Low-dimensional Manifold Research Articles

Unsupervised Feature Selection With Flexible Optimal Graph.

In the unsupervised feature selection method based on spectral analysis, constructing a similarity matrix is a very important part. In existing methods, the linear low-dimensional projection used in the process of constructing the similarity matrix is too hard, it is very challenging to construct a reliable similarity matrix. To this end, we propose a method to construct a flexible optimal graph. Based on this, we propose an unsupervised feature selection method named unsupervised feature selection with flexible optimal graph and l2,1 -norm regularization (FOG-R). Unlike other methods that use linear projection to approximate the low-dimensional manifold of the original data when constructing a similarity matrix, FOG-R can learn a flexible optimal graph, and by combining flexible optimal graph learning and feature selection into a unified framework to get an adaptive similarity matrix. In addition, an iterative algorithm with a strict convergence proof is proposed to solve FOG-R. l2,1 -norm regularization will introduce an additional regularization parameter, which will cause parameter-tuning trouble. Therefore, we propose another unsupervised feature selection method, that is, unsupervised feature selection with a flexible optimal graph and l2,0 -norm constraint (FOG-C), which can avoid tuning additional parameters and obtain a more sparse projection matrix. Most critically, we propose an effective iterative algorithm that can solve FOG-C globally with strict convergence proof. Comparative experiments conducted on 12 public datasets show that FOG-R and FOG-C perform better than the other nine state-of-the-art unsupervised feature selection algorithms.

Learning adaptive Grassmann neighbors for image-set analysis

Representing image sets as subspaces on Grassmann manifold and leveraging the Riemannian geometry of this space has proven to be highly effective in various visual recognition tasks. However, the computational cost associated with operating on Riemannian manifolds, especially of high-dimensional ones, poses a significant limitation to the applicability of existing techniques. Moreover, the image sets with labels are scarce and valuable in real-world scenarios, where the manual annotation is time-consuming and costly. To tackle these issues, in this paper, we propose an unsupervised Grassmannian dimensionality reduction method for image set classification and clustering, which simultaneously performs local structure learning and dimensionality reduction under the subspace view. Specifically, instead of relying on the pre-defined similarity matrix that obtained from raw data and may contain much noise, we adaptively learn the local structures from the projected low-dimensional Grassmann manifold. The refined structures then provide more discriminative power to learn the accurate manifold-to-manifold mapping. To better preserve the global structure of the data, this mapping is constrained to satisfy the orthogonal condition. In addition, our model can be compatible with F-norm OLPP for Grassmann manifold when the squared F-norm is transformed into projection metric. A re-weighted iterative scheme is carefully developed to optimize the problem. Experimental results on several benchmark datasets for image set classification and clustering tasks clearly demonstrate that our model consistently outperforms baselines, yielding significant improvements.

Latent neural population dynamics underlying breathing, opioid-induced respiratory depression and gasping

Breathing is vital and must be concurrently robust and flexible. This rhythmic behavior is generated and maintained within a rostrocaudally aligned set of medullary nuclei called the ventral respiratory column (VRC). The rhythmic properties of individual VRC nuclei are well known, yet technical challenges have limited the interrogation of the entire VRC population simultaneously. Here we characterize over 15,000 medullary units using high-density electrophysiology, opto-tagging and histological reconstruction. Population dynamics analysis reveals consistent rotational trajectories through a low-dimensional neural manifold. These rotations are robust and maintained even during opioid-induced respiratory depression. During severe hypoxia-induced gasping, the low-dimensional dynamics of the VRC reconfigure from rotational to all-or-none, ballistic efforts. Thus, latent dynamics provide a unifying lens onto the activities of large, heterogeneous populations of neurons involved in the simple, yet vital, behavior of breathing, and well describe how these populations respond to a variety of perturbations.

