We consider the problems of classification and intrinsic dimension estimation on image data. A new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation. The distribution of the data in each class is modeled by a union of of a finite number ofaffine subspaces of the feature space. The affine subspaces have a common dimension, which is assumed to be much less than the dimension of the feature space. The subspaces are found using regression based on the L0-norm. The proposed method is a generalisation of classical NN (Nearest Neighbor), NFL (Nearest Feature Line) classifiers and has a close relationship to NS (Nearest Subspace) classifier. The proposed classifier with an accurately estimated dimension parameter generally outperforms its competitors in terms of classification accuracy. We also propose a fast version of the classifier using a neighborhood representation to reduce its computational complexity. Experiments on publicly available datasets corroborate these claims.
Finding the nearest subspace is a fundamental problem and influential to many applications. In particular, a scalable solution that is fast and accurate for a large problem has a great impact. The existing methods for the problem are, however, useless in a large-scale problem with a large number of subspaces and high dimensionality of the feature space. A cause is that they are designed based on the traditional idea to represent a subspace by a single point. In this paper, we propose a scalable solution for the approximate nearest subspace search (ANSS) problem. Intuitively, the proposed metho…
The University of Sydney（悉尼大学）；Western Sydney University（西悉尼大学）
Sparse Subspace Clustering (SSC) has been used extensively for subspace identification tasks due to its theoretical guarantees and relative ease of implementation. However SSC has quadratic computation and memory requirements with respect to the number of input data points. This burden has prohibited SSCs use for all but the smallest datasets. To overcome this we propose a new method, k-SSC, that screens out a large number of data points to both reduce SSC to linear memory and computational requirements. We provide theoretical analysis for the bounds of success for k-SSC. Our experiments show …
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences（奥地利科学院约翰·拉东计算与应用数学研究所（RICAM））；Linköping University（林雪平大学）；RISE Research Institutes of Sweden AB（瑞典RISE研究院AB）
A windowed version of the Nearest Neighbour (WNN) classifier for images is described. While its construction is inspired by the architecture of Artificial Neural Networks, the underlying theoretical framework is based on approximation theory. We illustrate WNN on the datasets MNIST and EMNIST of images of handwritten digits. In order to calibrate the parameters of WNN, we first study it on the classical MNIST dataset. We then apply WNN with these parameters to the challenging EMNIST dataset. It is demonstrated that WNN misclassifies 0.42% of the images of EMNIST and therefore significantly out…
The present paper deals with optimisation of Nearest Neighbour rule Classifiers via Genetic Algorithms. The methodology consists on implement a Genetic Algorithm capable of search the input feature space used by the NNR classifier. Results show that is adequate to perform feature reduction and simultaneous improve the Recognition Rate. Some practical examples prove that is possible to Recognise Portuguese Granites in 100%, with only 3 morphological features (from an original set of 117 features), which is well suited for real time applications. Moreover, the present method represents a robust …
Cornell University（康奈尔大学）；Ohio State University（俄亥俄州立大学）；Facebook AI Research（脸书人工智能研究院）
Few-shot learners aim to recognize new object classes based on a small number of labeled training examples. To prevent overfitting, state-of-the-art few-shot learners use meta-learning on convolutional-network features and perform classification using a nearest-neighbor classifier. This paper studies the accuracy of nearest-neighbor baselines without meta-learning. Surprisingly, we find simple feature transformations suffice to obtain competitive few-shot learning accuracies. For example, we find that a nearest-neighbor classifier used in combination with mean-subtraction and L2-normalization …
Face recognition is a popular application of pat- tern recognition methods, and it faces challenging problems including illumination, expression, and pose. The most popular way is to learn the subspaces of the face images so that it could be project to another discriminant space where images of different persons can be separated. In this paper, a nearest line projection algorithm is developed to represent the face images for face recognition. Instead of projecting an image to its nearest image, we try to project it to its nearest line spanned by two different face images. The subspaces are lea…
Cornell University（康奈尔大学）；Meta AI；Fudan University（复旦大学）；University of Copenhagen（哥本哈根大学）
