapproach in the context of face recognition by training on an extremely reduced dataset of synthetic images, and report encouragingface verification results on two datasets - the Freiburg dataset, andthe Labeled Face in the Wild (LFW) dataset consisting of real world images, thus, substantiating the suitability of our approach for data starved domains.
Code (0)
등록된 구현이 없습니다.
Tasks
Face RecognitionObjectObject RecognitionTensor DecompositionSimilar Papers 제목 키워드 기반
Sparse Hierarchical Tucker Factorization and its Application to Healthcare
We propose a new tensor factorization method, called the Sparse Hierarchical-Tucker (Sparse H-Tucker), for sparse and high-order data tensors. Sparse H-Tucker is inspired by its namesake, the classical Hierarchical Tucke…
Implicit Regularization in Hierarchical Tensor Factorization and Deep Convolutional Neural Networks
In the pursuit of explaining implicit regularization in deep learning, prominent focus was given to matrix and tensor factorizations, which correspond to simplified neural networks. It was shown that these models exhibit…
A Generalized Hierarchical Nonnegative Tensor Decomposition
Nonnegative matrix factorization (NMF) has found many applications including topic modeling and document analysis. Hierarchical NMF (HNMF) variants are able to learn topics at various levels of granularity and illustrate…
Tensor DecompositionOn the Expressive Power of Deep Learning: A Tensor Analysis
It has long been conjectured that hypotheses spaces suitable for data that is compositional in nature, such as text or images, may be more efficiently represented with deep hierarchical networks than with shallow ones. D…
Deep LearningWhat is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?
This paper establishes a rigorous connection between circuit representations and tensor factorizations, two seemingly distinct yet fundamentally related areas. By connecting these fields, we highlight a series of opportu…