We present a general framework of semi-supervised dimensionality reduction for manifold learning which naturally generalizes existing supervised and unsupervised learning frameworks which apply the spectral decomposition. Algorithms derived under our framework are able to employ both labeled and unlabeled examples and are able to handle complex problems where data form separate clusters of manifolds. Our framework offers simple views, explains relationships among existing frameworks and provides further extensions which can improve existing algorithms. Furthermore, a new semi-supervised kernelization framework called ``KPCA trick'' is proposed to handle non-linear problems.
Semi-supervised learning (SSL) has recently received increased attention from machine learning researchers. By enabling effective propagation of known labels in graph-based deep learning (GDL) algorithms, SSL is poised to become an increasingly used technique in GDL in the coming years. However, there are currently few explorations in the graph-based SSL literature on exploiting classical dimensionality reduction techniques for improved label propagation. In this work, we investigate the use of dimensionality reduction techniques such as PCA, t-SNE, and UMAP to see their effect on the performa…
We show how to incorporate information from labeled examples into nonnegative matrix factorization (NMF), a popular unsupervised learning algorithm for dimensionality reduction. In addition to mapping the data into a space of lower dimensionality, our approach aims to preserve the nonnegative components of the data that are important for classification. We identify these components from the support vectors of large-margin classifiers and derive iterative updates to preserve them in a semi-supervised version of NMF. These updates have a simple multiplicative form like their unsupervised counter…
In our work, we propose a novel formulation for supervised dimensionality reduction based on a nonlinear dependency criterion called Statistical Distance Correlation, Szekely et. al. (2007). We propose an objective which is free of distributional assumptions on regression variables and regression model assumptions. Our proposed formulation is based on learning a low-dimensional feature representation $\mathbf{z}$, which maximizes the squared sum of Distance Correlations between low dimensional features $\mathbf{z}$ and response $y$, and also between features $\mathbf{z}$ and covariates $\mathb…
Huazhong University of Science and Technology（华中科技大学）；University of Technology Sydney（悉尼科技大学）
Dimensionality reduction is an important operation in information visualization, feature extraction, clustering, regression, and classification, especially for processing noisy high dimensional data. However, most existing approaches preserve either the global or the local structure of the data, but not both. Approaches that preserve only the global data structure, such as principal component analysis (PCA), are usually sensitive to outliers. Approaches that preserve only the local data structure, such as locality preserving projections, are usually unsupervised (and hence cannot use label inf…
LDReg: Local Dimensionality Regularized Self-Supervised Learning
School of Computing and Information Systems, The University of Melbourne（墨尔本大学计算与信息系统学院）；University of Southern Denmark（南丹麦大学）；School of Computer Science, Fudan University（复旦大学计算机科学学院）；New Jersey Institute of Technology（新泽西理工学院）
Supervised dimensionality reduction strategies have been of great interest. However, current supervised dimensionality reduction approaches are difficult to scale for situations characterized by large datasets given the high computational complexities associated with such methods. While stochastic approximation strategies have been explored for unsupervised dimensionality reduction to tackle this challenge, such approaches are not well-suited for accelerating computational speed for supervised dimensionality reduction. Motivated to tackle this challenge, in this study we explore a novel direct…
UiT The Arctic University of Norway（挪威北极大学）；Universidad Rey Juan Carlos（胡安·卡洛斯国王大学）
Noisy labeled data represent a rich source of information that often are easily accessible and cheap to obtain, but label noise might also have many negative consequences if not accounted for. How to fully utilize noisy labels has been studied extensively within the framework of standard supervised machine learning over a period of several decades. However, very little research has been conducted on solving the challenge posed by noisy labels in non-standard settings. This includes situations where only a fraction of the samples are labeled (semi-supervised) and each high-dimensional sample is…
The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a Convolutional Autoencoder for dimensionality reduction and a classifier composed by a Fully Connected Network, are combined to simultaneously produce supervised dimensionality reduction and predictions. It turned out that this methodology can also be greatly beneficial in enforcing explainability of deep learning architectures. Additionally, the resulting La…
