Spatial Factorization Research Articles

A spatial matrix factorization method to characterize ecological assemblages as a mixture of unobserved sources: An application to fish eDNA surveys

Abstract Understanding how ecological assemblages vary in space and time is essential for advancing our knowledge of biodiversity dynamics and ecosystem functioning. Metabarcoding of environmental DNA (eDNA) is an efficient method for documenting biodiversity changes in both marine and terrestrial ecosystems. However, current methods fail to detect and display the biodiversity structure within and between eDNA samples limiting ecological and biogeographical interpretations. We present a spatial matrix factorization method that identifies optimal eDNA sample assemblages—called pools—assuming that taxonomic unit composition is based on a fixed number of unknown sources. These sources, in turn, represent taxonomic units sharing similar habitat properties or characteristics. The method aims to reduce the multi‐taxa composition structure into a low number of dimensions defined by these sources. This method is inspired by admixture analysis in population genetics. Using a marine fish eDNA survey on 263 sampling stations detecting 2888 molecular operational taxonomic units (MOTUs), we apply this method to analyse the biogeography and mixing patterns of fish assemblages at regional and large scales. At large scale, our analysis reveals six primary pools of fish samples characterized by distinct biogeographic patterns, with some mixtures between these pools. We identify pools composed of unique sources, corresponding to distinct and more isolated regions such as the Mediterranean and Scotia Seas. We also identify pools composed of a greater mix of sources, corresponding to geographically connected areas, such as tropical regions. Additionally, we identify the taxa underpinning the formation of each pool. In the regional analysis of Mediterranean eDNA samples, our method successfully identifies different pools, allowing the detection of not only geographic gradients but also human‐induced gradients corresponding to protection levels. Spatial matrix factorization adds a new method in community ecology, where each sample is considered as a mixture of K unobserved sources, to assess the dissimilarity of ecological assemblages revealing environmental and human‐induced gradients. Beyond the study of fish eDNA samples, this method has the potential to shed new light on any biodiversity survey and provide new bioindicators of global change.

Parallel Channel Feature Weighted Seizure Prediction Based on Multi-Scale Spatial and Temporal Factorization

Epileptic seizure prediction based on electroencephalography (EEG) plays an important role in the field. However, the existing epilepsy prediction methods have little modeling ability to capture the interaction between features, and the high redundancy of features leads to the limitations of model performance. In addition, the feature information guided by the multi-channel spatial location of the brain region is ignored. To solve these problems, this paper proposes a parallel channel feature-weighted seizure prediction network based on multi-scale temporal and spatial factorization (MS-STFM-PCFWNet). Specifically, the feature information of time domain and multi-channel spatial domain of brain region can be extracted by using feature matrix to fully learn the correlation between channels. Secondly, the multi-scale spatiotemporal Factorizer (MS-STFM) is utilized to combine and interact the features, and the correlation information between the features is captured. Finally, by combining the multi-scale Inception module with an efficient channel attention mechanism, a parallel channel feature weighted network (PCFWNet) is constructed to effectively learn multi-domain features and map the discriminant representation of epilepsy prediction. The proposed MS-STFM-PCFWNet is evaluated on public CHB-MIT and BONN datasets. The experimental results show that compared with the most advanced methods, the proposed method achieves excellent predictive performance, which can be used for early warning of epileptic seizures in specific patients.

FICTURE: scalable segmentation-free analysis of submicron-resolution spatial transcriptomics.

Spatial transcriptomics (ST) technologies have advanced to enable transcriptome-wide gene expression analysis at submicron resolution over large areas. However, analysis of high-resolution ST is often challenged by complex tissue structure, where existing cell segmentation methods struggle due to the irregular cell sizes and shapes, and by the absence of segmentation-free methods scalable to whole-transcriptome analysis. Here we present FICTURE (Factor Inference of Cartographic Transcriptome at Ultra-high REsolution), a segmentation-free spatial factorization method that can handle transcriptome-wide data labeled with billions of submicron-resolution spatial coordinates and is compatible with both sequencing-based and imaging-based ST data. FICTURE uses the multilayered Dirichlet model for stochastic variational inference of pixel-level spatial factors, and is orders of magnitude more efficient than existing methods. FICTURE reveals the microscopic ST architecture for challenging tissues, such as vascular, fibrotic, muscular and lipid-laden areas in real data where previous methods failed. FICTURE's cross-platform generality, scalability and precision make it a powerful tool for exploring high-resolution ST.

