Exact Tensor Completion Using t-SVD Zemin Zhang; Aeron, Shuchin
IEEE transactions on signal processing,
03/2017, Letnik:
65, Številka:
6
Journal Article
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In this paper, we focus on the problem of completion of multidimensional arrays (also referred to as tensors), in particular three-dimensional (3-D) arrays, from limited sampling. Our approach is ...based on a recently proposed tensor algebraic framework where 3-D tensors are treated as linear operators over the set of 2-D tensors. In this framework, one can obtain a factorization for 3-D data, referred to as the tensor singular value decomposition (t-SVD), which is similar to the SVD for matrices. t-SVD results in a notion of rank referred to as the tubal-rank. Using this approach we consider the problem of sampling and recovery of 3-D arrays with low tubal-rank. We show that by solving a convex optimization problem, which minimizes a convex surrogate to the tubal-rank, one can guarantee exact recovery with high probability as long as number of samples is of the order O(rnk log(nk)), given a tensor of size n × n × k with tubal-rank r. The conditions under which this result holds are similar to the incoherence conditions for low-rank matrix completion under random sampling. The difference is that we define incoherence under the algebraic setup of t-SVD, which is different from the standard matrix incoherence conditions. We also compare the numerical performance of the proposed algorithm with some state-of-the-art approaches on real-world datasets.
Cellular heterogeneity within and across tumors has been a major obstacle in understanding and treating cancer, and the complex heterogeneity is masked if bulk tumor tissues are used for analysis. ...The advent of rapidly developing single-cell sequencing technologies, which include methods related to single-cell genome, epigenome, transcriptome, and multi-omics sequencing, have been applied to cancer research and led to exciting new findings in the fields of cancer evolution, metastasis, resistance to therapy, and tumor microenvironment. In this review, we discuss recent advances and limitations of these new technologies and their potential applications in cancer studies.
Single-cell RNA sequencing (scRNA-seq) is generally used for profiling transcriptome of individual cells. The droplet-based 10X Genomics Chromium (10X) approach and the plate-based Smart-seq2 ...full-length method are two frequently used scRNA-seq platforms, yet there are only a few thorough and systematic comparisons of their advantages and limitations. Here, by directly comparing the scRNA-seq data generated by these two platforms from the same samples of CD45− cells, we systematically evaluated their features using a wide spectrum of analyses. Smart-seq2 detected more genes in a cell, especially low abundance transcripts as well as alternatively spliced transcripts, but captured higher proportion of mitochondrial genes. The composite of Smart-seq2 data also resembled bulk RNA-seq data more. For 10X-based data, we observed higher noise for mRNAs with low expression levels. Approximately 10%−30% of all detected transcripts by both platforms were from non-coding genes, with long non-coding RNAs (lncRNAs) accounting for a higher proportion in 10X. 10X-based data displayed more severe dropout problem, especially for genes with lower expression levels. However, 10X-data can detect rare cell types given its ability to cover a large number of cells. In addition, each platform detected distinct groups of differentially expressed genes between cell clusters, indicating the different characteristics of these technologies. Our study promotes better understanding of these two platforms and offers the basis for an informed choice of these widely used technologies.
A major obstacle in precision cancer medicine is the inevitable resistance to targeted therapies. Tremendous effort and progress has been made over the past few years to understand the biochemical ...and genetic mechanisms underlying drug resistance, with the goal to eventually overcome such daunting challenges. Diverse mechanisms, such as secondary mutations, oncogene bypass, and epigenetic alterations, can all lead to drug resistance, and the number of known involved genes is growing rapidly, thus providing many possibilities to overcome resistance. The finding of these mechanisms and genes invariably requires the application of genomic and functional genomic approaches to tumors or cancer models. In this review, we briefly highlight the major drug-resistance mechanisms known today, and then focus primarily on the technological approaches leading to the advancement of this field.
Systematic interrogation of single-nucleotide variants (SNVs) is one of the most promising approaches to delineate the cellular heterogeneity and phylogenetic relationships at the single-cell level. ...While SNV detection from abundant single-cell RNA sequencing (scRNA-seq) data is applicable and cost-effective in identifying expressed variants, inferring sub-clones, and deciphering genotype-phenotype linkages, there is a lack of computational methods specifically developed for SNV calling in scRNA-seq. Although variant callers for bulk RNA-seq have been sporadically used in scRNA-seq, the performances of different tools have not been assessed.
Here, we perform a systematic comparison of seven tools including SAMtools, the GATK pipeline, CTAT, FreeBayes, MuTect2, Strelka2, and VarScan2, using both simulation and scRNA-seq datasets, and identify multiple elements influencing their performance. While the specificities are generally high, with sensitivities exceeding 90% for most tools when calling homozygous SNVs in high-confident coding regions with sufficient read depths, such sensitivities dramatically decrease when calling SNVs with low read depths, low variant allele frequencies, or in specific genomic contexts. SAMtools shows the highest sensitivity in most cases especially with low supporting reads, despite the relatively low specificity in introns or high-identity regions. Strelka2 shows consistently good performance when sufficient supporting reads are provided, while FreeBayes shows good performance in the cases of high variant allele frequencies.
We recommend SAMtools, Strelka2, FreeBayes, or CTAT, depending on the specific conditions of usage. Our study provides the first benchmarking to evaluate the performances of different SNV detection tools for scRNA-seq data.
