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We use the standard linear algebra technique singular value decomposition (SVD) to find a decomposition of stories onto an orthogonal basis of emotional arcs. Starting with the sentiment time series for each book \(b_i\) as row i in the matrix A, we apply the SVD to find

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where U contains the projection of each sentiment time series onto each of the right singular vectors (rows of \(V^T\), eigenvectors of \(A^TA\)), which have singular values given along the diagonal of Σ, with \(W = U \Sigma\). Different intuitive interpretations of the matrices U, Σ, and \(V^T\) are useful in the various domains in which the SVD is applied; here, we focus on right singular vectors as an orthonormal basis for the sentiment time series in the rows of A, which we will refer to as the modes. We combine Σ and U into the single coefficient matrix W for clarity and convenience, such that W now represents the mode coefficients.

Results of the SOM applied to Project Gutenberg books. Left panel: Nodes on the 2D SOM grid are shaded by the number of stories for which they are the winner. Right panel: The B-matrix shows that there are clear clusters of stories in the 2D space imposed by the SOM network.

To connect to the Matrix federation, you will use a client. These are some of the most popular Matrix clients available today, and more are available at try-matrix-now. To get started using Matrix, pick a client and join #matrix:matrix.org. To see more clients in a features matrix, see the Clients Matrix.

Kernel function used to compute the elements of the Gram matrix, specified as the comma-separated pair consisting of 'KernelFunction' and a kernel function name. Suppose G(xj,xk) is element (j,k) of the Gram matrix, where xj and xk are p-dimensional vectors representing observations j and k in X. This table describes supported kernel function names and their functional forms.

Kernel scale parameter, specified as the comma-separated pairconsisting of 'KernelScale' and 'auto' ora positive scalar. The software divides all elements of the predictormatrix X by the value of KernelScale.Then, the software applies the appropriate kernel norm to computethe Gram matrix.

By default, if the predictor data is in a table (Tbl), fitcsvm assumes that a variable is categorical if it is a logical vector, categorical vector, character array, string array, or cell array of character vectors. If the predictor data is a matrix (X), fitcsvm assumes that all predictors are continuous. To identify any other predictors as categorical predictors, specify them by using the CategoricalPredictors name-value argument.

If you specify the square matrix Cost and the true class of an observation is i, then Cost(i,j) is the cost of classifying a point into class j. That is, rows correspond to the true classes and columns correspond to predicted classes. To specify the class order for the corresponding rows and columns of Cost, also specify the ClassNames name-value pair argument.

If you specify a cost matrix, then the software updates the prior probabilities by incorporating the penalties described in the cost matrix for training, and stores the user-specified value in the Cost property of the trained SVM model object. For more details on the relationships and algorithmic behavior of BoxConstraint, Cost, Prior, Standardize, and Weights, see Algorithms.

If you specify a cost matrix, then the software updates the prior probabilities by incorporating the penalties described in the cost matrix for training. The software stores the user-specified prior probabilities in the Prior property of the trained model object after normalizing the probabilities to sum to 1. For more details on the relationships and algorithmic behavior of BoxConstraint, Cost, Prior, Standardize, and Weights, see Algorithms.

For a MATLAB function or a function you define, use its function handle for the score transform. The function handle must accept a matrix (the original scores) and return a matrix of the same size (the transformed scores).

If you specify the Cost, Prior, and Weights name-value arguments, the output model object stores the specified values in the Cost, Prior, and W properties, respectively. The Cost property stores the user-specified cost matrix (C) without modification. The Prior and W properties store the prior probabilities and observation weights, respectively, after normalization. For model training, the software updates the prior probabilities and observation weights to incorporate the penalties described in the cost matrix. For details, see Misclassification Cost Matrix, Prior Probabilities, and Observation Weights.

The SupportVectors property storesthe predictor values for the support vectors, including the dummyvariables. For example, assume that there are m supportvectors and three predictors, one of which is a categorical variablewith three levels. Then SupportVectors is an n-by-5matrix.

The solver in ocsvm is computationally less expensive than the solver in fitcsvm for a large data set (large n). Unlike solvers in fitcsvm, which require computation of the n-by-n Gram matrix, the solver in ocsvm only needs to form a matrix of size n-by-m. Here, m is the number of dimensions of expanded space, which is typically much less than n for big data.