Facial Image Compression via Neural Image Manifold Compression

Although the recent learning-based image and video coding techniques achieve rapid development, the signal fidelity-driven target in these methods leads to the divergence to a highly effective and efficient coding framework for both human and machine. In this paper, we aim to address the issue by making use of the power of generative models to bridge the gap between full fidelity (for human vision) and high discrimination (for machine vision). Therefore, relying on existing pretrained generative adversarial networks (GAN), we build a GAN inversion framework that projects the image into a low-dimensional natural image manifold. In this manifold, the feature is highly discriminative and also encodes the appearance information of the image, named as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">latent code</i> . Taking a variational bit-rate constraint with a hyperprior model to model/suppress the entropy of image manifold code, our method is capable of fulfilling the needs of both machine and human visions at very low bit-rates. To improve the visual quality of image reconstruction, we further propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multiple latent codes</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">scalable inversion</i> . The former gets several latent codes in the inversion, while the latter additionally compresses and transmits a shallow compact feature to support visual reconstruction. Experimental results demonstrate the superiority of our method in both human vision tasks, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e</i> . image reconstruction, and machine vision tasks, including semantic parsing and attribute prediction.

How do kernel-based sensor fusion algorithms behave under high-dimensional noise?

Abstract We study the behavior of two kernel based sensor fusion algorithms, nonparametric canonical correlation analysis (NCCA) and alternating diffusion (AD), under the nonnull setting that the clean datasets collected from two sensors are modeled by a common low-dimensional manifold embedded in a high-dimensional Euclidean space and the datasets are corrupted by high-dimensional noise. We establish the asymptotic limits and convergence rates for the eigenvalues of the associated kernel matrices assuming that the sample dimension and sample size are comparably large, where NCCA and AD are conducted using the Gaussian kernel. It turns out that both the asymptotic limits and convergence rates depend on the signal-to-noise ratio (SNR) of each sensor and selected bandwidths. On one hand, we show that if NCCA and AD are directly applied to the noisy point clouds without any sanity check, it may generate artificial information that misleads scientists’ interpretation. On the other hand, we prove that if the bandwidths are selected adequately, both NCCA and AD can be made robust to high-dimensional noise when the SNRs are relatively large.

Generative interpolation via a diffusion probabilistic model

Seismic data interpolation is essential in a seismic data processing workflow, recovering data from sparse sampling. Traditional and deep-learning-based methods have been widely used in the seismic data interpolation field and have achieved remarkable results. In this paper, we develop a seismic data interpolation method through the novel application of diffusion probabilistic models (DPMs). DPM transforms the complex end-to-end mapping problem into a progressive denoising problem, enhancing the ability to reconstruct complex situations of missing data, such as large proportions and large-gap missing data. The interpolation process begins with a standard Gaussian distribution and seismic data with missing traces and then removes noise iteratively with a UNet trained for different noise levels. Our DPM-based interpolation method allows interpolation for various missing cases, including regularly missing, irregularly missing, consecutively missing, noisy missing, and different ratios of missing cases. The ability to generalize to different seismic data sets is also discussed in this paper. Numerical results of synthetic and field data indicate satisfactory interpolation performance of the DPM-based interpolation method in comparison with the f- x prediction filtering method, the curvelet transform method, the low-dimensional manifold method (LDMM), and the coordinate attention-based UNet method, particularly in cases with large proportions and large-gap missing data. Diffusion is all we need for seismic data interpolation.

Data-driven modelling of brain activity using neural networks, diffusion maps, and the Koopman operator.

We propose a machine-learning approach to construct reduced-order models (ROMs) to predict the long-term out-of-sample dynamics of brain activity (and in general, high-dimensional time series), focusing mainly on task-dependent high-dimensional fMRI time series. Our approach is a three stage one. First, we exploit manifold learning and, in particular, diffusion maps (DMs) to discover a set of variables that parametrize the latent space on which the emergent high-dimensional fMRI time series evolve. Then, we construct ROMs on the embedded manifold via two techniques: Feedforward Neural Networks (FNNs) and the Koopman operator. Finally, for predicting the out-of-sample long-term dynamics of brain activity in the ambient fMRI space, we solve the pre-image problem, i.e., the construction of a map from the low-dimensional manifold to the original high-dimensional (ambient) space by coupling DMs with Geometric Harmonics (GH) when using FNNs and the Koopman modes per se. For our illustrations, we have assessed the performance of the two proposed schemes using two benchmark fMRI time series: (i) a simplistic five-dimensional model of stochastic discrete-time equations used just for a "transparent" illustration of the approach, thus knowing a priori what one expects to get, and (ii) a real fMRI dataset with recordings during a visuomotor task. We show that the proposed Koopman operator approach provides, for any practical purposes, equivalent results to the FNN-GH approach, thus bypassing the need to train a non-linear map and to use GH to extrapolate predictions in the ambient space; one can use instead the low-frequency truncation of the DMs function space of L2-integrable functions to predict the entire list of coordinate functions in the ambient space and to solve the pre-image problem.