Neural network classifiers have become the de-facto choice for current "pre-train then fine-tune" paradigms of visual classification. In this paper, we investigate k-Nearest-Neighbor (k-NN) classifiers, a classical model-free learning method from the pre-deep learning era, as an augmentation to modern neural network based approaches. As a lazy learning method, k-NN simply aggregates the distance between the test image and top-k neighbors in a training set. We adopt k-NN with pre-trained visual representations produced by either supervised or self-supervised methods in two steps: (1) Leverage k…
NRI Institute of Technology-Guntur（NRI理工学院（贡图尔校区））
K-Nearest neighbor classifier (k-NNC) is simple to use and has little design time like finding k values in k-nearest neighbor classifier, hence these are suitable to work with dynamically varying data-sets. There exists some fundamental improvements over the basic k-NNC, like weighted k-nearest neighbors classifier (where weights to nearest neighbors are given based on linear interpolation), using artificially generated training set called bootstrapped training set, etc. These improvements are orthogonal to space reduction and classification time reduction techniques, hence can be coupled with…
Continuous learning seeks to perform the learning on the data that arrives from time to time. While prior works have demonstrated several possible solutions, these approaches require excessive training time as well as memory usage. This is impractical for applications where time and storage are constrained, such as edge computing. In this work, a novel training algorithm, regularized subspace approximation classifier (RSAC), is proposed to achieve lightweight continuous learning. RSAC contains a feature reduction module and classifier module with regularization. Extensive experiments show that…
As a representation learning method, nearest regularized subspace(NRS) algorithm is an effective tool to obtain both accuracy and speed for PolSAR image classification. However, existing NRS methods use the polarimetric feature vector but the PolSAR original covariance matrix(known as Hermitian positive definite(HPD)matrix) as the input. Without considering the matrix structure, existing NRS-based methods cannot learn correlation among channels. How to utilize the original covariance matrix to NRS method is a key problem. To address this limit, a Riemannian NRS method is proposed, which consid…
The MNIST dataset of the handwritten digits is known as one of the commonly used datasets for machine learning and computer vision research. We aim to study a widely applicable classification problem and apply a simple yet efficient K-nearest neighbor classifier with an enhanced heuristic. We evaluate the performance of the K-nearest neighbor classification algorithm on the MNIST dataset where the $L2$ Euclidean distance metric is compared to a modified distance metric which utilizes the sliding window technique in order to avoid performance degradation due to slight spatial misalignments. The…
Deep neural networks have been shown to be vulnerable to adversarial examples---maliciously crafted examples that can trigger the target model to misbehave by adding imperceptible perturbations. Existing attack methods for k-nearest neighbor~(kNN) based algorithms either require large perturbations or are not applicable for large k. To handle this problem, this paper proposes a new method called AdvKNN for evaluating the adversarial robustness of kNN-based models. Firstly, we propose a deep kNN block to approximate the output of kNN methods, which is differentiable thus can provide gradients f…
Learning useful representations of complex data has been the subject of extensive research for many years. With the diffusion of Deep Neural Networks, Variational Autoencoders have gained lots of attention since they provide an explicit model of the data distribution based on an encoder/decoder architecture which is able to both generate images and encode them in a low-dimensional subspace. However, the latent space is not easily interpretable and the generation capabilities show some limitations since images typically look blurry and lack details. In this paper, we propose the Introspective V…
University of Toronto（多伦多大学）；LG AI Research（LG人工智能研究院）
Online class-incremental continual learning (CL) studies the problem of learning new classes continually from an online non-stationary data stream, intending to adapt to new data while mitigating catastrophic forgetting. While memory replay has shown promising results, the recency bias in online learning caused by the commonly used Softmax classifier remains an unsolved challenge. Although the Nearest-Class-Mean (NCM) classifier is significantly undervalued in the CL community, we demonstrate that it is a simple yet effective substitute for the Softmax classifier. It addresses the recency bias…
University of Edinburgh（爱丁堡大学）；University of Cambridge（剑桥大学）
We derive a new asymptotic expansion for the global excess risk of a local-$k$-nearest neighbour classifier, where the choice of $k$ may depend upon the test point. This expansion elucidates conditions under which the dominant contribution to the excess risk comes from the decision boundary of the optimal Bayes classifier, but we also show that if these conditions are not satisfied, then the dominant contribution may arise from the tails of the marginal distribution of the features. Moreover, we prove that, provided the $d$-dimensional marginal distribution of the features has a finite $ρ$th m…
Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space, and a query point (image), efficiently determine the nearest subspace to the query in $\ell^1$ distance. In contrast to the naive exhaustive search which entails large-scale linear programs, we show that the computational burden can be cut down significantly by a simple two-stage algorithm: (1) projecting the query and data-base subspaces into lower-dimensional space by random Cauchy …
Zhejiang University（浙江大学）；Rochester Institute of Technology（罗切斯特理工学院）；ETH Zurich（苏黎世联邦理工学院）
We devise deep nearest centroids (DNC), a conceptually elegant yet surprisingly effective network for large-scale visual recognition, by revisiting Nearest Centroids, one of the most classic and simple classifiers. Current deep models learn the classifier in a fully parametric manner, ignoring the latent data structure and lacking simplicity and explainability. DNC instead conducts nonparametric, case-based reasoning; it utilizes sub-centroids of training samples to describe class distributions and clearly explains the classification as the proximity of test data and the class sub-centroids in…
Dimensionality reduction is a crucial preprocessing for hyperspectral data analysis - finding an appropriate subspace is often required for subsequent image classification. In recent work, we proposed supervised angular information based dimensionality reduction methods to find effective subspaces. Since unlabeled data are often more readily available compared to labeled data, we propose an unsupervised projection that finds a lower dimensional subspace where local angular information is preserved. To exploit spatial information from the hyperspectral images, we further extend our unsupervised…
UiT The Arctic University of Norway（挪威北极大学UiT）；Norwegian Computing Center（挪威计算中心）；University of Copenhagen（哥本哈根大学）
Distance-based classification is frequently used in transductive few-shot learning (FSL). However, due to the high-dimensionality of image representations, FSL classifiers are prone to suffer from the hubness problem, where a few points (hubs) occur frequently in multiple nearest neighbour lists of other points. Hubness negatively impacts distance-based classification when hubs from one class appear often among the nearest neighbors of points from another class, degrading the classifier's performance. To address the hubness problem in FSL, we first prove that hubness can be eliminated by distr…
University College London（伦敦大学学院）；Duke University（杜克大学）
This paper considers the classification of linear subspaces with mismatched classifiers. In particular, we assume a model where one observes signals in the presence of isotropic Gaussian noise and the distribution of the signals conditioned on a given class is Gaussian with a zero mean and a low-rank covariance matrix. We also assume that the classifier knows only a mismatched version of the parameters of input distribution in lieu of the true parameters. By constructing an asymptotic low-noise expansion of an upper bound to the error probability of such a mismatched classifier, we provide suf…
Classification of Visual Object Classes represents one of the most elaborated areas of interest in Computer Vision. It is always challenging to get one specific detector, descriptor or classifier that provides the expected object classification result. Consequently, it critical to compare the different detection, descriptor and classifier methods available and chose a single or combination of two or three to get an optimal result. In this paper, we have presented a comparative survey of different feature descriptors and classifiers. From feature descriptors, SIFT (Sparse & Dense) and HeuSIFT c…
In this study, a new Stacked Generalization technique called Fuzzy Stacked Generalization (FSG) is proposed to minimize the difference between N -sample and large-sample classification error of the Nearest Neighbor classifier. The proposed FSG employs a new hierarchical distance learning strategy to minimize the error difference. For this purpose, we first construct an ensemble of base-layer fuzzy k- Nearest Neighbor (k-NN) classifiers, each of which receives a different feature set extracted from the same sample set. The fuzzy membership values computed at the decision space of each fuzzy k-N…
Feature selection is an important problem in high-dimensional data analysis and classification. Conventional feature selection approaches focus on detecting the features based on a redundancy criterion using learning and feature searching schemes. In contrast, we present an approach that identifies the need to select features based on their discriminatory ability among classes. Area of overlap between inter-class and intra-class distances resulting from feature to feature comparison of an attribute is used as a measure of discriminatory ability of the feature. A set of nearest attributes in a …
