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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.
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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.
Majority of the modern meta-learning methods for few-shot classification tasks operate in two phases: a meta-training phase where the meta-learner learns a generic representation by solving multiple few-shot tasks sampled from a large dataset and a testing phase, where the meta-learner leverages its learnt internal representation for a specific few-shot task involving classes which were not seen during the meta-training phase. To the best of our knowledge, all such meta-learning methods use a single base dataset for meta-training to sample tasks from and do not adapt the algorithm after meta-training. This strategy may not scale to real-world use-cases where the meta-learner does not potentially have access to the full meta-training dataset from the very beginning and we need to update the meta-learner in an incremental fashion when additional training data becomes available. Through our experimental setup, we develop a notion of incremental learning during the meta-training phase of meta-learning and propose a method which can be used with multiple existing metric-based meta-learning algorithms. Experimental results on benchmark dataset show that our approach performs favorably at test time as compared to training a model with the full meta-training set and incurs negligible amount of catastrophic forgetting
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.
In large-scale classification problems, the data set always be faced with frequent updates when a part of the data is added to or removed from the original data set. In this case, conventional incremental learning, which updates an existing classifier by explicitly modeling the data modification, is more efficient than retraining a new classifier from scratch. However, sometimes, we are more interested in determining whether we should update the classifier or performing some sensitivity analysis tasks. To deal with these such tasks, we propose an algorithm to make rational inferences about the updated linear classifier without exactly updating the classifier. Specifically, the proposed algorithm can be used to estimate the upper and lower bounds of the updated classifiers coefficient matrix with a low computational complexity related to the size of the updated dataset. Both theoretical analysis and experiment results show that the proposed approach is superior to existing methods in terms of tightness of coefficients bounds and computational complexity.
A deep neural network (DNN) consists of a nonlinear transformation from an input to a feature representation, followed by a common softmax linear classifier. Though many efforts have been devoted to designing a proper architecture for nonlinear transformation, little investigation has been done on the classifier part. In this paper, we show that a properly designed classifier can improve robustness to adversarial attacks and lead to better prediction results. Specifically, we define a Max-Mahalanobis distribution (MMD) and theoretically show that if the input distributes as a MMD, the linear discriminant analysis (LDA) classifier will have the best robustness to adversarial examples. We further propose a novel Max-Mahalanobis linear discriminant analysis (MM-LDA) network, which explicitly maps a complicated data distribution in the input space to a MMD in the latent feature space and then applies LDA to make predictions. Our results demonstrate that the MM-LDA networks are significantly more robust to adversarial attacks, and have better performance in class-biased classification.
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