Robust Decoding of Upper-Limb Movement Direction Under Cognitive Distraction With Invariant Patterns in Embedding Manifold.

Motor brain-computer interfaces (BCIs) have gained growing research interest in motor rehabilitation, restoration, and prostheses control. Decoding upper-limb movement direction with noninvasive BCIs has been extensively investigated. However, few of them address the intervention of cognitive distraction that impairs decoding performance in practice. In this study, we propose a novel decoding model with invariant patterns in embedding manifold on a mixed dataset pooled from electroencephalograph (EEG) signals under different attentional states. We reconstruct an embedding low-dimensional manifold that intrinsically characterizes movements of the upper limb and transfer patterns of neural activities decomposed from brain functional connectivity (FC) to the manifold subspace to further preserve movement-related information. Experimental results showed that the proposed decoding model had higher robustness on the mixed dataset of attentive and distracted states compared to the baseline method. Our research provides insights into modeling a uniform underlying mechanism of movement-related EEG signals and can help enhance the practicability of BCI systems under real-world situations.

Data-driven modeling of resolved and filtered thermo-diffusively unstable hydrogen–air flames

Hydrogen premixed flames, under technically relevant conditions, are affected by intrinsic instabilities due to hydrodynamic and thermodiffusive effects, which are not taken into account by traditional turbulent combustion models. In this work, a data-driven approach is proposed for lean, premixed, unstable, self-wrinkling, hydrogen flames, based on a tabulated lower-dimensional manifold representation, wherein two scalars are defined based on species mass fractions. The model leverages a fully-resolved, two-dimensional, multi-step chemistry DNS dataset for the development of the tables. Both a flame-resolved and a filtered formulation are presented, and the additional terms that appear in the latter are closed following the filtered tabulated chemistry formalism. Two sets of tables are generated, using as a data source a small-scale and a medium-scale DNS, respectively. The a-priori analysis demonstrated the capability of the model to reproduce the flame structure with limited errors for both formulations. The flame-resolved formulation is validated a-posteriori for both table sets, showing that the flame correctly transitions to a fully-developed, corrugated state, although with a systematic small underestimation of the consumption speed. Given the agreement between the results obtained with the two sets of tables, the filtered a-posteriori analysis is conducted only for the table originating from the small-scale DNS, considering three different filter sizes. A set of one-dimensional flames is first simulated to assess the grid requirements for the non-trivial filtered simulations. Then, both the small-scale and large-scale domains are simulated. For both, it is observed that the characteristic flame structures are fairly reproduced using the small filter size, whereas the medium and large filter sizes produce a significant underestimation of consumption speed, as they fail to generate sufficient flame area through self-wrinkling. Overall, this approach represents a starting point for the development of turbulent combustion models including multi-step chemistry and the intrinsic instabilities effects.

A study on ship hull form transformation using convolutional autoencoder

Abstract The optimal ship hull form in contemporary design practice primarily consists of three parts: hull form modification, performance prediction, and optimization. Hull form modification is a crucial step to affect optimization efficiency because the baseline hull form is varied to search for performance improvements. The conventional hull form modification methods mainly rely on human decisions and intervention. As a direct expression of the three-dimensional hull form, the lines are not appropriate for machine learning techniques. This is because they do not explicitly express a meaningful performance metric despite their relatively large data dimension. To solve this problem and develop a novel machine-based hull form design technique, an autoencoder, which is a dimensional reduction technique based on an artificial neural network, was created in this study. Specifically, a convolutional autoencoder was designed; firstly, a convolutional neural network (CNN) preprocessor was used to effectively train the offsets, which are the half-width coordinate values on the hull surface, to extract feature maps. Secondly, the stacked encoder compressed the feature maps into an optimal lower dimensional-latent vector. Finally, a transposed convolution layer restored the dimension of the lines. In this study, 21 250 hull forms belonging to three different ship types of containership, LNG carrier, and tanker, were used as training data. To describe the hull form in more detail, each was divided into several zones, which were then input into the CNN preprocessor separately. After the training, a low-dimensional manifold consisting of the components of the latent vector was derived to represent the distinctive hull form features of the three ship types considered. The autoencoder technique was then combined with another novel approach of the surrogate model to form an objective function neural network. Further combination with the deterministic particle swarm optimization method led to a successful hull form optimization example. In summary, the present convolutional autoencoder has demonstrated its significance within the machine learning-based design process for ship hull forms.

