Neural Information Processing Systems http://nips.cc/

Surface anomaly classification is critical for manufacturing system fault diagnosis and quality control. However, the following challenges always hinder accurate anomaly classification in practice: (i) Anomaly patterns exhibit intra-class variation and inter-class similarity, presenting challenges in the accurate classification of each sample. (ii) Despite the predefined classes, new types of anomalies can occur during production that require to be detected accurately. (iii) Anomalous data is rare in manufacturing processes, leading to limited data for model learning. To tackle the above challenges simultaneously, this paper proposes a novel deep subspace learning-based 3D anomaly classification model. Specifically, starting from a lightweight encoder to extract the latent representations, we model each class as a subspace to account for the intra-class variation, while promoting distinct subspaces of different classes to tackle the inter-class similarity. Moreover, the explicit modeling of subspaces offers the capability to detect out-of-distribution samples, i.e., new types of anomalies, and the regularization effect with much fewer learnable parameters of our proposed subspace classifier, compared to the popular Multi-Layer Perceptions (MLPs). Extensive numerical experiments demonstrate our method achieves better anomaly classification results than benchmark methods, and can effectively identify the new types of anomalies.

Subspace inference for neural networks assumes that a subspace of their parameter space suffices to produce a reliable uncertainty quantification. In this work, we mathematically derive the optimal subspace model to a Bayesian inference scenario based on the Laplace approximation. We demonstrate empirically that, in the optimal case, often a fraction of parameters less than 1% is sufficient to obtain a reliable estimate of the full Laplace approximation. Since the optimal solution is derived, we can evaluate all other subspace models against a baseline. In addition, we give an approximation of our method that is applicable to larger problem settings, in which the optimal solution is not computable, and compare it to existing subspace models from the literature. In general, our approximation scheme outperforms previous work. Furthermore, we present a metric to qualitatively compare different subspace models even if the exact Laplace approximation is unknown.

Motivated by recent progress in natural image statistics, we use newly available datasets with ground truth optical flow to learn the local statistics of optical flow and compare the learned models to prior models assumed by computer vision researchers. We find that a Gaussian mixture model (GMM) with 64 components provides a significantly better model for local flow statistics when compared to commonly used models. We investigate the source of the GMM's success and show it is related to an explicit representation of flow boundaries. We also learn a model that jointly models the local intensity pattern and the local optical flow. In accordance with the assumptions often made in computer vision, the model learns that flow boundaries are more likely at intensity boundaries. However, when evaluated on a large dataset, this dependency is very weak and the benefit of conditioning flow estimation on the local intensity pattern is marginal.

We address the problem of recovering a high-dimensional but structured vector from linear observations in a general setting where the vector can come from an arbitrary union of subspaces. This setup includes well-studied problems such as compressive sensing and low-rank matrix recovery. We show how to design more efficient algorithms for the union-of-subspace recovery problem by using approximate projections. Instantiating our general framework for the low-rank matrix recovery problem gives the fastest provable running time for an algorithm with optimal sample complexity. Moreover, we give fast approximate projections for 2D histograms, another well-studied low-dimensional model of data. We complement our theoretical results with experiments demonstrating that our framework also leads to improved time and sample complexity empirically.

Recent studies on Generative Adversarial Network (GAN) reveal that different layers of a generative CNN hold different semantics of the synthesized images. However, few GAN models have explicit dimensions to control the semantic attributes represented in a specific layer. This paper proposes EigenGAN which is able to unsupervisedly mine interpretable and controllable dimensions from different generator layers. Specifically, EigenGAN embeds one linear subspace with orthogonal basis into each generator layer. Via the adversarial training to learn a target distribution, these layer-wise subspaces automatically discover a set of "eigen-dimensions" at each layer corresponding to a set of semantic attributes or interpretable variations. By traversing the coefficient of a specific eigen-dimension, the generator can produce samples with continuous changes corresponding to a specific semantic attribute. Taking the human face for example, EigenGAN can discover controllable dimensions for high-level concepts such as pose and gender in the subspace of deep layers, as well as low-level concepts such as hue and color in the subspace of shallow layers. Moreover, under the linear circumstance, we theoretically prove that our algorithm derives the principal components as PCA does. Codes can be found in https://github.com/LynnHo/EigenGAN-Tensorflow.

Subspace clustering methods based on expressing each data point as a linear combination of other data points have achieved great success in computer vision applications such as motion segmentation, face and digit clustering. In face clustering, the subspaces are linear and subspace clustering methods can be applied directly. In motion segmentation, the subspaces are affine and an additional affine constraint on the coefficients is often enforced. However, since affine subspaces can always be embedded into linear subspaces of one extra dimension, it is unclear if the affine constraint is really necessary. This paper shows, both theoretically and empirically, that when the dimension of the ambient space is high relative to the sum of the dimensions of the affine subspaces, the affine constraint has a negligible effect on clustering performance. Specifically, our analysis provides conditions that guarantee the correctness of affine subspace clustering methods both with and without the affine constraint, and shows that these conditions are satisfied for high-dimensional data. Underlying our analysis is the notion of affinely independent subspaces, which not only provides geometrically interpretable correctness conditions, but also clarifies the relationships between existing results for affine subspace clustering.

We address the problem of recovering a high-dimensional but structured vector from linear observations in a general setting where the vector can come from an arbitrary union of subspaces. This setup includes well-studied problems such as compressive sensing and low-rank matrix recovery. We show how to design more efficient algorithms for the union-of subspace recovery problem by using *approximate* projections. Instantiating our general framework for the low-rank matrix recovery problem gives the fastest provable running time for an algorithm with optimal sample complexity. Moreover, we give fast approximate projections for 2D histograms, another well-studied low-dimensional model of data. We complement our theoretical results with experiments demonstrating that our framework also leads to improved time and sample complexity empirically.

Matrix completion refers to the recovery of a low-rank matrix from a (small) subset of its entries or a (small) number of linear combinations of its entries [1-4]. In essence, the methods are aimed at recovering the column/row subspaces from limited measurements. Even the sketching methods [8] aim to find the best column (or row) subspace of a matrix. However, in many practical applications, the columns of the data matrix can belong to different low rank subspaces (or affine subspaces) [5-7, 9].

The Nearest subspace classifier (NSS) finds an estimation of the underlying subspace within each class and assigns data points to the class that corresponds to its nearest subspace. This paper mainly studies how well NSS can be generalized to new samples. It is proved that NSS is strongly consistent under certain assumptions. For completeness, NSS is evaluated through experiments on various simulated and real data sets, in comparison with some other linear model based classifiers. It is also shown that NSS can obtain effective classification results and is very efficient, especially for large scale data sets.