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1.
Artigo em Inglês | MEDLINE | ID: mdl-38556038

RESUMO

BACKGROUND: Although regional wall motion abnormality (RWMA) detection is foundational to transthoracic echocardiography, current methods are prone to interobserver variability. We aimed to develop a deep learning (DL) model for RWMA assessment and compare it to expert and novice readers. METHODS: We used 15,746 transthoracic echocardiography studies-including 25,529 apical videos-which were split into training, validation, and test datasets. A convolutional neural network was trained and validated using apical 2-, 3-, and 4-chamber videos to predict the presence of RWMA in 7 regions defined by coronary perfusion territories, using the ground truth derived from clinical transthoracic echocardiography reports. Within the test cohort, DL model accuracy was compared to 6 expert and 3 novice readers using F1 score evaluation, with the ground truth of RWMA defined by expert readers. Significance between the DL model and novices was assessed using the permutation test. RESULTS: Within the test cohort, the DL model accurately identified any RWMA with an area under the curve of 0.96 (0.92-0.98). The mean F1 scores of the experts and the DL model were numerically similar for 6 of 7 regions: anterior (86 vs 84), anterolateral (80 vs 74), inferolateral (83 vs 87), inferoseptal (86 vs 86), apical (88 vs 87), inferior (79 vs 81), and any RWMA (90 vs 94), respectively, while in the anteroseptal region, the F1 score of the DL model was lower than the experts (75 vs 89). Using F1 scores, the DL model outperformed both novices 1 (P = .002) and 2 (P = .02) for the detection of any RWMA. CONCLUSIONS: Deep learning provides accurate detection of RWMA, which was comparable to experts and outperformed a majority of novices. Deep learning may improve the efficiency of RWMA assessment and serve as a teaching tool for novices.

2.
Med Phys ; 51(5): 3555-3565, 2024 May.
Artigo em Inglês | MEDLINE | ID: mdl-38167996

RESUMO

BACKGROUND: Magnetic Resonance acquisition is a time consuming process, making it susceptible to patient motion during scanning. Even motion in the order of a millimeter can introduce severe blurring and ghosting artifacts, potentially necessitating re-acquisition. Magnetic Resonance Imaging (MRI) can be accelerated by acquiring only a fraction of k-space, combined with advanced reconstruction techniques leveraging coil sensitivity profiles and prior knowledge. Artificial intelligence (AI)-based reconstruction techniques have recently been popularized, but generally assume an ideal setting without intra-scan motion. PURPOSE: To retrospectively detect and quantify the severity of motion artifacts in undersampled MRI data. This may prove valuable as a safety mechanism for AI-based approaches, provide useful information to the reconstruction method, or prompt for re-acquisition while the patient is still in the scanner. METHODS: We developed a deep learning approach that detects and quantifies motion artifacts in undersampled brain MRI. We demonstrate that synthetically motion-corrupted data can be leveraged to train the convolutional neural network (CNN)-based motion artifact estimator, generalizing well to real-world data. Additionally, we leverage the motion artifact estimator by using it as a selector for a motion-robust reconstruction model in case a considerable amount of motion was detected, and a high data consistency model otherwise. RESULTS: Training and validation were performed on 4387 and 1304 synthetically motion-corrupted images and their uncorrupted counterparts, respectively. Testing was performed on undersampled in vivo motion-corrupted data from 28 volunteers, where our model distinguished head motion from motion-free scans with 91% and 96% accuracy when trained on synthetic and on real data, respectively. It predicted a manually defined quality label ('Good', 'Medium' or 'Bad' quality) correctly in 76% and 85% of the time when trained on synthetic and real data, respectively. When used as a selector it selected the appropriate reconstruction network 93% of the time, achieving near optimal SSIM values. CONCLUSIONS: The proposed method quantified motion artifact severity in undersampled MRI data with high accuracy, enabling real-time motion artifact detection that can help improve the safety and quality of AI-based reconstructions.