As annotations of data can be scarce in large-scale practical problems, leveraging unlabelled examples is one of the most important aspects of machine learning. This is the aim of semi-supervised learning. To benefit from the access to unlabelled data, it is natural to diffuse smoothly knowledge of labelled data to unlabelled one. This induces to the use of Laplacian regularization. Yet, current implementations of Laplacian regularization suffer from several drawbacks, notably the well-known curse of dimensionality. In this paper, we provide a statistical analysis to overcome those issues, and…
With the abundance of industrial datasets, imbalanced classification has become a common problem in several application domains. Oversampling is an effective method to solve imbalanced classification. One of the main challenges of the existing oversampling methods is to accurately label the new synthetic samples. Inaccurate labels of the synthetic samples would distort the distribution of the dataset and possibly worsen the classification performance. This paper introduces the idea of weakly supervised learning to handle the inaccurate labeling of synthetic samples caused by traditional oversa…
University of Tsukuba（筑波大学）；JST/CREST（日本科学技术振兴机构/核心研究集群）
Spectral dimensionality reduction methods enable linear separations of complex data with high-dimensional features in a reduced space. However, these methods do not always give the desired results due to irregularities or uncertainties of the data. Thus, we consider aggressively modifying the scales of the features to obtain the desired classification. Using prior knowledge on the labels of partial samples to specify the Fiedler vector, we formulate an eigenvalue problem of a linear matrix pencil whose eigenvector has the feature scaling factors. The resulting factors can modify the features o…
Faculty of Mathematics and Physics of Charles University（查理大学数学与物理学院）；Luxembourg Centre for Systems Biomedicine, University of Luxembourg（卢森堡大学卢森堡系统生物医学中心）；Institute of Haematology and Blood Transfusion（血液学与输血研究所）；Institute of Organic Chemistry and Biochemistry（有机化学与生物化学研究所）
Dimensionality reduction methods have found vast application as visualization tools in diverse areas of science. Although many different methods exist, their performance is often insufficient for providing quick insight into many contemporary datasets, and the unsupervised mode of use prevents the users from utilizing the methods for dataset exploration and fine-tuning the details for improved visualization quality. We present BlosSOM, a high-performance semi-supervised dimensionality reduction software for interactive user-steerable visualization of high-dimensional datasets with millions of …
Florida Institute of Technology（佛罗里达理工学院）；University of Florida（佛罗里达大学）
Supervised dimensionality reduction has emerged as an important theme in the last decade. Despite the plethora of models and formulations, there is a lack of a simple model which aims to project the set of patterns into a space defined by the classes (or categories). To this end, we set up a model in which each class is represented as a 1D subspace of the vector space formed by the features. Assuming the set of classes does not exceed the cardinality of the features, the model results in multi-class supervised learning in which the features of each class are projected into the class subspace. …
Thanks to their versatility, ease of deployment and high-performance, surrogate models have become staple tools in the arsenal of uncertainty quantification (UQ). From local interpolants to global spectral decompositions, surrogates are characterised by their ability to efficiently emulate complex computational models based on a small set of model runs used for training. An inherent limitation of many surrogate models is their susceptibility to the curse of dimensionality, which traditionally limits their applicability to a maximum of $\mathcal{O}(10^2)$ input dimensions. We present a novel ap…
Indian Institute of Technology, Kharagpur（印度理工学院卡拉格普尔分校）
Hyperspectral images (HSI) contain a wealth of information over hundreds of contiguous spectral bands, making it possible to classify materials through subtle spectral discrepancies. However, the classification of this rich spectral information is accompanied by the challenges like high dimensionality, singularity, limited training samples, lack of labeled data samples, heteroscedasticity and nonlinearity. To address these challenges, we propose a semi-supervised graph based dimensionality reduction method named `semi-supervised spatial spectral regularized manifold local scaling cut' (S3RMLSC…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying smooth manifold, and define intra-class and inter-class similarities using pairwise local kernel distances. We aim to find a linear projection to maximize the intra-class similarities and minimize the inter-class similarities simultaneously, so that the projected low dimensional data has optimized pairwise distances based on the label information, which is mor…
Technical University of Crete（克里特技术大学）；National Technical University of Athens（雅典国家技术大学）；University of West Attica（西阿提卡大学）
In this work we propose a method for reducing the dimensionality of tensor objects in a binary classification framework. The proposed Common Mode Patterns method takes into consideration the labels' information, and ensures that tensor objects that belong to different classes do not share common features after the reduction of their dimensionality. We experimentally validate the proposed supervised subspace learning technique and compared it against Multilinear Principal Component Analysis using a publicly available hyperspectral imaging dataset. Experimental results indicate that the proposed…