The 1,544,489 biallelic segregating sites were used to construct a neighbour-joining tree (Fig. 1), using the R packages ape and SNPrelate. The .gvcf matrix was first converted into a .gds file and individual dissimilarities were estimated for each pair of individuals with the snpgdsDiss function. The bionj algorithm was then run on the distance matrix that was obtained.

(5) Materials used in composite armor could include layers of metals, plastics, elastomers, fibers, glass, ceramics, ceramic-glass reinforced plastic laminates, encapsulated ceramics in a metallic or non-metallic matrix, functionally gradient ceramic-metal materials, or ceramic balls in a cast metal matrix.

Based on the fact that similar cell lines and similar drugs exhibit similar drug responses, we adopted a similarity-regularized matrix factorization (SRMF) method to predict anticancer drug responses of cell lines using chemical structures of drugs and baseline gene expression levels in cell lines. Specifically, chemical structural similarity of drugs and gene expression profile similarity of cell lines were considered as regularization terms, which were incorporated to the drug response matrix factorization model.

Machine learning algorithms such as elastic net regularization and random forests were used to search for genomic biomarkers of drug sensitivity in cancer cell lines for individual drugs [3,4,5, 9, 10]. Recently, Seashore-Ludlow et al. developed a cluster analysis method integrating information from multiple drugs and multiple cancer cell lines to identify genomic biomarkers [6]. Geeleher et al. improved genomic biomarker discovery by accounting for variability in general levels of drug sensitivity in pre-clinical models [11]. In contrast to genomic biomarker identification, some research works focused on drug response prediction. Before-treatment baseline gene expression levels and in vitro drug sensitivity in cell lines were used to predict anticancer drug responses [12, 13]. Daemen et al. used least square-support vector machines and random forests algorithms integrating molecular features at various levels of the genome to predict drug responses from breast cancer cell line panel [14]. Menden et al. predicted drug responses using neural network where each drug-cell line pair integrated genomic features of cell lines with chemical properties of drugs as predictors [15]. Ammad-ud-din et al. applied kernelized Bayesian matrix factorization (KBMF) method to predict drug responses in GDSC dataset [16]. The method utilized genomic and chemical properties in addition to drug target information. Liu et al. used drug similarity network and cell similarity network to predict drug response, respectively, meaning that predictions were done twice separately. Then the final prediction is obtained as a weighted average of the two predictions based on dual-layer network (DLN) [17]. Cortés-Ciriano et al. proposed the modelling of chemical and cell line information in a machine learning model such as random forests (RF) or support vector regression to predict the drug sensitivity of numerous compounds screened against 59 cancer cell lines from the NCI60 panel [18]. Although various methods have been developed to computationally predict drug responses of cell lines, there are many challenges in obtaining accurate prediction.

Based on the fact that similar cell lines and similar drugs exhibit similar drug responses [17], here we propose a similarity-regularized matrix factorization (SRMF) method for drug response prediction which incorporates similarities of drugs and of cell lines simultaneously. To demonstrate its effectiveness, we applied SRMF to a set of simulated data and compared it with two typical similarity-based methods: KBMF and DLN. The evaluation metrics include Pearson correlation coefficient (PCC) and root mean square error (RMSE). The results showed that SRMF performed significantly better than KBMF and DLN in terms of drug-averaged PCC and RMSE. Moreover, we applied SRMF to GDSC and CCLE drug response datasets using ten-fold cross validation which showed that the performance of SRMF significantly exceeded other existing methods, such as KBMF, DLN and RF. We have also applied SRMF to infer the missing drug response values in the GDSC dataset. Even though the SRMF model does not specifically model mutation information, it correctly predicted the associations between EGFR and ERBB2 mutations and sensitivity to lapatinib that targets the product of these genes. Similar fact was observed with predicted response of CDKN2A-mutated cell lines to PD-0332991. Furthermore, by combining newly predicted drug responses with existing drug responses, SRMF can identify novel drug-cancer gene associations that do not exist in the available data. For example, MET amplification and TSC1 mutation are significantly associated with c-Met inhibitor PHA-665752 and mTOR inhibitor rapamycin, respectively. Finally, the newly predicted drug responses can guide drug repositioning. The mTOR inhibitor rapamycin is sensitive to non-small cell lung cancer (NSCLC) based on newly predicted drug responses versus available observations. Besides, expression of AK1RC3 and HINT1 were identified as biomarkers of cell line sensitivity to rapamycin. 350c69d7ab

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