Assuntos
Artefatos , Processamento de Imagem Assistida por Computador , Imageamento por Ressonância Magnética , Movimento , Imageamento por Ressonância Magnética/métodos , Processamento de Imagem Assistida por Computador/métodos , Humanos , Inteligência Artificial , Encéfalo/diagnóstico por imagem , Aprendizado Profundo
3.
IEEE Trans Vis Comput Graph ; 30(1): 164-174, 2024 Jan.
Artigo em Inglês | MEDLINE | ID: mdl-37874722

RESUMO

Data features and class probabilities are two main perspectives when, e.g., evaluating model results and identifying problematic items. Class probabilities represent the likelihood that each instance belongs to a particular class, which can be produced by probabilistic classifiers or even human labeling with uncertainty. Since both perspectives are multi-dimensional data, dimensionality reduction (DR) techniques are commonly used to extract informative characteristics from them. However, existing methods either focus solely on the data feature perspective or rely on class probability estimates to guide the DR process. In contrast to previous work where separate views are linked to conduct the analysis, we propose a novel approach, class-constrained t-SNE, that combines data features and class probabilities in the same DR result. Specifically, we combine them by balancing two corresponding components in a cost function to optimize the positions of data points and iconic representation of classes - class landmarks. Furthermore, an interactive user-adjustable parameter balances these two components so that users can focus on the weighted perspectives of interest and also empowers a smooth visual transition between varying perspectives to preserve the mental map. We illustrate its application potential in model evaluation and visual-interactive labeling. A comparative analysis is performed to evaluate the DR results.

4.
Artigo em Inglês | MEDLINE | ID: mdl-37535493

RESUMO

Deep learning (DL) models have shown performance benefits across many applications, from classification to image-to-image translation. However, low interpretability often leads to unexpected model behavior once deployed in the real world. Usually, this unexpected behavior is because the training data domain does not reflect the deployment data domain. Identifying a model's breaking points under input conditions and domain shifts, i.e., input transformations, is essential to improve models. Although visual analytics (VA) has shown promise in studying the behavior of model outputs under continually varying inputs, existing methods mainly focus on per-class or instance-level analysis. We aim to generalize beyond classification where classes do not exist and provide a global view of model behavior under co-occurring input transformations. We present a DL model-agnostic VA method (ProactiV) to help model developers proactively study output behavior under input transformations to identify and verify breaking points. ProactiV relies on a proposed input optimization method to determine the changes to a given transformed input to achieve the desired output. The data from this optimization process allows the study of global and local model behavior under input transformations at scale. Additionally, the optimization method provides insights into the input characteristics that result in desired outputs and helps recognize model biases. We highlight how ProactiV effectively supports studying model behavior with example classification and image-to-image translation tasks.

5.
Sensors (Basel) ; 23(3)2023 Jan 19.
Artigo em Inglês | MEDLINE | ID: mdl-36772208

RESUMO

Modeling and representing 3D shapes of the human body and face is a prominent field due to its applications in the healthcare, clothes, and movie industry. In our work, we tackled the problem of 3D face and body synthesis by reducing 3D meshes to 2D image representations. We show that the face can naturally be modeled on a 2D grid. At the same time, for more challenging 3D body geometries, we proposed a novel non-bijective 3D-2D conversion method representing the 3D body mesh as a plurality of rendered projections on the 2D grid. Then, we trained a state-of-the-art vector-quantized variational autoencoder (VQ-VAE-2) to learn a latent representation of 2D images and fit a PixelSNAIL autoregressive model to sample novel synthetic meshes. We evaluated our method versus a classical one based on principal component analysis (PCA) by sampling from the empirical cumulative distribution of the PCA scores. We used the empirical distributions of two commonly used metrics, specificity and diversity, to quantitatively demonstrate that the synthetic faces generated with our method are statistically closer to real faces when compared with the PCA ones. Our experiment on the 3D body geometry requires further research to match the test set statistics but shows promising results.

6.
Artigo em Inglês | MEDLINE | ID: mdl-36327191

RESUMO

In recent years, visual analytics (VA) has shown promise in alleviating the challenges of interpreting black-box deep learning (DL) models. While the focus of VA for explainable DL has been mainly on classification problems, DL is gaining popularity in high-dimensional-to-high-dimensional (H-H) problems such as image-to-image translation. In contrast to classification, H-H problems have no explicit instance groups or classes to study. Each output is continuous, high-dimensional, and changes in an unknown non-linear manner with changes in the input. These unknown relations between the input, model and output necessitate the user to analyze them in conjunction, leveraging symmetries between them. Since classification tasks do not exhibit some of these challenges, most existing VA systems and frameworks allow limited control of the components required to analyze models beyond classification. Hence, we identify the need for and present a unified conceptual framework, the Transform-and-Perform framework (T&P), to facilitate the design of VA systems for DL model analysis focusing on H-H problems. T&P provides a checklist to structure and identify workflows and analysis strategies to design new VA systems, and understand existing ones to uncover potential gaps for improvements. The goal is to aid the creation of effective VA systems that support the structuring of model understanding and identifying actionable insights for model improvements. We highlight the growing need for new frameworks like T&P with a real-world image-to-image translation application. We illustrate how T&P effectively supports the understanding and identification of potential gaps in existing VA systems.

