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In this paper, we carry out null space analysis for Class-Specific Discriminant Analysis (CSDA) and formulate a number of solutions based on the analysis. We analyze both theoretically and experimentally the significance of each algorithmic step. The innate subspace dimensionality resulting from the proposed solutions is typically quite high and we discuss how the need for further dimensionality reduction changes the situation. Experimental evaluation of the proposed solutions shows that the straightforward extension of null space analysis approaches to the class-specific setting can outperform the standard CSDA method. Furthermore, by exploiting a recently proposed out-of-class scatter definition encoding the multi-modality of the negative class naturally appearing in class-specific problems, null space projections can lead to a performance comparable to or outperforming the most recent CSDA methods.
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This paper proposes an incremental solution to Fast Subclass Discriminant Analysis (fastSDA). We present an exact and an approximate linear solution, along with an approximate kernelized variant. Extensive experiments on eight image datasets with different incremental batch sizes show the superiority of the proposed approach in terms of training time and accuracy being equal or close to fastSDA solution and outperforming other methods.
In recent years, a number of tools have become available that recover the underlying control policy from constrained movements. However, few have explicitly considered learning the constraints of the motion and ways to cope with unknown environment. In this paper, we consider learning the null space projection matrix of a kinematically constrained system in the absence of any prior knowledge either on the underlying policy, the geometry, or dimensionality of the constraints. Our evaluations have demonstrated the effectiveness of the proposed approach on problems of differing dimensionality, and with different degrees of non-linearity.
In this paper, we propose a speed-up approach for subclass discriminant analysis and formulate a novel efficient multi-view solution to it. The speed-up approach is developed based on graph embedding and spectral regression approaches that involve eigendecomposition of the corresponding Laplacian matrix and regression to its eigenvectors. We show that by exploiting the structure of the between-class Laplacian matrix, the eigendecomposition step can be substituted with a much faster process. Furthermore, we formulate a novel criterion for multi-view subclass discriminant analysis and show that an efficient solution for it can be obtained in a similar to the single-view manner. We evaluate the proposed methods on nine single-view and nine multi-view datasets and compare them with related existing approaches. Experimental results show that the proposed solutions achieve competitive performance, often outperforming the existing methods. At the same time, they significantly decrease the training time.
Overparametrization has been remarkably successful for deep learning studies. This study investigates an overlooked but important aspect of overparametrized neural networks, that is, the null components in the parameters of neural networks, or the ghosts. Since deep learning is not explicitly regularized, typical deep learning solutions contain null components. In this paper, we present a structure theorem of the null space for a general class of neural networks. Specifically, we show that any null element can be uniquely written by the linear combination of ridgelet transforms. In general, it is quite difficult to fully characterize the null space of an arbitrarily given operator. Therefore, the structure theorem is a great advantage for understanding a complicated landscape of neural network parameters. As applications, we discuss the roles of ghosts on the generalization performance of deep learning.
We study many-class few-shot (MCFS) problem in both supervised learning and meta-learning settings. Compared to the well-studied many-class many-shot and few-class few-shot problems, the MCFS problem commonly occurs in practical applications but has been rarely studied in previous literature. It brings new challenges of distinguishing between many classes given only a few training samples per class. In this paper, we leverage the class hierarchy as a prior knowledge to train a coarse-to-fine classifier that can produce accurate predictions for MCFS problem in both settings. The propose model, memory-augmented hierarchical-classification network (MahiNet), performs coarse-to-fine classification where each coarse class can cover multiple fine classes. Since it is challenging to directly distinguish a variety of fine classes given few-shot data per class, MahiNet starts from learning a classifier over coarse-classes with more training data whose labels are much cheaper to obtain. The coarse classifier reduces the searching range over the fine classes and thus alleviates the challenges from many classes. On architecture, MahiNet firstly deploys a convolutional neural network (CNN) to extract features. It then integrates a memory-augmented attention module and a multi-layer perceptron (MLP) together to produce the probabilities over coarse and fine classes. While the MLP extends the linear classifier, the attention module extends the KNN classifier, both together targeting the few-shot problem. We design several training strategies of MahiNet for supervised learning and meta-learning. In addition, we propose two novel benchmark datasets mcfsImageNet and mcfsOmniglot specially designed for MCFS problem. In experiments, we show that MahiNet outperforms several state-of-the-art models on MCFS problems in both supervised learning and meta-learning.
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