Approximately-isometric diffusion maps

Salhov, Moshe; Bermanis, Amit; Wolf, Guy; Averbuch, Amir

doi:10.1016/j.acha.2014.05.002

Cited by 13 publications

(17 citation statements)

References 30 publications

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“…To test this hypothesis, we applied a previously published sampling technique to our PhEMD embedding [18]. The sampling technique used incompletely pivoted QR decomposition to identify "landmark points" (inhibition or control conditions) that approximately spanned the subspace of the single-cell sample embedding (Online Methods).…”

Section: Imputing the Effects Of Inhibitors Based On A Small Measuredmentioning

confidence: 99%

“…To assess whether the network geometry of all 300 inhibition and control conditions could be captured using a smaller subset of conditions, we applied a previously published sampling technique for identifying landmark points of an embedding [18]. First, the PhEMD distance matrix containing pairwise distances between our 300 experimental conditions was converted to an affinity matrix…”

Section: Imputing the Effects Of Inhibitions Based On A Small Measurementioning

confidence: 99%

“…The incompletely pivoted QR-based (ICPQR) dimensionality reduction technique was then applied, using a µ distortion parameter of 0.01, to identify 30 landmark points. The landmark points identified were then used to impute the geometric coordinates of the remaining (non-landmark) points using the out-of-sample extension technique associated with ICPQR[18]. The result was an 30-dimensional embedding of all 300 samples.…”

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confidence: 99%

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Embedding single-cell experimental conditions to reveal manifold structure of cancer drug perturbation effects

Chen

Zivanovic

Dijk

et al. 2018

Preprint

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Previously, the effect of a drug on a cell population was measured based on simple metrics such as cell viability. However, as single-cell technologies are becoming more advanced, drug screen experiments can now be conducted with more complex readouts such as gene expression profiles of individual cells. The increasing complexity of measurements from these multi-sample experiments calls for more sophisticated analytical approaches than are currently available. We develop a novel method called PhEMD (Phenotypic Earth Mover's Distance) and show that it can be used to embed the space of drug perturbations on the basis of the drugs' effects on cell populations. When testing PhEMD on a newly-generated, 300-sample CyTOF kinase inhibition screen experiment, we find that the state space of the perturbation conditions is surprisingly low-dimensional and that the network of drugs demonstrates manifold structure. We show that because of the fairly simple manifold geometry of the 300 samples, we can accurately capture the full range of drug effects using a dictionary of only 30 experimental conditions. We also show that new drugs can be added to our PhEMD embedding using similarities inferred from other characterizations of drugs using a technique called Nystrom extension. Our findings suggest that large-scale drug screens can be conducted by measuring only a small fraction of the drugs using the most expensive high-throughput single-cell technologies-the effects of other drugs may be inferred by mapping and extending the perturbation space. We additionally show that PhEMD can be useful for analyzing other types of single-cell samples, such as patient tumor biopsies, by mapping the patient state space in a similar way as the drug state space. We demonstrate that PhEMD is highly scalable, compatible with leading batch effect correction techniques, and generalizable to multiple experimental designs. Altogether, our analyses suggest that PhEMD may facilitate drug discovery efforts and help uncover the network geometry of a collection of single-cell samples.

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Section: Imputing the Effects Of Inhibitors Based On A Small Measuredmentioning

confidence: 99%

Section: Imputing the Effects Of Inhibitions Based On A Small Measurementioning

confidence: 99%

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confidence: 99%

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Embedding single-cell experimental conditions to reveal manifold structure of cancer drug perturbation effects

Chen

Zivanovic

Dijk

et al. 2018

Preprint

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“…The labeling of each test data point was determined by using the label of the nearest training data point where the pairwise distance was computed by the Frobenius norm of the difference between the corresponding embedded tensors. The software-based implementation of the PTEA algorithm is described in Salhov et al (2015).…”

Section: Example I: Mnist Handwritten Digit Classificationmentioning

confidence: 99%

Learning from patches by efficient spectral decomposition of a structured kernel

et al. 2015

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We present a kernel based method that learns from a small neighborhoods (patches) of multidimensional data points. This method is based on spectral decomposition of a large structured kernel accompanied by an out-of-sample extension method. In many cases, the performance of a spectral based learning mechanism is limited due to the use of a distance metric among the multidimensional data points in the kernel construction. Recently, different distance metrics have been proposed that are based on a spectral decomposition of an appropriate kernel prior to the application of learning mechanisms. The diffusion distance metric is a typical example where a distance metric is computed by incorporating the relation of a single measurement to the entire input dataset. A method, which is called patch-to-tensor embedding (PTE), generalizes the diffusion distance metric that incorporates matrix similarity relations into the kernel construction that replaces its scalar entries with matrices. The use of multidimensional similarities in PTE based spectral decomposition results in a bigger kernel that significantly increases its computational complexity. In this paper, we propose an efficient dictionary construction that approximates the oversized PTE kernel and its associated spectral decomposition. It is supplemented by providing an out-of-sample extension for vector fields. Furthermore, the approximation error is analyzed and the advantages of the proposed dictionary construction are demonstrated on several image processing tasks.

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“…First, one can use a small training set, which is either sampled from the entire data, or selected using dictionary construction (e.g. [13,26]), to alleviate the aforementioned computational limitations of DM. In this approach, the DM kernel and embedding are computed over the training set, and then extended, via interpolation, to the rest of the data, using out-of-sample methods such as [7,2,24].…”

Section: Introductionmentioning

confidence: 99%