7.
Nat Immunol ; 22(5): 654-665, 2021 05.
Artigo em Inglês | MEDLINE | ID: mdl-33888898

RESUMO

Controlled human infections provide opportunities to study the interaction between the immune system and malaria parasites, which is essential for vaccine development. Here, we compared immune signatures of malaria-naive Europeans and of Africans with lifelong malaria exposure using mass cytometry, RNA sequencing and data integration, before and 5 and 11 days after venous inoculation with Plasmodium falciparum sporozoites. We observed differences in immune cell populations, antigen-specific responses and gene expression profiles between Europeans and Africans and among Africans with differing degrees of immunity. Before inoculation, an activated/differentiated state of both innate and adaptive cells, including elevated CD161+CD4+ T cells and interferon-γ production, predicted Africans capable of controlling parasitemia. After inoculation, the rapidity of the transcriptional response and clusters of CD4+ T cells, plasmacytoid dendritic cells and innate T cells were among the features distinguishing Africans capable of controlling parasitemia from susceptible individuals. These findings can guide the development of a vaccine effective in malaria-endemic regions.


Assuntos
Imunidade Adaptativa/imunologia , Suscetibilidade a Doenças/imunologia , Malária Falciparum/imunologia , Plasmodium falciparum/imunologia , Imunidade Adaptativa/genética , Adolescente , Adulto , Anticorpos Antiprotozoários/sangue , Anticorpos Antiprotozoários/imunologia , Antígenos de Protozoários/imunologia , População Negra/genética , Células Dendríticas/imunologia , Suscetibilidade a Doenças/sangue , Suscetibilidade a Doenças/parasitologia , Feminino , Voluntários Saudáveis , Interações Hospedeiro-Parasita/genética , Interações Hospedeiro-Parasita/imunologia , Humanos , Imunidade Inata/genética , Imunidade Inata/imunologia , Interferon gama/metabolismo , Malária Falciparum/sangue , Malária Falciparum/parasitologia , Masculino , RNA-Seq , Análise de Sistemas , Linfócitos T/imunologia , Linfócitos T/metabolismo , População Branca/genética , Adulto Jovem
8.
IEEE Trans Vis Comput Graph ; 26(1): 1172-1181, 2020 Jan.
Artigo em Inglês | MEDLINE | ID: mdl-31449023

RESUMO

In recent years the t-distributed Stochastic Neighbor Embedding (t-SNE) algorithm has become one of the most used and insightful techniques for exploratory data analysis of high-dimensional data. It reveals clusters of high-dimensional data points at different scales while only requiring minimal tuning of its parameters. However, the computational complexity of the algorithm limits its application to relatively small datasets. To address this problem, several evolutions of t-SNE have been developed in recent years, mainly focusing on the scalability of the similarity computations between data points. However, these contributions are insufficient to achieve interactive rates when visualizing the evolution of the t-SNE embedding for large datasets. In this work, we present a novel approach to the minimization of the t-SNE objective function that heavily relies on graphics hardware and has linear computational complexity. Our technique decreases the computational cost of running t-SNE on datasets by orders of magnitude and retains or improves on the accuracy of past approximated techniques. We propose to approximate the repulsive forces between data points by splatting kernel textures for each data point. This approximation allows us to reformulate the t-SNE minimization problem as a series of tensor operations that can be efficiently executed on the graphics card. An efficient implementation of our technique is integrated and available for use in the widely used Google TensorFlow.js, and an open-source C++ library.

