diff --git a/summary/main.tex b/summary/main.tex index 3b5c10b..437c794 100644 --- a/summary/main.tex +++ b/summary/main.tex @@ -1,3 +1,4 @@ +\DocumentMetadata{} \documentclass[sigconf]{acmart} \usepackage{amsmath} \usepackage{bbm} @@ -15,7 +16,7 @@ \providecommand\BibTeX{{% \normalfont B\kern-0.5em{\scshape i\kern-0.25em b}\kern-0.8em\TeX}}} -\acmConference{Cross-Model Pseudo-Labeling}{2023}{Linz} +\acmConference{De-cluttering Scatterplots with Integral Images}{2026}{Linz} %% %% end of the preamble, start of the body of the document source. @@ -24,7 +25,7 @@ %% %% The "title" command has an optional parameter, %% allowing the author to define a "short title" to be used in page headers. -\title{Cross-Model Pseudo-Labeling for Semi-Supervised Action recognition} +\title{De-cluttering Scatterplots with Integral Images} %% %% The "author" command and its associated commands are used to define @@ -54,16 +55,16 @@ %% The abstract is a short summary of the work to be presented in the %% article. \begin{abstract} - Cross-Model Pseudo-Labeling is a new framework for generating Pseudo-Labels - for supervised learning tasks where only a subset of true labels is known. - It builds upon the existing approach of FixMatch and improves it further by - using two different sized models complementing each other. + Visualizing large multidimensional datasets using classical scatterplots often results in severe overplotting and visual clutter, which obscure data density and hinder the analysis of underlying structures. + This paper presents a summarization of a novel density-equalizing technique proposed by Rave, Molchanov, and Linsen, designed to de-clutter scatterplots through a smooth, iterative transformation of the visual domain. + The core algorithm utilizes integral images (summed-area tables) to compute a global regularization mapping that redistributes data samples into a nearly uniform configuration. + Unlike previous displacement methods that may alter local sample ordering or require expensive collision detection, this approach guarantees the preservation of neighborhood relations and operates deterministically. \end{abstract} %% %% Keywords. The author(s) should pick words that accurately describe %% the work being presented. Separate the keywords with commas. -\keywords{neural networks, videos, pseudo-labeling, action recognition} +\keywords{Scatterplots, Overplotting, Integral Images, Density Equalization, Information Visualization} %\received{20 February 2007} %\received[revised]{12 March 2009} @@ -74,172 +75,103 @@ %% information and builds the first part of the formatted document. \maketitle -\section{Introduction}\label{sec:introduction} -For most supervised learning tasks are lots of training samples essential. -With too less training data the model will not gerneralize well and not fit a real world task. -Labeling datasets is commonly seen as an expensive task and wants to be avoided as much as possible. -Thats why there is a machine-learning field called semi-supervised learning. -The general approach is to train a model that predicts Pseudo-Labels which then can be used to train the main model. +\section{Introduction} +Scatterplots remain one of the most effective and widely utilized methods for visualizing multidimensional data, allowing analysts to relate pairs of data dimensions to reveal clusters, trends, and outliers. +However, as dataset sizes increase, classical scatterplots suffer significantly from scalability issues. +When the number of data samples grows, rendering them on a screen with fixed resolution inevitably leads to occlusion and overplotting. +This visual clutter negatively impacts the data analysis process by making it difficult to estimate sample density in crowded regions and restricting access to individual data points, thereby impeding detailed exploration. -The goal of this paper is video action recognition. -Given are approximately 10 seconds long videos which should be classified. -In this paper datasets with 400 and 101 different classes are used. -The proposed approach is tested with 1\% and 10\% of known labels of all data points. +To alleviate these issues, visualization research has traditionally employed three main strategies: appearance modification, data reduction, and spatial transformation. +Appearance modification, such as adjusting sample transparency (opacity), is a common technique to