Removal of electrical stimulus artifact in local field potential recorded from subthalamic nucleus by using manifold denoising

Background:Deep brain stimulation (DBS) is an effective treatment for movement disorders such as Parkinson’s disease (PD). However, local field potentials (LFPs) recorded through lead externalization during high-frequency stimulation (HFS) are contaminated by stimulus artifacts, which require to be removed before further analysis. New Method:In this study, a novel stimulus artifact removal algorithm based on manifold denoising, termed Shrinkage and Manifold-based Artifact Removal using Template Adaptation (SMARTA), was proposed to remove artifacts by deriving a template for each stimulus artifact and subtracting it from the signal. Under a low-dimensional manifold assumption, a matrix denoising technique called optimal shrinkage was applied to design a similarity metric such that the template for stimulus artifacts could be accurately recovered. Result:SMARTA was evaluated using semirealistic signals, which were the combination of semirealistic stimulus artifacts recorded in an agar brain model and LFPs of PD patients with no stimulation, and realistic LFP signals recorded in patients with PD during HFS. The results indicated that SMARTA removes stimulus artifacts with a modest distortion in LFP estimates. Comparison with Existing Methods:SMARTA was compared with moving-average subtraction, sample-and-interpolate technique, and Hampel filtering. Conclusion:The proposed SMARTA algorithm helps the exploration of the neurophysiological mechanisms of DBS effects.

Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds

We present the Julia package Manifolds.jl , providing a fast and easy-to-use library of Riemannian manifolds and Lie groups. This package enables working with data defined on a Riemannian manifold, such as the circle, the sphere, symmetric positive definite matrices, or one of the models for hyperbolic spaces. We introduce a common interface, available in ManifoldsBase.jl , with which new manifolds, applications, and algorithms can be implemented. We demonstrate the utility of Manifolds.jl using Bézier splines, an optimization task on manifolds, and principal component analysis on nonlinear data. In a benchmark, Manifolds.jl outperforms all comparable packages for low-dimensional manifolds in speed; over Python and Matlab packages, the improvement is often several orders of magnitude, while over C/C++ packages, the improvement is two-fold. For high-dimensional manifolds, it outperforms all packages except for Tensorflow-Riemopt, which is specifically tailored for high-dimensional manifolds.

Unsupervised Neural Manifold Alignment for Stable Decoding of Movement from Cortical Signals.

The stable decoding of movement parameters using neural activity is crucial for the success of brain-machine interfaces (BMIs). However, neural activity can be unstable over time, leading to changes in the parameters used for decoding movement, which can hinder accurate movement decoding. To tackle this issue, one approach is to transfer neural activity to a stable, low-dimensional manifold using dimensionality reduction techniques and align manifolds across sessions by maximizing correlations of the manifolds. However, the practical use of manifold stabilization techniques requires knowledge of the true subject intentions such as target direction or behavioral state. To overcome this limitation, an automatic unsupervised algorithm is proposed that determines movement target intention before manifold alignment in the presence of manifold rotation and scaling across sessions. This unsupervised algorithm is combined with a dimensionality reduction and alignment method to overcome decoder instabilities. The effectiveness of the BMI stabilizer method is represented by decoding the two-dimensional (2D) hand velocity of two rhesus macaque monkeys during a center-out-reaching movement task. The performance of the proposed method is evaluated using correlation coefficient and R-squared measures, demonstrating higher decoding performance compared to a state-of-the-art unsupervised BMI stabilizer. The results offer benefits for the automatic determination of movement intents in long-term BMI decoding. Overall, the proposed method offers a promising automatic solution for achieving stable and accurate movement decoding in BMI applications.