9.
PLoS One ; 13(8): e0200818, 2018.
Artigo em Inglês | MEDLINE | ID: mdl-30089176

RESUMO

Auto-reactive CD8 T-cells play an important role in the destruction of pancreatic ß-cells resulting in type 1 diabetes (T1D). However, the phenotype of these auto-reactive cytolytic CD8 T-cells has not yet been extensively described. We used high-dimensional mass cytometry to phenotype autoantigen- (pre-proinsulin), neoantigen- (insulin-DRIP) and virus- (cytomegalovirus) reactive CD8 T-cells in peripheral blood mononuclear cells (PBMCs) of T1D patients. A panel of 33 monoclonal antibodies was designed to further characterise these cells at the single-cell level. HLA-A2 class I tetramers were used for the detection of antigen-specific CD8 T-cells. Using a novel Hierarchical Stochastic Neighbor Embedding (HSNE) tool (implemented in Cytosplore), we identified 42 clusters within the CD8 T-cell compartment of three T1D patients and revealed profound heterogeneity between individuals, as each patient displayed a distinct cluster distribution. Single-cell analysis of pre-proinsulin, insulin-DRIP and cytomegalovirus-specific CD8 T-cells showed that the detected specificities were heterogeneous between and within patients. These findings emphasize the challenge to define the obscure nature of auto-reactive CD8 T-cells.


Assuntos
Linfócitos T CD8-Positivos/citologia , Diabetes Mellitus Tipo 1/imunologia , Adulto , Autoantígenos/imunologia , Biomarcadores/sangue , Linfócitos T CD8-Positivos/imunologia , Linfócitos T CD8-Positivos/fisiologia , Feminino , Antígeno HLA-A2/imunologia , Humanos , Células Secretoras de Insulina/imunologia , Leucócitos Mononucleares/imunologia , Masculino , Fenótipo , Análise de Célula Única/métodos
10.
J Exp Med ; 215(5): 1383-1396, 2018 05 07.
Artigo em Inglês | MEDLINE | ID: mdl-29511064

RESUMO

Innate lymphoid cells (ILCs) are abundant in mucosal tissues and involved in tissue homeostasis and barrier function. Although several ILC subsets have been identified, it is unknown if additional heterogeneity exists, and their differentiation pathways remain largely unclear. We applied mass cytometry to analyze ILCs in the human fetal intestine and distinguished 34 distinct clusters through a t-SNE-based analysis. A lineage (Lin)-CD7+CD127-CD45RO+CD56+ population clustered between the CD127+ ILC and natural killer (NK) cell subsets, and expressed diverse levels of Eomes, T-bet, GATA3, and RORγt. By visualizing the dynamics of the t-SNE computation, we identified smooth phenotypic transitions from cells within the Lin-CD7+CD127-CD45RO+CD56+ cluster to both the NK cells and CD127+ ILCs, revealing potential differentiation trajectories. In functional differentiation assays, the Lin-CD7+CD127-CD45RO+CD56+CD8a- cells could develop into CD45RA+ NK cells and CD127+RORγt+ ILC3-like cells. Thus, we identified a previously unknown intermediate innate subset that can differentiate into ILC3 and NK cells.


Assuntos
Diferenciação Celular , Feto/citologia , Citometria de Fluxo/métodos , Imunidade Inata , Intestinos/citologia , Intestinos/embriologia , Linfócitos/citologia , Antígenos CD/metabolismo , Citocinas/metabolismo , Humanos , Células Matadoras Naturais/citologia , Células Matadoras Naturais/metabolismo , Processos Estocásticos , Fatores de Transcrição/metabolismo
11.
J Proteome Res ; 17(3): 1054-1064, 2018 03 02.
Artigo em Inglês | MEDLINE | ID: mdl-29430923

RESUMO

Technological advances in mass spectrometry imaging (MSI) have contributed to growing interest in 3D MSI. However, the large size of 3D MSI data sets has made their efficient analysis and visualization and the identification of informative molecular patterns computationally challenging. Hierarchical stochastic neighbor embedding (HSNE), a nonlinear dimensionality reduction technique that aims at finding hierarchical and multiscale representations of large data sets, is a recent development that enables the analysis of millions of data points, with manageable time and memory complexities. We demonstrate that HSNE can be used to analyze large 3D MSI data sets at full mass spectral and spatial resolution. To benchmark the technique as well as demonstrate its broad applicability, we have analyzed a number of publicly available 3D MSI data sets, recorded from various biological systems and spanning different mass-spectrometry ionization techniques. We demonstrate that HSNE is able to rapidly identify regions of interest within these large high-dimensionality data sets as well as aid the identification of molecular ions that characterize these regions of interest; furthermore, through clearly separating measurement artifacts, the HSNE analysis exhibits a degree of robustness to measurement batch effects, spatially correlated noise, and mass spectral misalignment.