This paper discusses the critical decision process of extracting or selecting the features in a supervised learning context. It is often confusing to find a suitable method to reduce dimensionality. There are pros and cons to deciding between a feature selection and feature extraction according to the data's nature and the user's preferences. Indeed, the user may want to emphasize the results toward integrity or interpretability and a specific data resolution. This paper proposes a new method to choose the best dimensionality reduction method in a supervised learning context. It also helps to …
Visualizing high-dimensional data is an essential task in Data Science and Machine Learning. The Centroid-Encoder (CE) method is similar to the autoencoder but incorporates label information to keep objects of a class close together in the reduced visualization space. CE exploits nonlinearity and labels to encode high variance in low dimensions while capturing the global structure of the data. We present a detailed analysis of the method using a wide variety of data sets and compare it with other supervised dimension reduction techniques, including NCA, nonlinear NCA, t-distributed NCA, t-dist…
University of São Paulo（圣保罗大学）；Advanced Institute for Artificial Intelligence (AI2)（高级人工智能研究所）；Experian DataLab LatAm（益百利拉丁美洲数据实验室）
In supervised learning, training and test datasets are often sampled from distinct distributions. Domain adaptation techniques are thus required. Covariate shift adaptation yields good generalization performance when domains differ only by the marginal distribution of features. Covariate shift adaptation is usually implemented using importance weighting, which may fail, according to common wisdom, due to small effective sample sizes (ESS). Previous research argues this scenario is more common in high-dimensional settings. However, how effective sample size, dimensionality, and model performanc…
Explicitly or implicitly, most of dimensionality reduction methods need to determine which samples are neighbors and the similarity between the neighbors in the original highdimensional space. The projection matrix is then learned on the assumption that the neighborhood information (e.g., the similarity) is known and fixed prior to learning. However, it is difficult to precisely measure the intrinsic similarity of samples in high-dimensional space because of the curse of dimensionality. Consequently, the neighbors selected according to such similarity might and the projection matrix obtained a…
Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on large k-NN graphs or complicated optimization solvers. On the other hand, self-supervised learning approaches, typically used to learn representations from scratch, rely on simple and more scalable frameworks for learning. In this paper, we propose TLDR, a dimensionality reduction method for generic input spaces that is porting the recent self-supervised lear…
The most effective dimensionality reduction procedures produce interpretable features from the raw input space while also providing good performance for downstream supervised learning tasks. For many methods, this requires optimizing one or more hyperparameters for a specific task, which can limit generalizability. In this study we propose sparse compressed agglomeration (SparCA), a novel dimensionality reduction procedure that involves a multistep hierarchical feature grouping, compression, and feature selection process. We demonstrate the characteristics and performance of the SparCA method …
In this paper we introduce and analyze the learning scenario of \emph{coupled nonlinear dimensionality reduction}, which combines two major steps of machine learning pipeline: projection onto a manifold and subsequent supervised learning. First, we present new generalization bounds for this scenario and, second, we introduce an algorithm that follows from these bounds. The generalization error bound is based on a careful analysis of the empirical Rademacher complexity of the relevant hypothesis set. In particular, we show an upper bound on the Rademacher complexity that is in $\widetilde O(\sq…
Utah State University（犹他州立大学）；Université de Montréal（蒙特利尔大学）
Dimensionality reduction is often used as an initial step in data exploration, either as preprocessing for classification or regression or for visualization. Most dimensionality reduction techniques to date are unsupervised; they do not take class labels into account (e.g., PCA, MDS, t-SNE, Isomap). Such methods require large amounts of data and are often sensitive to noise that may obfuscate important patterns in the data. Various attempts at supervised dimensionality reduction methods that take into account auxiliary annotations (e.g., class labels) have been successfully implemented with go…
The Ohio State University（俄亥俄州立大学）；New York University（纽约大学）
Given labeled points in a high-dimensional vector space, we seek a low-dimensional subspace such that projecting onto this subspace maintains some prescribed distance between points of differing labels. Intended applications include compressive classification. Taking inspiration from large margin nearest neighbor classification, this paper introduces a semidefinite relaxation of this problem. Unlike its predecessors, this relaxation is amenable to theoretical analysis, allowing us to provably recover a planted projection operator from the data.
