Dimensionality Reduction by Learning an Invariant Mapping
17 Jun 2006-Vol. 2, pp 1735-1742
TL;DR: This work presents a method - called Dimensionality Reduction by Learning an Invariant Mapping (DrLIM) - for learning a globally coherent nonlinear function that maps the data evenly to the output manifold.
Abstract: Dimensionality reduction involves mapping a set of high dimensional input points onto a low dimensional manifold so that 'similar" points in input space are mapped to nearby points on the manifold. We present a method - called Dimensionality Reduction by Learning an Invariant Mapping (DrLIM) - for learning a globally coherent nonlinear function that maps the data evenly to the output manifold. The learning relies solely on neighborhood relationships and does not require any distancemeasure in the input space. The method can learn mappings that are invariant to certain transformations of the inputs, as is demonstrated with a number of experiments. Comparisons are made to other techniques, in particular LLE.
Citations
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TL;DR: This historical survey compactly summarizes relevant work, much of it from the previous millennium, review deep supervised learning, unsupervised learning, reinforcement learning & evolutionary computation, and indirect search for short programs encoding deep and large networks.
14,635 citations
Posted Content•
TL;DR: It is shown that composition of data augmentations plays a critical role in defining effective predictive tasks, and introducing a learnable nonlinear transformation between the representation and the contrastive loss substantially improves the quality of the learned representations, and contrastive learning benefits from larger batch sizes and more training steps compared to supervised learning.
Abstract: This paper presents SimCLR: a simple framework for contrastive learning of visual representations. We simplify recently proposed contrastive self-supervised learning algorithms without requiring specialized architectures or a memory bank. In order to understand what enables the contrastive prediction tasks to learn useful representations, we systematically study the major components of our framework. We show that (1) composition of data augmentations plays a critical role in defining effective predictive tasks, (2) introducing a learnable nonlinear transformation between the representation and the contrastive loss substantially improves the quality of the learned representations, and (3) contrastive learning benefits from larger batch sizes and more training steps compared to supervised learning. By combining these findings, we are able to considerably outperform previous methods for self-supervised and semi-supervised learning on ImageNet. A linear classifier trained on self-supervised representations learned by SimCLR achieves 76.5% top-1 accuracy, which is a 7% relative improvement over previous state-of-the-art, matching the performance of a supervised ResNet-50. When fine-tuned on only 1% of the labels, we achieve 85.8% top-5 accuracy, outperforming AlexNet with 100X fewer labels.
7,951 citations
Cites background from "Dimensionality Reduction by Learnin..."
...Discriminative approaches based on contrastive learning in the latent space have recently shown great promise, achieving state-of-theart results (Hadsell et al., 2006; Dosovitskiy et al., 2014; Oord et al., 2018; Bachman et al., 2019)....
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...Dating back to Hadsell et al. (2006), these approaches learn representations by contrasting positive pairs against negative pairs....
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Book•
01 Jan 2009TL;DR: The motivations and principles regarding learning algorithms for deep architectures, in particular those exploiting as building blocks unsupervised learning of single-layer modelssuch as Restricted Boltzmann Machines, used to construct deeper models such as Deep Belief Networks are discussed.
Abstract: Can machine learning deliver AI? Theoretical results, inspiration from the brain and cognition, as well as machine learning experiments suggest that in order to learn the kind of complicated functions that can represent high-level abstractions (e.g. in vision, language, and other AI-level tasks), one would need deep architectures. Deep architectures are composed of multiple levels of non-linear operations, such as in neural nets with many hidden layers, graphical models with many levels of latent variables, or in complicated propositional formulae re-using many sub-formulae. Each level of the architecture represents features at a different level of abstraction, defined as a composition of lower-level features. Searching the parameter space of deep architectures is a difficult task, but new algorithms have been discovered and a new sub-area has emerged in the machine learning community since 2006, following these discoveries. Learning algorithms such as those for Deep Belief Networks and other related unsupervised learning algorithms have recently been proposed to train deep architectures, yielding exciting results and beating the state-of-the-art in certain areas. Learning Deep Architectures for AI discusses the motivations for and principles of learning algorithms for deep architectures. By analyzing and comparing recent results with different learning algorithms for deep architectures, explanations for their success are proposed and discussed, highlighting challenges and suggesting avenues for future explorations in this area.
7,767 citations
Cites methods from "Dimensionality Reduction by Learnin..."
...The same criterion had already been used successfully to learn a low-dimensional embedding with an unsupervised manifold learning algorithm [59] but is here [202] applied at one or more intermediate layer of the neural network....
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07 Dec 2015
TL;DR: A novel deep learning framework for attribute prediction in the wild that cascades two CNNs, LNet and ANet, which are fine-tuned jointly with attribute tags, but pre-trained differently.
Abstract: Predicting face attributes in the wild is challenging due to complex face variations. We propose a novel deep learning framework for attribute prediction in the wild. It cascades two CNNs, LNet and ANet, which are fine-tuned jointly with attribute tags, but pre-trained differently. LNet is pre-trained by massive general object categories for face localization, while ANet is pre-trained by massive face identities for attribute prediction. This framework not only outperforms the state-of-the-art with a large margin, but also reveals valuable facts on learning face representation. (1) It shows how the performances of face localization (LNet) and attribute prediction (ANet) can be improved by different pre-training strategies. (2) It reveals that although the filters of LNet are fine-tuned only with image-level attribute tags, their response maps over entire images have strong indication of face locations. This fact enables training LNet for face localization with only image-level annotations, but without face bounding boxes or landmarks, which are required by all attribute recognition works. (3) It also demonstrates that the high-level hidden neurons of ANet automatically discover semantic concepts after pre-training with massive face identities, and such concepts are significantly enriched after fine-tuning with attribute tags. Each attribute can be well explained with a sparse linear combination of these concepts.