Spectral clustering and embedding with inter-class topology-preserving

Spectral clustering and embedding are critical in data mining and rely heavily on pre-computed graph structure quality. Some methods simultaneously learn graph structures and low-dimensional embeddings to achieve high-quality graph structures with separable categories. However, existing approaches prioritize inter-class separability while overlooking the inter-class topological structure. Consequently, the learned low-dimensional manifold representations may fail to capture inter-class semantic information, causing the learned graph structures to represent categories partitioning inaccurately. To address these issues, we come up with the inter-class topology and utilize category anchors to indicate class locations in low-dimensional space. The inter-class topology reflects the elaborate structural neighbor information of class, which makes the neighbor classes rationally separable and helps to learn better low-dimensional embedding representations. The spectral embedded clustering method and some variants are proposed to preserve inter-class topology while making categories separable. Furthermore, we ensure intra-class sample compactness in low-dimensional space by assigning sample embeddings near the anchors. We analyze the importance of inter-class topology preserving and intra-class compactness learning. Extensive experiments on publicly available datasets demonstrate that our method is competitive with popular graph clustering and embedding baselines and effectively captures the inter-class topology.

Booster-Driven Consistency Training Framework for Semi-Supervised Learning

The paper proposes an inductive semi-supervised learning method, called Booster-Driven Consistency Training (BDCT). In our work, we extend consistency training by designing a “booster” module for aggregating multi-view information, preventing the networks from collapsing into each other, and constructing better targets in parallel with the existing consistency training method. By booster, we mean that the one network is treated as the booster to help the training of the other two co-trained and superior networks, “spacecraft”. Furthermore, BDCT integrates smoothness enforcing into the designed fast feedback loop to ensure the effectiveness and the robustness of training. Meanwhile, adversarial examples are exploited to maintain the diversity among the networks that are learned to be smooth on the low dimensional manifold. BDCT demonstrates satisfactory performance in comparison with state-of-the-art semi-supervised deep learning methods and extensive experiments validate the effectiveness of the “booster” module.

Locating saddle points using gradient extremals on manifolds adaptively revealed as point clouds.

Steady states are invaluable in the study of dynamical systems. High-dimensional dynamical systems, due to separation of time scales, often evolve toward a lower dimensional manifold M. We introduce an approach to locate saddle points (and other fixed points) that utilizes gradient extremals on such a priori unknown (Riemannian) manifolds, defined by adaptively sampled point clouds, with local coordinates discovered on-the-fly through manifold learning. The technique, which efficiently biases the dynamical system along a curve (as opposed to exhaustively exploring the state space), requires knowledge of a single minimum and the ability to sample around an arbitrary point. We demonstrate the effectiveness of the technique on the Müller-Brown potential mapped onto an unknown surface (namely, a sphere). Previous work employed a similar algorithmic framework to find saddle points using Newton trajectories and gentlest ascent dynamics; we, therefore, also offer a brief comparison with these methods.

Approximation of curve-based sleeve functions in high dimensions

Sleeve functions are generalizations of the well-established ridge functions that play a major role in the theory of partial differential equation, medical imaging, statistics, and neural networks. Where ridge functions are non-linear, univariate functions of the distance to hyperplanes, sleeve functions are based on the squared distance to lower-dimensional manifolds. The present work is a first step to study general sleeve functions by starting with sleeve functions based on finite-length curves. To capture these curve-based sleeve functions, we propose and study a two-step method, where first the outer univariate function—the profile—is recovered, and second, the underlying curve is represented by a polygonal chain. Introducing a concept of well-separation, we ensure that the proposed method always terminates and approximates the true sleeve function with a certain quality. Investigating the local geometry, we study an inexact version of our method and show its success under certain conditions.

On the application of principal component transport for compression ignition of lean fuel/air mixtures under engine relevant conditions