Multi-sample non-negative spatial factorization.

It is important to model biological variation when analyzing spatial transcriptomics data from multiple samples. One approach to multi-sample analysis is to spatially align samples, but this is a challenging problem. Here, we provide an alignment-free framework for generalizing a one-sample spatial factorization model to multi-sample data. Using this framework, we develop a method, called multi-sample non-negative spatial factorization (mNSF) that extends the one-sample non-negative spatial factorization (NSF) framework to a multi-sample dataset. Our model allows for a sample-specific model for the spatial correlation structure and extracts a low-dimensional representation of the data. We illustrate the performance of mNSF by simulation studies and real data. mNSF identifies true factors in simulated data, identifies shared anatomical regions across samples in real data and reveals region-specific biological functions. mNSFs performance is similar to alignment based methods when alignment is possible, but extends analysis to situations where spatial alignment is impossible. We expect multi-sample factorization methods to be a powerful class of methods for analyzing spatially resolved transcriptomics data.

Anomaly Metrics on Class Variations For Face Anti-Spoofing

Abstract In face anti-spoofing tasks, distinguishing between live and spoof faces across different data domains presents challenges due to inter-class similarities, intra-class variations and unknown spoof patterns. This hampers generalization in real-world applications. To address this, we propose a novel convolutional neural network framework that utilizes spatial-frequency cues for 2D and 3D attacks. Furthermore, we introduce compact anomaly metrics and design three anomaly metrics-based supervisions from the perspective of Reed-Xiaoli anomaly detection, aiming to tackle the challenge posed by unknown attacks. Thanks to our proposed spatial frequency factorization network and its frequency-related supervisions, the spoofing cues are significantly enhanced, resulting in remarkable improvements in our experimental results. These outcomes demonstrate that our proposed framework achieves state-of-the-art performance on both monocular and multi-spectral benchmark datasets.

Nonnegative spatial factorization applied to spatial genomics

Nonnegative matrix factorization (NMF) is widely used to analyze high-dimensional count data because, in contrast to real-valued alternatives such as factor analysis, it produces an interpretable parts-based representation. However, in applications such as spatial transcriptomics, NMF fails to incorporate known structure between observations. Here, we present nonnegative spatial factorization (NSF), a spatially-aware probabilistic dimension reduction model based on transformed Gaussian processes that naturally encourages sparsity and scales to tens of thousands of observations. NSF recovers ground truth factors more accurately than real-valued alternatives such as MEFISTO in simulations, and has lower out-of-sample prediction error than probabilistic NMF on three spatial transcriptomics datasets from mouse brain and liver. Since not all patterns of gene expression have spatial correlations, we also propose a hybrid extension of NSF that combines spatial and nonspatial components, enabling quantification of spatial importance for both observations and features. A TensorFlow implementation of NSF is available from https://github.com/willtownes/nsf-paper.

AUTISTIC DISORDER SPECTRUM USING INCEPTION V3

When diagnosed early, autism spectrum disorder (ASD) can cut healthcare expenses by as much as 80% if not more. On the ImageNet dataset, Inception v3 has been demonstrated to achieve above 75% accuracy in picture recognition. One of the techniques used in the healthcare industry is called Deep Transfer Learning (DTL). Inception V3 gives 86% accuracy for Image dataset of Autistic Kids, train loss 0.6695, Val loss 0.9823 .The model made up many convolution layers with wide range of parameters, pooling layers helps in reducing the dimensions which helps in nding feature maps efciently. Batch Normalization, spatial factorization, using Auxiliary lters and reduce Grid size are the major highlights.

A Novel Constrained Non-negative Matrix Factorization Method for Group Functional Magnetic Resonance Imaging Data Analysis of Adult Attention-Deficit/Hyperactivity Disorder.

