Dimensionality reduction techniques such as principal component analy- sis and factor analysis are used to discover a linear mapping between high dimensional data samples and points in a lower dimensional subspace. In [6], Jojic and Frey introduced mixture of transformation-invariant component analyzers (MTCA) that can account for global transforma- tions such as translations and rotations, perform clustering and learn lo- cal appearance deformations by dimensionality reduction. However, due to enormous computational requirements of the EM algorithm for learn- ing the model, O( is the dimensionality of a data sample, MTCA was not practical for most applications. In this paper, we demon- strate how fast Fourier transforms can reduce the computation to the or- . With this speedup, we show the effectiveness of MTCA der of in various applications - tracking, video textures, clustering video se- quences, object recognition, and object detection in images.

Earnings call (EC), as a periodic teleconference of a publicly-traded company, has been extensively studied as an essential market indicator because of its high analytical value in corporate fundamentals. The recent emergence of deep learning techniques has shown great promise in creating automated pipelines to benefit the EC-supported financial applications. However, these methods presume all included contents to be informative without refining valuable semantics from long-text transcript and suffer from EC scarcity issue. Meanwhile, these black-box methods possess inherent difficulties in providing human-understandable explanations. To this end, in this paper, we propose a Multi-Domain Transformer-Based Counterfactual Augmentation, named MTCA, to address the above problems. Specifically, we first propose a transformer-based EC encoder to attentively quantify the task-inspired significance of critical EC content for market inference. Then, a multi-domain counterfactual learning framework is developed to evaluate the gradient-based variations after we perturb limited EC informative texts with plentiful cross-domain documents, enabling MTCA to perform unsupervised data augmentation. As a bonus, we discover a way to use non-training data as instance-based explanations for which we show the result with case studies. Extensive experiments on the real-world financial datasets demonstrate the effectiveness of interpretable MTCA for improving the volatility evaluation ability of the state-of-the-art by 14.2\% in accuracy.

Dimensionality reduction techniques such as principal component analysis and factor analysis are used to discover a linear mapping between high dimensional data samples and points in a lower dimensional subspace. In [6], Jojic and Frey introduced mixture of transformation-invariant component analyzers (MTCA) that can account for global transformations such as translations and rotations, perform clustering and learn local appearance deformations by dimensionality reduction.

Dimensionality reduction techniques such as principal component analysis and factor analysis are used to discover a linear mapping between high dimensional data samples and points in a lower dimensional subspace. In [6], Jojic and Frey introduced mixture of transformation-invariant component analyzers (MTCA) that can account for global transformations such as translations and rotations, perform clustering and learn local appearance deformations by dimensionality reduction.

Dimensionality reduction techniques such as principal component analysis andfactor analysis are used to discover a linear mapping between high dimensional data samples and points in a lower dimensional subspace. In [6], Jojic and Frey introduced mixture of transformation-invariant component analyzers (MTCA) that can account for global transformations suchas translations and rotations, perform clustering and learn local appearance deformations by dimensionality reduction.