Principal component transport-based data-driven reduced-order models (PC-transport ROM) are being increasingly adopted as a combustion model of turbulent reactive flows to mitigate the computational cost associated with incorporating detailed chemical kinetics. Previous studies were mainly limited to replicating relatively-simple chemistry in canonical configurations. The objective of the present study, therefore, is to further explore the accuracy of PC-transport ROM on more complex combustion phenomenon where, for example, large hydrocarbon fuel chemistry spanning a broad range of thermochemical space governs sequential multi-stage compression ignition processes. The cumulative error of PC-transport for this problem, and for others that depend upon sequential highly nonlinear physics, has to be minimal as the combustion phasing and heat release rate in internal combustion engines depends upon accurate predictions of minor ignition species whose concentrations start from ashes and grow orders of magnitude over the course of low- and high-temperature autoignition. Specifically, the PC-transport ROM is applied to predict the compression ignition characteristics of lean n-heptane/air and primary reference fuel (PRF)/air mixtures in a two-dimensional (2-D) constant volume computational domain initialized with a two-dimensional isotropic turbulence spectrum and temperature inhomogeneities. PCA is used to define the low-dimensional manifold that represents the original thermochemical state vector, and artificial neural network (ANN) models are adopted to tabulate chemical kinetics, transport, and thermodynamic properties. A series of 2-D pseudo-turbulent simulations are performed at engine pressures by varying the initial mean and r.m.s. of temperature, turbulence intensity, and the composition of fuel/air mixture. The results show that the PC-transport ROM accurately reproduces the instantaneous and statistical ignition characteristics of the fuel/air mixture, aided by pre-processing techniques including species subsetting, data clustering, and data transformation. It is found that PCs are not properly scaled with a power transformer if reactants are included in the species subset, which leads to a decrease in the accuracy of the PC-transport ROM. A separation of the reactants from the species subset ensures that the temporal evolution of the PCs starts from zero and spans orders of magnitude with time, and as such, this approach is found to effectively redistribute both PCs and their source terms with a power transformer. The computational speed-up factor of the PC-transport ROM ranges between 5.1 and 15.0 for the cases with n-heptane/air mixture and PRF/air mixture, respectively. Moreover, a potential further speed-up is anticipated through a combination of reduction in grid resolution requirements and in the stiffness of the chemical system. As an example, many of the pre-processing methods for inhomogeneous compression ignition may also apply to other complex intermittent combustion phenomena.Novelty and significance statement• The PCA-based reduced-order model (PC-transport ROM) has been applied to the multi-stage compression ignition of large hydrocarbon fuels under HCCI-relevant conditions. The present work presents a systematic procedure to accurately capture the two-stage ignition behavior of lean n-heptane/air or PRF50/air mixture.• The present work demonstrates an advantage of the PC-transport ROM in terms of computational speed-up. The computational speed-up factor for the ROM is up to 15, and moreover, a potential additional speed-up is anticipated through the reduction in the spatial and temporal resolution required.• A series of 2-D PC-transport ROMs are conducted to demonstrate the robustness of the ROM. A limitation of the ROM against different operating conditions is also discussed.

A Dynamic Latent-Space Model for Asset Clustering

Abstract Periods of financial turmoil are not only characterized by higher correlation across assets but also by modifications in their overall clustering structure. In this work, we develop a dynamic Latent-Space mixture model for capturing changes in the clustering structure of financial assets at a fine scale. Through this model, we are able to project stocks onto a lower dimensional manifold and detect the presence of clusters. The infinite-mixture assumption ensures tractability in inference and accommodates cases in which the number of clusters is large. The Bayesian framework we rely on accounts for uncertainty in the parameters’ space and allows for the inclusion of prior knowledge. After having tested our model’s effectiveness and inference on a suitable synthetic dataset, we apply the model to the cross-correlation series of two reference stock indices. Our model correctly captures the presence of time-varying asset clustering. Moreover, we notice how assets’ latent coordinates may be related to relevant financial factors such as market capitalization and volatility. Finally, we find further evidence that the number of clusters seems to soar in periods of financial distress.

Autoencoder-based conditional optimal transport generative adversarial network for medical image generation

Medical image generation has recently garnered significant interest among researchers. However, the primary generative models, such as Generative Adversarial Networks (GANs), often encounter challenges during training, including mode collapse. To address these issues, we proposed the AE-COT-GAN model (Autoencoder-based Conditional Optimal Transport Generative Adversarial Network) for the generation of medical images belonging to specific categories. The training process of our model comprises three fundamental components. The training process of our model encompasses three fundamental components. First, we employ an autoencoder model to obtain a low-dimensional manifold representation of real images. Second, we apply extended semi-discrete optimal transport to map Gaussian noise distribution to the latent space distribution and obtain corresponding labels effectively. This procedure leads to the generation of new latent codes with known labels. Finally, we integrate a GAN to train the decoder further to generate medical images. To evaluate the performance of the AE-COT-GAN model, we conducted experiments on two medical image datasets, namely DermaMNIST and BloodMNIST. The model’s performance was compared with state-of-the-art generative models. Results show that the AE-COT-GAN model had excellent performance in generating medical images. Moreover, it effectively addressed the common issues associated with traditional GANs.