improve the visibility of local density. +hile effective for density estimation, it does not resolve the overlap of interaction targets, leaving individual samples inaccessible. +Data reduction techniques, such as down-sampling, reduce the number of rendered elements but inevitably discard information, altering the representation of the underlying phenomenon. -\section{Semi-Supervised learning}\label{sec:semi-supervised-learning} -In traditional supervised learning we have a labeled dataset. -Each datapoint is associated with a corresponding target label. -The goal is to fit a model to predict the labels from datapoints. +The third category, spatial transformation, involves distorting the visualization domain to utilize screen space more efficiently. +This paper focuses on this domain, specifically addressing the limitations of existing deformation techniques. +Many prior spatial distortion methods rely on local collision detection or force-directed layouts, which can be computationally expensive (often $\mathcal{O}(n^2)$ or $\mathcal{O}(n^3)$) and may fail to preserve essential neighborhood relations. +Furthermore, previous attempts to use Integral Images (InIms) for smooth deformation, such as the work by Molchanov and Linsen, lacked stability and failed to converge to a uniform distribution in general cases. -In traditional unsupervised learning there are also datapoints but no labels are known. -The goal is to find patterns or structures in the data. -Moreover, it can be used for clustering or downprojection. +This work proposes a novel, deterministic algorithm for de-cluttering scatterplots using a corrected, stable regularization mapping based on Integral Images. +Unlike methods that rely on local collision handling, this approach evaluates the global density distribution to compute a smooth transformation. +This ensures that sample neighborhood relations are preserved without the need for expensive collision checks, enabling the processing of large datasets at interactive rates. +The authors present a parallel GPU-based implementation for fast computation and introduce visual encodings—such as deformed grids and density textures—to help users interpret the spatial distortions applied to the data. -Those two techniques combined yield semi-supervised learning. -Some of the labels are known, but for most of the data we have only the raw datapoints. -The basic idea is that the unlabeled data can significantly improve the model performance when used in combination with the labeled data. +\section{Method} +The core of the proposed summarization technique is a deterministic, iterative algorithm that uses global density information to redistribute data samples. +The method consists of three primary stages: constructing a density field, applying a smooth global deformation, and optimizing the process for real-time performance on a GPU. -\section{FixMatch}\label{sec:fixmatch} -There is an already existing approach called FixMatch. -This was introduced in a Google Research paper from 2020~\cite{fixmatch}. -The key idea of FixMatch is to leverage the unlabeled data by predicting pseudo-labels out of the known labels. -Then both, the known labels and the predicted ones are used side by side to train the model. -The labeled samples guide the learning process and the unlabeled samples gain additional information. - -Not every pseudo prediction is kept to train the model further. -A confidence threshold is defined to evaluate how `confident` the model is about its prediction. -The prediction is dropped if the model is too less confident. -The quantity and quality of the obtained labels is crucial and they have a significant impact on the overall accuracy. -This means improving the pseudo-label framework as much as possible is essential. - -FixMatch results in some major limitations. -It relies on a single model for generating pseudo-labels which can introduce errors and uncertainty in the labels. -Incorrect pseudo-labels may effect the learning process negatively. -Furthermore, Fixmatch uses a compareably small model for label prediction which has a limited capacity. -This can negatively affect the learning process as well. -%There is no measure defined how certain the model is about its prediction. -%Such a measure improves overall performance by filtering noisy and unsure predictions. -Cross-Model Pseudo-Labeling tries to address all of