Invertible Manifold Learning for Dimension Reduction

Liu, Siyuan; Lin, Haitao; Zang, Zelin; Wu, Lirong; Xia, Jun; Li, Stan Z.

doi:10.1007/978-3-030-86523-8_43

Cited by 5 publications

(9 citation statements)

References 13 publications

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“…Panoramap is a deep learning neural network framework enhanced by geometry-preserving constraints [ 23 , 24 ]. The major differences between t-SNE/UMAP and Panoramap are that Panoramap is a learnable and reusable neural network transformation, and Panoramap uses a different definition of similarity.…”

Section: Methodsmentioning

confidence: 99%

“…We also introduced a hyperparameter

, the continuous change of which modulates the balance between attractive forces and repulsive forces, resulting in a better preservation of global structures while keeping a similar performance of preservation of local structures. For details, please refer to [ 23 , 24 ].…”

Section: Methodsmentioning

confidence: 99%

“…We simplified the cost function by removing the

and the

on top of the fractions because they are fixed values given a dataset. The undirectional similarities

are defined as follows [ 2 , 4 , 23 ]:

where

is a directional similarity based on a normalized squared t -distribution, which converted from the Euclidean distance

between point

and point

[ 4 , 23 ] is

where

is the degrees of freedom in the t-distribution, and

is the normalizing function of

which sets the limit

.…”

Section: Methodsmentioning

confidence: 99%

“…The

is used to calibrate locally about

at the input layer, where

is the nearest neighbor set. The scaling parameter

is estimated from the data by best fitting to the following equation [ 2 , 4 , 23 ]:

where

is a given perplexity-like hyper-parameter. In the input layer, we assume that the input layer data distance satisfies a normal distribution and use a t-distribution with

to approximate it.…”

Section: Methodsmentioning

confidence: 99%

“…However, the above leading NLDR methods can suffer from problems in that they may violate the geometrical and topological structures of data [ 23 ]. This can result in a low-dimensional embedding that may give misleading information for downstream data exploration tasks.…”

Section: Introductionmentioning

confidence: 99%

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RETRACTED: Panoramic Manifold Projection (Panoramap) for Single-Cell Data Dimensionality Reduction and Visualization

Wang

Zang

et al. 2022

IJMS

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Nonlinear dimensionality reduction (NLDR) methods such as t-Distributed Stochastic Neighbour Embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP) have been widely used for biological data exploration, especially in single-cell analysis. However, the existing methods have drawbacks in preserving data’s geometric and topological structures. A high-dimensional data analysis method, called Panoramic manifold projection (Panoramap), was developed as an enhanced deep learning framework for structure-preserving NLDR. Panoramap enhances deep neural networks by using cross-layer geometry-preserving constraints. The constraints constitute the loss for deep manifold learning and serve as geometric regularizers for NLDR network training. Therefore, Panoramap has better performance in preserving global structures of the original data. Here, we apply Panoramap to single-cell datasets and show that Panoramap excels at delineating the cell type lineage/hierarchy and can reveal rare cell types. Panoramap can facilitate trajectory inference and has the potential to aid in the early diagnosis of tumors. Panoramap gives improved and more biologically plausible visualization and interpretation of single-cell data. Panoramap can be readily used in single-cell research domains and other research fields that involve high dimensional data analysis.

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Section: Methodsmentioning

confidence: 99%

“…We also introduced a hyperparameter

Section: Methodsmentioning

confidence: 99%

“…We simplified the cost function by removing the

and the

on top of the fractions because they are fixed values given a dataset. The undirectional similarities

are defined as follows [ 2 , 4 , 23 ]:

where

is a directional similarity based on a normalized squared t -distribution, which converted from the Euclidean distance

between point

and point

[ 4 , 23 ] is

where

is the degrees of freedom in the t-distribution, and

is the normalizing function of

which sets the limit

.…”

Section: Methodsmentioning

confidence: 99%

“…The

is used to calibrate locally about

at the input layer, where

is the nearest neighbor set. The scaling parameter

is estimated from the data by best fitting to the following equation [ 2 , 4 , 23 ]:

where

is a given perplexity-like hyper-parameter. In the input layer, we assume that the input layer data distance satisfies a normal distribution and use a t-distribution with

to approximate it.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

RETRACTED: Panoramic Manifold Projection (Panoramap) for Single-Cell Data Dimensionality Reduction and Visualization

Wang

Zang

et al. 2022

IJMS

Self Cite

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Hierarchical Neighbors Embedding

Liu

et al. 2024

IEEE Trans. Neural Netw. Learning Syst.

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BUPNN: Manifold Learning Regularizer‐Based Blood Usage Prediction Neural Network for Blood Centers

Pan

Zang

et al. 2023

Computational Intelligence and Neuroscience

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Blood centers are an essential component of the healthcare system, as timely blood collection, processing, and efficient blood dispatch are critical to the treatment of patients and the performance of the entire healthcare system. At the same time, an efficient blood dispatching system through the high-precision predictive capability of artificial intelligence is crucial for the efficiency improvement of the blood centers. However, the current artificial intelligence (AI) models for predicting blood usage do not meet the needs of blood centers. The challenges of AI models mainly include lower generalization ability in different hospitals, limited stability under missing values, and low interpretability. An artificial neural network-based model named the blood usage prediction neural network (BUPNN) has been developed to address these challenges. BUPNN includes a novel similarity-based manifold regularizer that aims to enhance network mapping consistency and, thus, overcome the domain bise of different hospitals. Moreover, BUPNN diminishes the performance degradation caused by missing values through data enhancement. Experimental results on a large amount of accurate data demonstrate that BUPNN outperforms the baseline method in classification and regression tasks and excels in generalization and consistency. Moreover, BUPNN has solid potential to be interpreted. Therefore, the decision-making process of BUPNN is explored to the extent that it acts as an aid to the experts in the blood center.

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Invertible Manifold Learning for Dimension Reduction

Cited by 5 publications

References 13 publications

RETRACTED: Panoramic Manifold Projection (Panoramap) for Single-Cell Data Dimensionality Reduction and Visualization

RETRACTED: Panoramic Manifold Projection (Panoramap) for Single-Cell Data Dimensionality Reduction and Visualization

Hierarchical Neighbors Embedding

BUPNN: Manifold Learning Regularizer‐Based Blood Usage Prediction Neural Network for Blood Centers

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