6,273 citations
Cites methods from "Dimensionality Reduction by Learnin..."
...To improve intra-class invariance, we employ the similarity loss similar to [26, 10]....
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Posted Content•
TL;DR: This article proposed Momentum Contrast (MoCo) for unsupervised visual representation learning, which enables building a large and consistent dictionary on-the-fly that facilitates contrastive learning.
Abstract: We present Momentum Contrast (MoCo) for unsupervised visual representation learning. From a perspective on contrastive learning as dictionary look-up, we build a dynamic dictionary with a queue and a moving-averaged encoder. This enables building a large and consistent dictionary on-the-fly that facilitates contrastive unsupervised learning. MoCo provides competitive results under the common linear protocol on ImageNet classification. More importantly, the representations learned by MoCo transfer well to downstream tasks. MoCo can outperform its supervised pre-training counterpart in 7 detection/segmentation tasks on PASCAL VOC, COCO, and other datasets, sometimes surpassing it by large margins. This suggests that the gap between unsupervised and supervised representation learning has been largely closed in many vision tasks.
4,272 citations
Cites background from "Dimensionality Reduction by Learnin..."
...Learning is formulated as minimizing a contrastive loss [29]....
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...Contrastive losses [29] measure the similarities of sample pairs in a representation space....
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...The contrastive loss serves as an unsupervised objective function for training the encoder networks that represent the queries and keys [29]....
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...A contrastive loss [29] is a function whose value is low when q is similar to its positive key k+ and dissimilar to all other keys (considered negative keys for q)....
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...Contrastive loss functions can also be based on other forms [29, 59, 61, 36], such as margin-based losses and variants of NCE losses....
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References
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01 Jan 1998
TL;DR: In this article, a graph transformer network (GTN) is proposed for handwritten character recognition, which can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters.
Abstract: Multilayer neural networks trained with the back-propagation algorithm constitute the best example of a successful gradient based learning technique. Given an appropriate network architecture, gradient-based learning algorithms can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters, with minimal preprocessing. This paper reviews various methods applied to handwritten character recognition and compares them on a standard handwritten digit recognition task. Convolutional neural networks, which are specifically designed to deal with the variability of 2D shapes, are shown to outperform all other techniques. Real-life document recognition systems are composed of multiple modules including field extraction, segmentation recognition, and language modeling. A new learning paradigm, called graph transformer networks (GTN), allows such multimodule systems to be trained globally using gradient-based methods so as to minimize an overall performance measure. Two systems for online handwriting recognition are described. Experiments demonstrate the advantage of global training, and the flexibility of graph transformer networks. A graph transformer network for reading a bank cheque is also described. It uses convolutional neural network character recognizers combined with global training techniques to provide record accuracy on business and personal cheques. It is deployed commercially and reads several million cheques per day.
42,067 citations
Book•
01 May 1986TL;DR: In this article, the authors present a graphical representation of data using Principal Component Analysis (PCA) for time series and other non-independent data, as well as a generalization and adaptation of principal component analysis.
Abstract: Introduction * Properties of Population Principal Components * Properties of Sample Principal Components * Interpreting Principal Components: Examples * Graphical Representation of Data Using Principal Components * Choosing a Subset of Principal Components or Variables * Principal Component Analysis and Factor Analysis * Principal Components in Regression Analysis * Principal Components Used with Other Multivariate Techniques * Outlier Detection, Influential Observations and Robust Estimation * Rotation and Interpretation of Principal Components * Principal Component Analysis for Time Series and Other Non-Independent Data * Principal Component Analysis for Special Types of Data * Generalizations and Adaptations of Principal Component Analysis
17,446 citations
TL;DR: Locally linear embedding (LLE) is introduced, an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs that learns the global structure of nonlinear manifolds.
Abstract: Many areas of science depend on exploratory data analysis and visualization. The need to analyze large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact representations of high-dimensional data. Here, we introduce locally linear embedding (LLE), an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs. Unlike clustering methods for local dimensionality reduction, LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations do not involve local minima. By exploiting the local symmetries of linear reconstructions, LLE is able to learn the global structure of nonlinear manifolds, such as those generated by images of faces or documents of text.
15,106 citations
"Dimensionality Reduction by Learnin..." refers background or methods in this paper
...Recently proposed algorithms include ISOMAP (2000) by Tenenbaumet al. [1], Local Linear Embedding - LLE (2000) by Roweis and Saul [ 15 ], Laplacian Eigenmaps (2003) due to Belkin and Niyogi [2] and Hessian LLE (2003) by Donoho and Grimes [8]....
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...For example, Locally Linear Embedding (LLE) [ 15 ] linearly combines input vectors that are identified as neighbors....
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TL;DR: This work treats image segmentation as a graph partitioning problem and proposes a novel global criterion, the normalized cut, for segmenting the graph, which measures both the total dissimilarity between the different groups as well as the total similarity within the groups.
Abstract: We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We applied this approach to segmenting static images, as well as motion sequences, and found the results to be very encouraging.
13,789 citations
TL;DR: An approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set and efficiently computes a globally optimal solution, and is guaranteed to converge asymptotically to the true structure.
Abstract: Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputs-30,000 auditory nerve fibers or 10(6) optic nerve fibers-a manageably small number of perceptually relevant features. Here we describe an approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set. Unlike classical techniques such as principal component analysis (PCA) and multidimensional scaling (MDS), our approach is capable of discovering the nonlinear degrees of freedom that underlie complex natural observations, such as human handwriting or images of a face under different viewing conditions. In contrast to previous algorithms for nonlinear dimensionality reduction, ours efficiently computes a globally optimal solution, and, for an important class of data manifolds, is guaranteed to converge asymptotically to the true structure.
13,652 citations