those limitations. - -\subsection{Math of FixMatch}\label{subsec:math-of-fixmatch} -Equation~\ref{eq:fixmatch} defines the loss-function that trains the model. -The sum over a batch size $B_u$ takes the average loss of this batch and should be familiar. -The input data is augmented in two different ways. -At first there is a weak augmentation $\mathcal{T}_{\text{weak}}(\cdot)$ which only applies basic transformation such as filtering and bluring. -Moreover, there is the strong augmentation $\mathcal{T}_{\text{strong}}(\cdot)$ which does cropouts and random augmentations. +\subsection{Density Field Construction} +To represent the distribution of n data samples zi within the scatterplot domain, the algorithm first generates a smooth scalar-valued density function dr(x,y). +This is achieved by summing contributions from individual samples using a smooth radial basis function, such as a 2D Gaussian kernel with a dilation parameter r. +To ensure numerical stability—particularly in `empty` regions where the mapping might otherwise become singular—a global constant d0 is added to the density field: \begin{equation} - \label{eq:fixmatch} - \mathcal{L}_u = \frac{1}{B_u} \sum_{i=1}^{B_u} \mathbbm{1}(\max(p_i) \geq \tau) \mathcal{H}(\hat{y}_i,F(\mathcal{T}_{\text{strong}}(u_i))) + \label{eq:dfc} + d(i,j) = d_r(i,j) + D_{0} \end{equation} -The indicator function $\mathbbm{1}(\cdot)$ applies a principle called `confidence-based masking`. -It retains a label only if its largest probability is above a threshold $\tau$. -Where $p_i \coloneqq F(\mathcal{T}_{\text{weak}}(u_i))$ is a model evaluation with a weakly augmented input. +This constant d0 is typically set to the average number of samples per pixel, representing the theoretical density of a perfectly uniform distribution. + +\subsection{Smooth Global Deformation} +The transformation utilizes Integral Images (InIms), which provide a pixel-centered description of the global density distribution. +While prior work by Molchanov and Linsen proposed a global mapping t(x,y;d), it failed to remain an identity transformation for constant density textures, making it unsuitable for iterative equalization. + +This work introduces a corrected transformation t(x,y) that subtracts the `defect` mapping of a constant texture d0 from the original formula: \begin{equation} - \label{eq:crossentropy} - \mathcal{H}(\hat{y}_i, y_i) = -\sum_{i=1} y_i \cdot log(\hat{y}_i) + \label{eq:sgd} + t(x,y) = (x,y) + t(x,y; d) - t(x,y; d_0) \end{equation} -The second part $\mathcal{H}(\cdot, \cdot)$ is a standard Cross-entropy loss function which takes two inputs, the predicted and the true label. -$\hat{y}_i$, the obtained pseudo-label and $F(\mathcal{T}_{\text{strong}}(u_i))$, a model evaluation with strong augmentation. -The indicator function evaluates in $0$ if the pseudo prediction is not confident and the current loss evaluation will be dropped. -Otherwise it evaluates to 1 and it will be kept and trains the model further. +By ensuring that t(x,y)=(x,y) when the density is already uniform (d=d0), the algorithm can be applied iteratively to converge toward a nearly uniform state. +This smooth deformation preserves essential neighborhood relations and the local ordering of data points without requiring expensive collision detection. -\section{Cross-Model Pseudo-Labeling}\label{sec:cross-model-pseudo-labeling} -The newly invented approach of this paper is called Cross-Model Pseudo-Labeling (CMPL)\cite{Xu_2022_CVPR}. -Figure~\ref{fig:cmpl-structure} visualizs the structure of CMPL\@. -Two different models, a smaller auxiliary model and a larger model are defined. -They provide pseudo-labels for each other. -The two different models have a different structural bias which leads to complementary representations. -This symetric design performs a boost in performance. -The SG label means 'Stop Gradient'. -The loss function evaluations are fed into the opposite model as loss. -The two models train each other. +\subsection{Efficient GPU Implementation} +To maintain interactivity with datasets containing millions of points, the authors developed a parallel GPU-based scheme for computing InIms. +The implementation uses a multi-pass approach in compute shaders: + +\begin{enumerate} +\item \textbf{Column Integrals:} Computes upper- and lower-column sums using a progressive 2D reduction technique. +\item \textbf{Full InIms:} Accumulates