Attention-deficit/hyperactivity disorder (ADHD) is a common childhood psychiatric disorder that often persists into adulthood. Extracting brain networks from functional magnetic resonance imaging (fMRI) data can help explore neurocognitive disorders in adult ADHD. However, there is still a lack of effective methods to extract large-scale brain networks to identify disease-related brain network changes. Hence, this study proposed a spatial constrained non-negative matrix factorization (SCNMF) method based on the fMRI real reference signal. First, non-negative matrix factorization analysis was carried out on each subject to select the brain network components of interest. Subsequently, the available spatial prior information was mined by integrating the interested components of all subjects. This prior constraint was then incorporated into the NMF objective function to improve its efficiency. For the sake of verifying the effectiveness and feasibility of the proposed method, we quantitatively compared the SCNMF method with other classical algorithms and applied it to the dynamic functional connectivity analysis framework. The algorithm successfully extracted ten resting-state brain functional networks from fMRI data of adult ADHD and healthy controls and found large-scale brain network changes in adult ADHD patients, such as enhanced connectivity between executive control network and right frontoparietal network. In addition, we found that older ADHD spent more time in the pattern of relatively weak connectivity. These findings indicate that the method can effectively extract large-scale functional networks and provide new insights into understanding the neurobiological mechanisms of adult ADHD from the perspective of brain networks.

Spatial feature extraction non-negative tensor factorization for hyperspectral unmixing

Estimating endmembers and corresponding abundances from mixed pixels are essential steps for hyperspectral unmixing. In hyperspectral unmixing, obtaining accurate unmixing results is difficult since less prior knowledge is available. Besides, the unmixing results are influenced by noise and highly correlated endmembers, so that the obtained abundance maps exist small values which are not present in the image. In this paper, we separate each abundance map into a feature layer and a sparse layer to protect the obtained abundance maps from the above-mentioned factors. The feature layer represents the main information of the abundance map. And the sparse layer contains outliers dominated by the above-mentioned factors. In particular, we design a feature extraction regularization to describe the feature layer and use a weighted ℓ1 norm to describe the sparse layer. Then, under the framework of non-negative tensor factorization (NTF), we propose a novel unmixing algorithm named spatial feature extraction NTF (SFE-NTF) for hyperspectral unmixing. The proposed SFE-NTF is based on an augmented multiplicative algorithm. Experimental results on both synthetic and real hyperspectral data demonstrate that the proposed algorithm outperforms other state-of-the-art algorithms.

Spatial Low-Rank Tensor Factorization and Unmixing of Hyperspectral Images

This work presents a method for hyperspectral image unmixing based on non-negative tensor factorization. While traditional approaches may process spectral information without regard for spatial structures in the dataset, tensor factorization preserves the spectral-spatial relationship which we intend to exploit. We used a rank-(L, L, 1) decomposition, which approximates the original tensor as a sum of R components. Each component is a tensor resulting from the multiplication of a low-rank spatial representation and a spectral vector. Our approach uses spatial factors to identify high abundance areas where pure pixels (endmembers) may lie. Unmixing is done by applying Fully Constrained Least Squares such that abundance maps are produced for each inferred endmember. The results of this method are compared against other approaches based on non-negative matrix and tensor factorization. We observed a significant reduction of spectral angle distance for extracted endmembers and equal or better RMSE for abundance maps as compared with existing benchmarks.

Bottom-up action modeling via spatial factorization for serving food

The goal state of the robot motion involved in an action is determined by the action model based on the effect of the action and the scene state. This study focuses on serving food as a robot action; the action model of serving food is obtained based on demonstrations. The arrangement position is determined by considering the spatial relations between the object being served and the multiple selected reference objects. Therefore, it is necessary to learn the importance of the relations for the reference and the spatial relations between objects based on demonstrations. In this paper, bottom-up action modeling is proposed as an action modeling approach based on the demonstration. In this method, the spatial relations between labeled objects and the importance of the relations are learned through spatial factorization of the scene into partial relations. This approach enables the robot to determine the arrangement position intended by the demonstrator, even in unknown scenes. The effectiveness of the proposed method was evaluated by simulation, which the action of serving food.