In machine learning or statistics, it is often desirable to reduce the dimensionality of a sample of data points in a high dimensional space $\mathbb{R}^d$. This paper introduces a dimensionality reduction method where the embedding coordinates are the eigenvectors of a positive semi-definite kernel obtained as the solution of an infinite dimensional analogue of a semi-definite program. This embedding is adaptive and non-linear. We discuss this problem both with weak and strong smoothness assumptions about the learned kernel. A main feature of our approach is the existence of an out-of-sample …
In this paper we present a new approach to solve semi-supervised classification tasks for biomedical applications, involving a supervised autoencoder network. We create a network architecture that encodes labels into the latent space of an autoencoder, and define a global criterion combining classification and reconstruction losses. We train the Semi-Supervised AutoEncoder (SSAE) on labelled data using a double descent algorithm. Then, we classify unlabelled samples using the learned network thanks to a softmax classifier applied to the latent space which provides a classification confidence s…
We study semi-supervised learning (SSL) for vision transformers (ViT), an under-explored topic despite the wide adoption of the ViT architectures to different tasks. To tackle this problem, we propose a new SSL pipeline, consisting of first un/self-supervised pre-training, followed by supervised fine-tuning, and finally semi-supervised fine-tuning. At the semi-supervised fine-tuning stage, we adopt an exponential moving average (EMA)-Teacher framework instead of the popular FixMatch, since the former is more stable and delivers higher accuracy for semi-supervised vision transformers. In additi…
Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）
Dimensionality reduction (DR) is a popular method for preparing and analyzing high-dimensional data. Reduced data representations are less computationally intensive and easier to manage and visualize, while retaining a significant percentage of their original information. Aside from these advantages, these reduced representations can be difficult or impossible to interpret in most circumstances, especially when the DR approach does not provide further information about which features of the original space led to their construction. This problem is addressed by Interpretable Machine Learning, a…
Large amounts of labeled data are typically required to train deep learning models. For many real-world problems, however, acquiring additional data can be expensive or even impossible. We present semi-supervised deep kernel learning (SSDKL), a semi-supervised regression model based on minimizing predictive variance in the posterior regularization framework. SSDKL combines the hierarchical representation learning of neural networks with the probabilistic modeling capabilities of Gaussian processes. By leveraging unlabeled data, we show improvements on a diverse set of real-world regression tas…
We present a plug-in replacement for batch normalization (BN) called exponential moving average normalization (EMAN), which improves the performance of existing student-teacher based self- and semi-supervised learning techniques. Unlike the standard BN, where the statistics are computed within each batch, EMAN, used in the teacher, updates its statistics by exponential moving average from the BN statistics of the student. This design reduces the intrinsic cross-sample dependency of BN and enhances the generalization of the teacher. EMAN improves strong baselines for self-supervised learning by…
Ariel University（阿里埃勒大学）；Ben-Gurion University of the Negev（内盖夫本-古里安大学）；Weizmann Institute of Science（魏茨曼科学研究所）
We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are doubling, or nearly doubling. On the algorithmic front, we describe an analogue of PCA for metric spaces: namely an efficient procedure that approximates the data's intrinsic dimension, which is often much lower than the ambient dimension. Our approach thus leverages the dual benefits of low dimensionality: (1) more efficient algorithms, e.g., for proximity search, …
This work tackles the problem of semi-supervised learning of image classifiers. Our main insight is that the field of semi-supervised learning can benefit from the quickly advancing field of self-supervised visual representation learning. Unifying these two approaches, we propose the framework of self-supervised semi-supervised learning and use it to derive two novel semi-supervised image classification methods. We demonstrate the effectiveness of these methods in comparison to both carefully tuned baselines, and existing semi-supervised learning methods. We then show that our approach and exi…
This is a tutorial and survey paper on unification of spectral dimensionality reduction methods, kernel learning by Semidefinite Programming (SDP), Maximum Variance Unfolding (MVU) or Semidefinite Embedding (SDE), and its variants. We first explain how the spectral dimensionality reduction methods can be unified as kernel Principal Component Analysis (PCA) with different kernels. This unification can be interpreted as eigenfunction learning or representation of kernel in terms of distance matrix. Then, since the spectral methods are unified as kernel PCA, we say let us learn the best kernel fo…
