Dimensionality Reduction via Diffusion Map Improved with Supervised Linear Projection
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Bowen Jiang, Maohao Shen
备注：
This paper is accepted to be published in the 27th IEEE International Conference on Image Processing (ICIP 2020). Two authors contribute equally to the work
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 more suitable for a Diffusion Map to do further dimensionality reduction. Numerical experiments on several benchmark datasets show that our proposed approaches are able to extract low dimensional discriminate features that could help us achieve higher classification accuracy.
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…
Most dimensionality reduction methods employ frequency domain representations obtained from matrix diagonalization and may not be efficient for large datasets with relatively high intrinsic dimensions. To address this challenge, Correlated Clustering and Projection (CCP) offers a novel data domain strategy that does not need to solve any matrix. CCP partitions high-dimensional features into correlated clusters and then projects correlated features in each cluster into a one-dimensional representation based on sample correlations. Residue-Similarity (R-S) scores and indexes, the shape of data i…
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…
School of Computing, National University of Singapore（新加坡国立大学计算机学院）；Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）
Sensor drift is a well-known issue in the field of sensors and measurement and has plagued the sensor community for many years. In this paper, we propose a sensor drift correction method to deal with the sensor drift problem. Specifically, we propose a discriminative subspace projection approach for sensor drift reduction in electronic noses. The proposed method inherits the merits of the subspace projection method called domain regularized component analysis. Moreover, the proposed method takes the source data label information into consideration, which minimizes the within-class variance of …
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…
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 …
University of Cambridge（剑桥大学）；Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）
Recent advances in machine learning allow us to analyze and describe the content of high-dimensional data like text, audio, images or other signals. In order to visualize that data in 2D or 3D, usually Dimensionality Reduction (DR) techniques are employed. Most of these techniques, e.g., PCA or t-SNE, produce static projections without taking into account corrections from humans or other data exploration scenarios. In this work, we propose the interactive Similarity Projection (iSP), a novel interactive DR framework based on similarity embeddings, where we form a differentiable objective based…
Australian National University（澳大利亚国立大学）；Amazon（亚马逊）
Self-supervised learning (SSL) aims to produce useful feature representations without access to any human-labeled data annotations. Due to the success of recent SSL methods based on contrastive learning, such as SimCLR, this problem has gained popularity. Most current contrastive learning approaches append a parametrized projection head to the end of some backbone network to optimize the InfoNCE objective and then discard the learned projection head after training. This raises a fundamental question: Why is a learnable projection head required if we are to discard it after training? In this wo…
Principal Component Analysis (PCA) is known to be the most widely applied dimensionality reduction approach. A lot of improvements have been done on the traditional PCA, in order to obtain optimal results in the dimensionality reduction of various datasets. In this paper, we present an improvement to the traditional PCA approach called Multiplicative factoring Principal Component Analysis (MPCA). The advantage of MPCA over the traditional PCA is that a penalty is imposed on the occurrence space through a multiplier to make negligible the effect of outliers in seeking out projections. Here we a…
UC Berkeley（加州大学伯克利分校）；Massachusetts Institute of Technology（麻省理工学院）
t-SNE is a popular tool for embedding multi-dimensional datasets into two or three dimensions. However, it has a large computational cost, especially when the input data has many dimensions. Many use t-SNE to embed the output of a neural network, which is generally of much lower dimension than the original data. This limits the use of t-SNE in unsupervised scenarios. We propose using \textit{random} projections to embed high dimensional datasets into relatively few dimensions, and then using t-SNE to obtain a two dimensional embedding. We show that random projections preserve the desirable clu…
Bernoulli Institute/Department of Computer Science, University of Groningen（格罗宁根大学伯努利学院/计算机科学系）；University of Groningen（格罗宁根大学）；Bernoulli Institute（伯努利学院）；Department of Computer Science（计算机科学系）；Groningen（格罗宁根）