Collaborative Coupled Hyperspectral Unmixing Based Subpixel Change Detection for Analyzing Coastal Wetlands

Owing to the complicated and heterogeneous distribution characteristics of wetland features, the existing hyperspectral technology is difficult to investigate the inner-pixel subtle changes. In this article, we present a subpixel change detection method based on collaborative coupled unmixing (SCDUM) for monitoring coastal wetlands. A novel multitemporal and spatial scale collaborative endmember extraction method based on joint spatial and spectral information is proposed. In the proposed method, the multitemporal hyperspectral images are first jointly clustered and segmented based on multifeature fusion of spectral features, texture features, and shape features. Then, a different spatial scale nonnegative matrix factorization based on original and downsampled multitemporal hyperspectral images is proposed to accurately extract the pure endmembers of each segmented images. Finally, the global abundance of the multitemporal image is effectively estimated for change detection. In addition, in order to verify the accuracy of the change detection results without reference, an accuracy verification strategy by using high spatial resolution Sentinel-2A image as auxiliary data is implemented. The Yellow River Estuary coastal wetland was selected as the research area, and the Gaofen-5 and ZY-1 02D hyperspectral images were used as the research data. In particular, the proposed method not only provides the overall change information, but also obtains the component of change direction and intensity of each kind of endmember, and the experimental results show that the SCDUM gives more accurate detection results, with closer to the endmember spectral curves of real objects, compared with other state-of-the-art methods.

Travel Time Prediction on Un-Monitored Roads: A Spatial Factorization Machine Based Approach (Student Abstract)

Real-time traffic monitoring is one of the most important factors for route planning and estimated time of arrival (ETA). Many major roads in large cities are installed with live traffic monitoring systems, inferring the current traffic congestion status and ETAs to other locations. However, there are also many other roads, especially small roads and paths, that are not monitored. Yet, live traffic status on such un-monitored small roads can play a non-negligible role in personalized route planning and re-routing when road incident happens. How to estimate the traffic status on such un-monitored roads is thus a valuable problem to be addressed. In this paper, we propose a model called Spatial Factorization Machines (SFM) to address this problem. A major advantage of the SFM model is that it incorporates physical distances and structures of road networks into the estimation of traffic status on un-monitored roads. Our experiments on real world traffic data demonstrate that the SFM model significantly outperforms other existing models on ETA of un-monitored roads.

Spatial Factorization in Cyclic-Proof System for Separation Logic

Spatial Factorization in Cyclic-Proof System for Separation Logic

On the asymptotic behavior of the periodograms of periodically correlated spatial processes: Periodicity detection

ABSTRACTIn this work, the asymptotic unbiasedness and the asymptotic uncorrelatedness of periodograms for the periodically correlated spatial processes are given. This will be done using the time dependent spectral representation of periodically correlated spatial processes and Cholesky factorization of the spectral density. A graphical method is also proposed to detect the period of periodically correlated spatial processes. In order to support the theory, a simulation study and a real data example are performed.

Extracting non-negative basis images using pixel dispersion penalty

Non-negativity matrix factorization (NMF) and its variants have been explored in the last decade and are still attractive due to its ability of extracting non-negative basis images. However, most existing NMF based methods are not ready for encoding higher-order data information. One reason is that they do not directly/explicitly model structured data information during learning, and therefore the extracted basis images may not completely describe the “parts” in an image [1] very well. In order to solve this problem, the structured sparse NMF has been recently proposed in order to learn structured basis images. It however depends on some special prior knowledge, i.e. one needs to exhaustively define a set of structured patterns in advance. In this paper, we wish to perform structured sparsity learning as automatically as possible. To that end, we propose a pixel dispersion penalty (PDP), which effectively describes the spatial dispersion of pixels in an image without using any manually predefined structured patterns as constraints. In PDP, we consider each part-based feature pattern of an image as a cluster of non-zero pixels; that is the non-zero pixels of a local pattern should be spatially close to each other. Furthermore, by incorporating the proposed PDP, we develop a spatial non-negative matrix factorization (Spatial NMF) and a spatial non-negative component analysis (Spatial NCA). In Spatial NCA, the non-negativity constraint is only imposed on basis images and such constraint on coefficients is released, so both subtractive and additive combinations of non-negative basis images are allowed for reconstructing any images. Extensive experiments are conducted to validate the effectiveness of the proposed pixel dispersion penalty. We also experimentally show that Spatial NCA is more flexible for extracting non-negative basis images and obtains better and more stable performance.