Grain production is becoming increasingly vulnerable to climate change globally. Highland barley (HB) is the most important cereal crop in the Qinghai-Tibet Plateau (QTP), so assessing HB ...productivity and its response to climate change could help to understand the capacity of grain production and food security. This study simulated the potential yield of HB annually at 72 meteorological stations for 1978-2017 using the WOFOST model, and then analyzed the spatiotemporal changes of HB potential yield and climatic factors in the growing season. Further, the influence of climate change on HB potential yield was explored in different temperature zones (TZ). Results indicate that the annual average of HB potential yield ranged from 3.5 to 8.1 t/ha in the QTP, and it was averaged at 6.5 t/ha in TZ-3, higher than other zones. From 1978 to 2017, HB potential yield for the whole QTP decreased slightly by 2.1 kg/ha per year, and its change rates were 23.9, 10.1, - 15.9, - 23.8 and - 16.7 kg/ha/year from TZ-1 to TZ-5 (p < 0.05), respectively. In all zones, average (Tave), maximum (Tmax) and minimum temperature (Tmin) showed a significantly warming trend (p < 0.01), and Tmin increased by 0.53, 0.45, 0.44, 0.40 and 0.69 °C per decade, higher than that of Tave and Tmax. However, temperature diurnal range (TDR) and radiation (RA) showed a downward trend, and their decrease rates were far higher in TZ-5 and TZ-3. In TZ-1, ΔTDR was the critical factor to the change in HB potential yield, which would increase by 420.30 kg/ha for 1 °C increase of ΔTDR (p < 0.01). From TZ-2 to TZ-5, ΔRA was the critical factor, but the influence amplitude in terms of the elastic coefficient, decreased from 4.08 to 0.99 (p < 0.01). In addition, other factors such as ΔTmax in TZ-3 and ΔTmin in TZ-4 and TZ-5 also had an important influence on the potential yield. To improve the HB productivity in the QTP, suitable varieties should be developed and introduced to adapt the climate warming in different temperature zones. In addition, efforts are needed to adjust the strategies of fertilizers and irrigation applications.
The immune microenvironment of hepatocellular carcinoma (HCC) is poorly characterized. Combining two single-cell RNA sequencing technologies, we produced transcriptomes of CD45+ immune cells for HCC ...patients from five immune-relevant sites: tumor, adjacent liver, hepatic lymph node (LN), blood, and ascites. A cluster of LAMP3+ dendritic cells (DCs) appeared to be the mature form of conventional DCs and possessed the potential to migrate from tumors to LNs. LAMP3+ DCs also expressed diverse immune-relevant ligands and exhibited potential to regulate multiple subtypes of lymphocytes. Of the macrophages in tumors that exhibited distinct transcriptional states, tumor-associated macrophages (TAMs) were associated with poor prognosis, and we established the inflammatory role of SLC40A1 and GPNMB in these cells. Further, myeloid and lymphoid cells in ascites were predominantly linked to tumor and blood origins, respectively. The dynamic properties of diverse CD45+ cell types revealed by this study add new dimensions to the immune landscape of HCC.
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•Two scRNA-seq platforms reveal a high-resolution dynamic immune landscape in HCC•LAMP3+ DCs, arising from cDCs, can migrate from tumors to hepatic lymph nodes•Paired ligand-receptor analyses implicate the regulation of lymphocytes by LAMP3+ DCs•Macrophage subsets in tumors show distinct states and potentials to egress to ascites
Integrated single-cell RNA sequencing technologies and bioinformatics approaches reveal a high-resolution immune landscape of hepatocellular carcinoma, identifying inflammatory signatures and functional states of myeloid cells as well as predictions of complex cell-cell interactions.
Abstract
Computational deconvolution with single-cell RNA sequencing data as reference is pivotal to interpreting spatial transcriptomics data, but the current methods are limited to cell-type ...resolution. Here we present Redeconve, an algorithm to deconvolute spatial transcriptomics data at single-cell resolution, enabling interpretation of spatial transcriptomics data with thousands of nuanced cell states. We benchmark Redeconve with the state-of-the-art algorithms on diverse spatial transcriptomics platforms and datasets and demonstrate the superiority of Redeconve in terms of accuracy, resolution, robustness, and speed. Application to a human pancreatic cancer dataset reveals cancer-clone-specific T cell infiltration, and application to lymph node samples identifies differential cytotoxic T cells between IgA+ and IgG+ spots, providing novel insights into tumor immunology and the regulatory mechanisms underlying antibody class switch.
In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and ...de-noising. We exploit the recently proposed tensor-Singular Value Decomposition (t-SVD)11. Based on t-SVD, the notion of multilinear rank and a related tensor nuclear norm was proposed in 11 to characterize informational and structural complexity of multilinear data. We first show that videos with linear camera motion can be represented more efficiently using t-SVD compared to the approaches based on vectorizing or flattening of the tensors. Since efficiency in representation implies efficiency in recovery, we outline a tensor nuclear norm penalized algorithm for video completion from missing entries. Application of the proposed algorithm for video recovery from missing entries is shown to yield a superior performance over existing methods. We also consider the problem of tensor robust Principal Component Analysis (PCA) for de-noising 3-D video data from sparse random corruptions. We show superior performance of our method compared to the matrix robust PCA adapted to this setting as proposed in 4.
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