Sharpened dimensionality reduction (SDR), which belongs to the class of multidimensional projection techniques, has recently been introduced to tackle the challenges in the exploratory and visual analysis of high-dimensional data. SDR has been applied to various real-world datasets, such as human activity sensory data and astronomical datasets. However, manually labeling the samples from the generated projection are expensive. To address this problem, we propose here to use clustering methods such as k-means, Hierarchical Clustering, Density-Based Spatial Clustering of Applications with Noise …
Remote Sensing Technology Institute（遥感技术研究所）；Helmholtz Association（亥姆霍兹联合会）；German Research Foundation (DFG)（德国研究基金会（DFG））；European Research Council (ERC)（欧洲研究委员会（ERC））；German Federal Ministry of Education and Research (BMBF)（德国联邦教育和研究部（BMBF））；AXA Research Fund（安盛研究基金）
Conventional nonlinear subspace learning techniques (e.g., manifold learning) usually introduce some drawbacks in explainability (explicit mapping) and cost-effectiveness (linearization), generalization capability (out-of-sample), and representability (spatial-spectral discrimination). To overcome these shortcomings, a novel linearized subspace analysis technique with spatial-spectral manifold alignment is developed for a semi-supervised hyperspectral dimensionality reduction (HDR), called joint and progressive subspace analysis (JPSA). The JPSA learns a high-level, semantically meaningful, jo…
A general framework for adaptive nonparametric dimensionality reduction
Seminar for Statistics, Department of Mathematics, ETH Zurich（苏黎世联邦理工学院统计研究所，数学系）；Faculty of Economics, Euler Institute, Università della Svizzera italiana（瑞士意大利大学经济学院，欧拉研究所）；Faculty of Informatics, Università della Svizzera italiana（瑞士意大利大学信息学院）；Department of Science and High Technology, University of Insubria（意大利因布里亚大学科学与高科技系）
Over the past few decades, we have witnessed a large family of algorithms that have been designed to provide different solutions to the problem of dimensionality reduction (DR). The DR is an essential tool to excavate the important information from the high-dimensional data by mapping the data to a low-dimensional subspace. Furthermore, for the diversity of varied high-dimensional data, the multi-view features can be utilized for improving the learning performance. However, many DR methods fail to integrating multiple views. Although the features from different views are extracted by different…
A fundamental question in many data analysis settings is the problem of discerning the "natural" dimension of a data set. That is, when a data set is drawn from a manifold (possibly with noise), a meaningful aspect of the data is the dimension of that manifold. Various approaches exist for estimating this dimension, such as the method of Secant-Avoidance Projection (SAP). Intuitively, the SAP algorithm seeks to determine a projection which best preserves the lengths of all secants between points in a data set; by applying the algorithm to find the best projections to vector spaces of various d…
Dimensionality-reduction techniques are a fundamental tool for extracting useful information from high-dimensional data sets. Because secant sets encode manifold geometry, they are a useful tool for designing meaningful data-reduction algorithms. In one such approach, the goal is to construct a projection that maximally avoids secant directions and hence ensures that distinct data points are not mapped too close together in the reduced space. This type of algorithm is based on a mathematical framework inspired by the constructive proof of Whitney's embedding theorem from differential topology.…
Self-Supervised Coordinate Projection Network for Sparse-View Computed Tomography
ShanghaiTech University（上海科技大学）；Shanghai Advanced Research Institute, Chinese Academy of Sciences（中国科学院上海高等研究院）；University of Chinese Academy of Sciences（中国科学院大学）；Shanghai Jiao Tong University（上海交通大学）
Low-dose computed tomography (LDCT) became a clear trend in radiology with an aspiration to refrain from delivering excessive X-ray radiation to the patients. The reduction of the radiation dose decreases the risks to the patients but raises the noise level, affecting the quality of the images and their ultimate diagnostic value. One mitigation option is to consider pairs of low-dose and high-dose CT projections to train a denoising model using deep learning algorithms; however, such pairs are rarely available in practice. In this paper, we present a new self-supervised method for CT denoising…
In the intention of minimizing excessive X-ray radiation administration to patients, low-dose computed tomography (LDCT) has become a distinct trend in radiology. However, while lowering the radiation dose reduces the risk to the patient, it also increases noise and artifacts, compromising image quality and clinical diagnosis. In most supervised learning methods, paired CT images are required, but such images are unlikely to be available in the clinic. We present a self-supervised learning model (Noise2Projection) that fully exploits the raw projection images to reduce noise and improve the qu…