Semi-supervised learning, which has emerged from the beginning of this century, is a new type of learning method between traditional supervised learning and unsupervised learning. The main idea of semi-supervised learning is to introduce unlabeled samples into the model training process to avoid performance (or model) degeneration due to insufficiency of labeled samples. Semi-supervised learning has been applied successfully in many fields. This paper reviews the development process and main theories of semi-supervised learning, as well as its recent advances and importance in solving real-wor…
University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Nanyang Technological University（南洋理工大学）
Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method that learns linear embeddings jointly for two feature vectors representing data of different modalities or data from distinct types of entities. We also propose an efficient feature selection method that complements, and can be applied prior to, our joint dimensionality reduction method. Assuming that there exist true linear embeddings for these features, our a…
Irregular features disrupt the desired classification. In this paper, we consider aggressively modifying scales of features in the original space according to the label information to form well-separated clusters in low-dimensional space. The proposed method exploits spectral clustering to derive scaling factors that are used to modify the features. Specifically, we reformulate the Laplacian eigenproblem of the spectral clustering as an eigenproblem of a linear matrix pencil whose eigenvector has the scaling factors. Numerical experiments show that the proposed method outperforms well-establis…
We present local discriminative Gaussian (LDG) dimensionality reduction, a supervised dimensionality reduction technique for classification. The LDG objective function is an approximation to the leave-one-out training error of a local quadratic discriminant analysis classifier, and thus acts locally to each training point in order to find a mapping where similar data can be discriminated from dissimilar data. While other state-of-the-art linear dimensionality reduction methods require gradient descent or iterative solution approaches, LDG is solved with a single eigen-decomposition. Thus, it s…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；US Army Research Laboratory（美国陆军研究实验室）
This paper presents a semi-supervised learning framework that is new in being designed for automatic modulation classification (AMC). By carefully utilizing unlabeled signal data with a self-supervised contrastive-learning pre-training step, our framework achieves higher performance given smaller amounts of labeled data, thereby largely reducing the labeling burden of deep learning. We evaluate the performance of our semi-supervised framework on a public dataset. The evaluation results demonstrate that our semi-supervised approach significantly outperforms supervised frameworks thereby substan…
We present a new flavor of Variational Autoencoder (VAE) that interpolates seamlessly between unsupervised, semi-supervised and fully supervised learning domains. We show that unlabeled datapoints not only boost unsupervised tasks, but also the classification performance. Vice versa, every label not only improves classification, but also unsupervised tasks. The proposed architecture is simple: A classification layer is connected to the topmost encoder layer, and then combined with the resampled latent layer for the decoder. The usual evidence lower bound (ELBO) loss is supplemented with a supe…
We introduce semi-supervised data classification algorithms based on total variation (TV), Reproducing Kernel Hilbert Space (RKHS), support vector machine (SVM), Cheeger cut, labeled and unlabeled data points. We design binary and multi-class semi-supervised classification algorithms. We compare the TV-based classification algorithms with the related Laplacian-based algorithms, and show that TV classification perform significantly better when the number of labeled data is small.
LMU Munich（慕尼黑大学）；Fraunhofer Institute for Integrated Circuits (IIS)（弗劳恩霍夫集成电路研究所）
While Semi-supervised learning has gained much attention in computer vision on image data, yet limited research exists on its applicability in the time series domain. In this work, we investigate the transferability of state-of-the-art deep semi-supervised models from image to time series classification. We discuss the necessary model adaptations, in particular an appropriate model backbone architecture and the use of tailored data augmentation strategies. Based on these adaptations, we explore the potential of deep semi-supervised learning in the context of time series classification by evalu…
UC Santa Barbara（加州大学圣巴巴拉分校）；Lawrence Berkeley National Lab（劳伦斯伯克利国家实验室）
We summarize the model and results of PirouNet, a semi-supervised recurrent variational autoencoder. Given a small amount of dance sequences labeled with qualitative choreographic annotations, PirouNet conditionally generates dance sequences in the style of the choreographer.
AI Foundations, IBM Research（IBM研究院人工智能基础部）；IBM T.J Watson Research Center（IBM托马斯·J·沃森研究中心）
We propose discriminative adversarial networks (DAN) for semi-supervised learning and loss function learning. Our DAN approach builds upon generative adversarial networks (GANs) and conditional GANs but includes the key differentiator of using two discriminators instead of a generator and a discriminator. DAN can be seen as a framework to learn loss functions for predictors that also implements semi-supervised learning in a straightforward manner. We propose instantiations of DAN for two different prediction tasks: classification and ranking. Our experimental results on three datasets of diffe…