Assuntos
Imageamento Tridimensional/métodos , Imagem Molecular/métodos , Proteômica/métodos , Espectrometria de Massas por Ionização e Dessorção a Laser Assistida por Matriz/métodos , Animais , Carcinoma de Células Escamosas/química , Carcinoma de Células Escamosas/metabolismo , Carcinoma de Células Escamosas/ultraestrutura , Neoplasias Colorretais/química , Neoplasias Colorretais/metabolismo , Neoplasias Colorretais/ultraestrutura , Humanos , Imageamento Tridimensional/instrumentação , Rim/química , Rim/metabolismo , Rim/ultraestrutura , Camundongos , Imagem Molecular/instrumentação , Neoplasias Bucais/química , Neoplasias Bucais/metabolismo , Neoplasias Bucais/ultraestrutura , Redução Dimensional com Múltiplos Fatores , Pâncreas/química , Pâncreas/metabolismo , Pâncreas/ultraestrutura , Placa Aterosclerótica/química , Placa Aterosclerótica/metabolismo , Placa Aterosclerótica/ultraestrutura , Proteômica/instrumentação , Espectrometria de Massas por Ionização e Dessorção a Laser Assistida por Matriz/instrumentação , Processos Estocásticos
12.
IEEE Trans Vis Comput Graph ; 24(1): 739-748, 2018 01.
Artigo em Inglês | MEDLINE | ID: mdl-28866537

RESUMO

Single-cell analysis through mass cytometry has become an increasingly important tool for immunologists to study the immune system in health and disease. Mass cytometry creates a high-dimensional description vector for single cells by time-of-flight measurement. Recently, t-Distributed Stochastic Neighborhood Embedding (t-SNE) has emerged as one of the state-of-the-art techniques for the visualization and exploration of single-cell data. Ever increasing amounts of data lead to the adoption of Hierarchical Stochastic Neighborhood Embedding (HSNE), enabling the hierarchical representation of the data. Here, the hierarchy is explored selectively by the analyst, who can request more and more detail in areas of interest. Such hierarchies are usually explored by visualizing disconnected plots of selections in different levels of the hierarchy. This poses problems for navigation, by imposing a high cognitive load on the analyst. In this work, we present an interactive summary-visualization to tackle this problem. CyteGuide guides the analyst through the exploration of hierarchically represented single-cell data, and provides a complete overview of the current state of the analysis. We conducted a two-phase user study with domain experts that use HSNE for data exploration. We first studied their problems with their current workflow using HSNE and the requirements to ease this workflow in a field study. These requirements have been the basis for our visual design. In the second phase, we verified our proposed solution in a user evaluation.


Assuntos
Gráficos por Computador , Processamento de Imagem Assistida por Computador/métodos , Análise de Célula Única/métodos , Software , Análise por Conglomerados , Humanos
13.
IEEE Trans Vis Comput Graph ; 24(1): 98-108, 2018 01.
Artigo em Inglês | MEDLINE | ID: mdl-28866543

RESUMO

Deep neural networks are now rivaling human accuracy in several pattern recognition problems. Compared to traditional classifiers, where features are handcrafted, neural networks learn increasingly complex features directly from the data. Instead of handcrafting the features, it is now the network architecture that is manually engineered. The network architecture parameters such as the number of layers or the number of filters per layer and their interconnections are essential for good performance. Even though basic design guidelines exist, designing a neural network is an iterative trial-and-error process that takes days or even weeks to perform due to the large datasets used for training. In this paper, we present DeepEyes, a Progressive Visual Analytics system that supports the design of neural networks during training. We present novel visualizations, supporting the identification of layers that learned a stable set of patterns and, therefore, are of interest for a detailed analysis. The system facilitates the identification of problems, such as superfluous filters or layers, and information that is not being captured by the network. We demonstrate the effectiveness of our system through multiple use cases, showing how a trained network can be compressed, reshaped and adapted to different problems.