these column integrals horizontally to generate the standard and tilted InIms. +\item \textbf{Sample Mapping:} The final deformation is calculated at each pixel, and new sample positions are determined via bi-linear interpolation. +\end{enumerate} + +\subsection{Visual Encodings} +Since spatial distortion alters original distances, the method includes visual cues to help users interpret the transformation. +These include \textbf{deformed regular grids} to show area expansion/contraction, \textbf{density background textures} to highlight the original cluster locations, and \textbf{contour lines} to define the boundaries of the original data structures. + +\section{Results} +The effectiveness of the proposed density-equalization method was evaluated through a combination of algorithmic performance benchmarks, quantitative metrics for structure preservation, and a controlled user study. + +\subsection{Performance and Scalability} +A significant contribution of this work is the GPU-accelerated implementation of the integral image-based mapping. +By leveraging parallel compute shaders, the algorithm achieves linear time complexity, O(n), relative to the number of data points. +Benchmarks conducted on an NVIDIA GeForce RTX 3080 showed that the entire pipeline—including density estimation, InIm computation, and sample mapping—takes less than 10 milliseconds for datasets with up to 106 points. +This performance level enables seamless interactivity within visualization software, allowing users to adjust regularization parameters in real-time. + +\subsection{Quantitative Comparison} +The method was compared against `Hagrid`, a state-of-the-art grid-based de-cluttering technique. +Using metrics such as the preservation of k-nearest neighbors (KNN) and spatial stress, the proposed integral image approach demonstrated superior stability. +Unlike Hagrid, which can introduce artifacts due to its discrete grid-based nature, the continuous transformation provided by this method ensures that the relative ordering of points remains consistent. +The results showed that while both methods successfully utilize screen space, the InIm-based approach maintains a higher correlation with the original local data structure. +\subsection{User Study Findings} +A user study involving 20 participants was conducted to evaluate the practical utility of the regularized scatterplots. +The study focused on two primary tasks: estimating the relative size of clusters and analyzing class distributions within overlapping regions. + +\begin{itemize} +\item \textbf{Accuracy:} Participants were significantly more accurate at estimating the number of samples within dense clusters when using the regularized view compared to the original scatterplot (even with transparency). +\item \textbf{Confidence:} Users reported higher confidence levels when performing class-separation tasks in the equalized view, as the spatial expansion made individual color-coded classes more distinguishable. +\item \textbf{Interpretation:} While the distorted view required the use of visual cues (like background textures and grids) to understand the original density, participants found these encodings intuitive and effective for maintaining context. +\end{itemize} -\begin{figure}[h] - \centering - \includegraphics[width=\linewidth]{../presentation/rsc/structure} - \caption{Architecture of Cross-Model Pseudo-Labeling} - \label{fig:cmpl-structure} -\end{figure} +\section{Conclusion} +This paper presented a robust and scalable summarization technique for de-cluttering dense scatterplots using density-equalizing transformations. +By correcting previous mapping formulas and utilizing GPU-accelerated integral images, the authors established a deterministic framework that transforms cluttered, overlapping data into a nearly uniform distribution while strictly preserving neighborhood relationships. -\subsection{Math of CMPL}\label{subsec:math} -The loss function of CMPL is similar to that one explaind above. -But we have to differ from the loss generated from the supervised samples where the labels are known and the unsupervised loss where no labels are available. - -The two equations~\ref{eq:cmpl-losses1} and~\ref{eq:cmpl-losses2} are normal Cross-Entropy loss functions generated with the supervised labels of the two seperate models. - - -\begin{align} - \label{eq:cmpl-losses1} - \mathcal{L}_s^F &= \frac{1}{B_l} \sum_{i=1}^{B_l} \mathcal{H}(y_i,F(\mathcal{T}^F_{\text{standard}}(v_i)))\\ - \label{eq:cmpl-losses2} - \mathcal{L}_s^A &= \frac{1}{B_l} \sum_{i=1}^{B_l} \mathcal{H}(y_i,A(\mathcal{T}^F_{\text{standard}}(v_i))) -\end{align} - -Equation~\ref{eq:cmpl-loss3} and~\ref{eq:cmpl-loss4} are the unsupervised losses. -They are very similar to FastMatch, but important to note is that the confidence-based masking is applied to the opposite corresponding model. - -\begin{align} - \label{eq:cmpl-loss3} - \mathcal{L}_u^F &= \frac{1}{B_u} \sum_{i=1}^{B_u} \mathbbm{1}(\max(p_i^A) \geq \tau) \mathcal{H}(\hat{y}_i^A,F(\mathcal{T}_{\text{strong}}(u_i)))\\ - \label{eq:cmpl-loss4} - \mathcal{L}_u^A &= \frac{1}{B_u} \sum_{i=1}^{B_u} \mathbbm{1}(\max(p_i^F) \geq \tau) \mathcal{H}(\hat{y}_i^F,A(\mathcal{T}_{\text{strong}}(u_i))) -\end{align} - -Finally to train the main objective a overall loss is calculated by simply summing all the losses. -The loss is regulated by an hyperparamter $\lambda$ to enhance the importance of the supervised loss. - -\begin{equation} - \label{eq:loss-main-obj} - \mathcal{L} = (\mathcal{L}_s^F + \mathcal{L}_s^A) + \lambda(\mathcal{L}_u^F + \mathcal{L}_u^A) -\end{equation} - -\section{Architecture}\label{sec:Architecture} -The used model architectures depend highly on the task to be performed. -In this case the task is video action recognition. -A 3D-ResNet50 was chosen for the main model and a smaller 3D-ResNet18 for the auxiliary model. - -\section{Performance}\label{sec:performance} - -In figure~\ref{fig:results} a performance comparison is shown between just using the supervised samples for training against some different pseudo label frameworks. -One can clearly see that the performance gain with the new CMPL framework is quite significant. -For evaluation the Kinetics-400 and UCF-101 datasets are used. -And as a backbone model a 3D-ResNet18 and 3D-ResNet50 are used. -Even when only 1\% of true labels are known for the UCF-101 dataset 25.1\% of the labels could be predicted right. - -\begin{figure}[h] - \centering - \includegraphics[width=\linewidth]{../presentation/rsc/results} - \caption{Performance comparisons between CMPL, FixMatch and supervised learning only} - \label{fig:results} -\end{figure} - -\section{Further schemes}\label{sec:further-schemes} -How the pseudo-labels are generated may impact the overall performance. -In this paper the pseudo-labels are obtained by the cross-model approach. -But there might be other strategies as well. -For example: -\begin{enumerate*} - \item Self-First: Each network uses just its own prediction if its confident enough. - If not, it uses its sibling net prediction. - \item Opposite-First: Each net prioritizes the prediction of the sibling network. - \item Maximum: The most confident prediction is leveraged. - \item Average: The two predictions are averaged before deriving the pseudo-label -\end{enumerate*}. - -Those are just other approaches one can keep in mind. -This doesn't mean they are better, in fact they performed even worse in this study. - -\section{Conclusion}\label{sec:conclusion} -In conclusion, Cross-Model Pseudo-Labeling demonstrates the potential to significantly advance the field of semi-supervised action recognition. -Cross-Model Pseudo-Labeling outperforms the supervised-only approach over several experiments by a multiple. -It surpasses most of the other existing pseudo-labeling frameworks. -Through the integration of main and auxiliary models, consistency regularization, and uncertainty estimation, CMPL offers a powerful framework for leveraging unlabeled data and improving model performance. -It paves the way for more accurate and efficient action recognition systems. +The integration of visual aids, such as deformed grids and density contours, successfully bridges the gap between the equalized layout and the original data distribution, ensuring that analysts do not lose spatial context. +The quantitative results and user study confirm that this approach significantly improves the readability of large datasets without sacrificing the performance required for interactive exploratory analysis. +Future work may explore extending this density-equalizing mapping to 3D scatterplots or integrating it into automated dimensionality reduction pipelines to better visualize manifold structures. %% %% The next two lines define the bibliography style to be used, and