Extreme Compression and Modeling of Bidirectional Texture Function

The recent advanced representation for realistic real-world materials in virtual reality applications is the Bidirectional Texture Function (BTF) which describes rough texture appearance for varying illumination and viewing conditions. Such a function can be represented by thousands of measurements (images) per material sample. The resulting BTF size excludes its direct rendering in graphical applications and some compression of these huge BTF data spaces is obviously inevitable. In this paper we present a novel, fast probabilistic model-based algorithm for realistic BTF modeling allowing an extreme compression with the possibility of a fast hardware implementation. Its ultimate aim is to create a visual impression of the same material without a pixel-wise correspondence to the original measurements. The analytical step of the algorithm starts with a BTF space segmentation and a range map estimation by photometric stereo of the BTF surface, followed by the spectral and spatial factorization of selected sub-space color texture images. Single mono-spectral band-limited factors are independently modeled by their dedicated spatial probabilistic model. During rendering, the sub-space images of arbitrary size are synthesized and both color (possibly multi-spectral) and range information is combined in a bump-mapping filter according to the view and illumination directions. The presented model offers a huge BTF compression ratio unattainable by any alternative sampling-based BTF synthesis method. Simultaneously this model can be used to reconstruct missing parts of the BTF measurement space.

On Single-Sequence and Multi-Sequence Factorizations

Subspace based factorization methods are commonly used for a variety of applications, such as 3D reconstruction, multi-body segmentation and optical flow estimation. These are usually applied to a single video sequence. In this paper we present an analysis of the multi-sequence case and place it under a single framework with the single sequence case. In particular, we start by analyzing the characteristics of subspace based spatial and temporal segmentation. We show that in many cases objects moving with different 3D motions will be captured as a single object using multi-body (spatial) factorization approaches. Similarly, frames viewing different shapes might be grouped as displaying the same shape in the temporal factorization framework. Temporal factorization provides temporal grouping of frames by employing a subspace based approach to capture non-rigid shape changes (Zelnik-Manor and Irani, 2004). We analyze what causes these degeneracies and show that in the case of multiple sequences these can be made useful and provide information for both temporal synchronization of sequences and spatial matching of points across sequences.

A spatially-factored fully implicit solution method for block structured meshes with irregular nodes

The alternating direction multi-zone implicit (ADMZI) method for solving implicitly structured multi-zone domains by spatial factorization techniques is extended to block structured domains that include irregular nodes, i.e. nodes that have a different connectivity with the neighboring nodes. It is shown for fully implicit schemes that the presence of irregular nodes (in the two-dimensional case) imposes the use of a mixed stage in the ADI factorization, in addition to the two standard stages. In the mixed stage, there are parts where the equations of the first stage are solved, while in the other parts the first stage has been previously completed and the equations of the second stage are being solved. It is proven that the overall second-order temporal accuracy of the solution is preserved. Generalized ADMZI sweeps are defined to allow a consistent and unified approach to all the ADMZI factorization stages, including the mixed stage. This novel methodology can be employed for solving implicitly many existing solvers of systems of partial differential equations, such as the Navier–Stokes equations, using spatially factored techniques and block structured meshes with irregular nodes. The resulting scheme is efficient because the computational work is equivalent to a single iteration of most other existing iterative solvers.

Spatial operator factorization and inversion of the manipulator mass matrix

This paper advances two linear operator factorizations of the manipulator mass matrix. Embedded in the factorizations are many of the techniques that are regarded as very efficient computational solutions to inverse and forward dynamics problems. The operator factorizations provide a high-level architectural understanding of the mass matrix and its inverse, which is not visible in the detailed algorithms. They also lead to an approach to the development of computer programs or the organisation of complexity in robot dynamics. >