14.
Nat Commun ; 8(1): 1740, 2017 11 23.
Artigo em Inglês | MEDLINE | ID: mdl-29170529

RESUMO

Mass cytometry allows high-resolution dissection of the cellular composition of the immune system. However, the high-dimensionality, large size, and non-linear structure of the data poses considerable challenges for the data analysis. In particular, dimensionality reduction-based techniques like t-SNE offer single-cell resolution but are limited in the number of cells that can be analyzed. Here we introduce Hierarchical Stochastic Neighbor Embedding (HSNE) for the analysis of mass cytometry data sets. HSNE constructs a hierarchy of non-linear similarities that can be interactively explored with a stepwise increase in detail up to the single-cell level. We apply HSNE to a study on gastrointestinal disorders and three other available mass cytometry data sets. We find that HSNE efficiently replicates previous observations and identifies rare cell populations that were previously missed due to downsampling. Thus, HSNE removes the scalability limit of conventional t-SNE analysis, a feature that makes it highly suitable for the analysis of massive high-dimensional data sets.


Assuntos
Algoritmos , Técnicas Citológicas/estatística & dados numéricos , Antígenos CD/metabolismo , Biomarcadores/metabolismo , Linfócitos T CD4-Positivos/classificação , Linfócitos T CD4-Positivos/imunologia , Bases de Dados Factuais , Citometria de Fluxo/estatística & dados numéricos , Gastroenteropatias/imunologia , Gastroenteropatias/metabolismo , Gastroenteropatias/patologia , Humanos , Citometria por Imagem/estatística & dados numéricos , Linfócitos/imunologia , Linfócitos/metabolismo , Linfócitos/patologia , Análise de Célula Única/estatística & dados numéricos , Processos Estocásticos , Subpopulações de Linfócitos T/classificação , Subpopulações de Linfócitos T/imunologia
15.
Nucleic Acids Res ; 45(10): e83, 2017 Jun 02.
Artigo em Inglês | MEDLINE | ID: mdl-28132031

RESUMO

Spatial and temporal brain transcriptomics has recently emerged as an invaluable data source for molecular neuroscience. The complexity of such data poses considerable challenges for analysis and visualization. We present BrainScope: a web portal for fast, interactive visual exploration of the Allen Atlases of the adult and developing human brain transcriptome. Through a novel methodology to explore high-dimensional data (dual t-SNE), BrainScope enables the linked, all-in-one visualization of genes and samples across the whole brain and genome, and across developmental stages. We show that densities in t-SNE scatter plots of the spatial samples coincide with anatomical regions, and that densities in t-SNE scatter plots of the genes represent gene co-expression modules that are significantly enriched for biological functions. We also show that the topography of the gene t-SNE maps reflect brain region-specific gene functions, enabling hypothesis and data driven research. We demonstrate the discovery potential of BrainScope through three examples: (i) analysis of cell type specific gene sets, (ii) analysis of a set of stable gene co-expression modules across the adult human donors and (iii) analysis of the evolution of co-expression of oligodendrocyte specific genes over developmental stages. BrainScope is publicly accessible at www.brainscope.nl.


Assuntos
Encéfalo/metabolismo , Regulação da Expressão Gênica no Desenvolvimento , Redes Reguladoras de Genes , Genoma Humano , Software , Transcriptoma , Adolescente , Adulto , Atlas como Assunto , Encéfalo/crescimento & desenvolvimento , Criança , Pré-Escolar , Mapeamento Cromossômico/métodos , Marcadores Genéticos , Humanos , Lactente , Anotação de Sequência Molecular , Oligodendroglia/citologia , Oligodendroglia/metabolismo
16.
IEEE Trans Vis Comput Graph ; 23(7): 1739-1752, 2017 07.
Artigo em Inglês | MEDLINE | ID: mdl-28113434

RESUMO

Progressive Visual Analytics aims at improving the interactivity in existing analytics techniques by means of visualization as well as interaction with intermediate results. One key method for data analysis is dimensionality reduction, for example, to produce 2D embeddings that can be visualized and analyzed efficiently. t-Distributed Stochastic Neighbor Embedding (tSNE) is a well-suited technique for the visualization of high-dimensional data. tSNE can create meaningful intermediate results but suffers from a slow initialization that constrains its application in Progressive Visual Analytics. We introduce a controllable tSNE approximation (A-tSNE), which trades off speed and accuracy, to enable interactive data exploration. We offer real-time visualization techniques, including a density-based solution and a Magic Lens to inspect the degree of approximation. With this feedback, the user can decide on local refinements and steer the approximation level during the analysis. We demonstrate our technique with several datasets, in a real-world research scenario and for the real-time analysis of high-dimensional streams to illustrate its effectiveness for interactive data analysis.

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