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Diffstat (limited to 'docs/src/sci/normalize.md')
| -rw-r--r-- | docs/src/sci/normalize.md | 46 |
1 files changed, 23 insertions, 23 deletions
diff --git a/docs/src/sci/normalize.md b/docs/src/sci/normalize.md index e6056d6..3cb5dbd 100644 --- a/docs/src/sci/normalize.md +++ b/docs/src/sci/normalize.md @@ -34,7 +34,7 @@ Our goal during the normalization procedure is two-fold: ```@raw html <p align="center"> <figure> - <img src="/assets/heteroskedastic.png" width="79%" /> + <img src="/assets/drosophila/heteroskedastic.png" width="79%" /> <figurecaption> Count matrix is heteroskedastic: variation of scales across genes (rows) and cells (columns) </figurecaption> @@ -54,8 +54,8 @@ Owing to dropout and other sources of overdispersion, as shown empircally in the ```@raw html <p align="center"> <figure> - <img src="/assets/overdispersed_mean_vs_variance.png" width="49%" /> - <img src="/assets/overdispersed_zeros.png" width="49%" /> + <img src="/assets/drosophila/overdispersed_mean_vs_variance.png" width="49%" /> + <img src="/assets/drosophila/overdispersed_zeros.png" width="49%" /> <figurecaption> scRNAseq data for Drosophila is overdispersed. </figurecaption> @@ -80,7 +80,7 @@ As such, singular values would be bounded by ``\bar{\lambda} \equiv 1+\sigma\sqr ```@raw html <p align="center"> -<img src="/assets/marchenko-pastur.png" width="49%" class="center"/> +<img src="/assets/drosophila/marchenko-pastur.png" width="49%" class="center"/> </p> <p align="center"> Marchenko pastur distribution (orange) vs random matrix eigenvalues (blue) @@ -101,8 +101,8 @@ This is exhibited empirically below. ```@raw html <p align="center"> -<img src="/assets/gaussian_svd.png" width="49%" class="center"/> -<img src="/assets/gaussian_overlap.png" width="49%" class="center"/> +<img src="/assets/drosophila/gaussian_svd.png" width="49%" class="center"/> +<img src="/assets/drosophila/gaussian_overlap.png" width="49%" class="center"/> </p> ``` @@ -127,8 +127,8 @@ An example is shown below: ```@raw html <p align="center"> -<img src="/assets/poisson_svd.png" width="49%" class="center"/> -<img src="/assets/poisson_overlap.png" width="49%" class="center"/> +<img src="/assets/drosophila/poisson_svd.png" width="49%" class="center"/> +<img src="/assets/drosophila/poisson_overlap.png" width="49%" class="center"/> </p> ``` @@ -201,8 +201,8 @@ The result is shown below. ```@raw html <p align="center"> -<img src="/assets/negbinom.png" width="49%" class="center"/> -<img src="/assets/negbinom_mean.png" width="49%" class="center"/> +<img src="/assets/drosophila/negbinom.png" width="49%" class="center"/> +<img src="/assets/drosophila/negbinom_mean.png" width="49%" class="center"/> </p> ``` As shown, we underestimate the true rank as a few components have singular values below the Marchenko-Pastur noise floor. @@ -218,9 +218,9 @@ This can be seen in the below figure, which shows the scatter plot of the parame ```@raw html <p align="center"> <figure> - <img src="/assets/nb_1_uncertainty_vs_expression.png" width="32%" /> - <img src="/assets/nb_2_uncertainty_vs_expression.png" width="32%" /> - <img src="/assets/nb_3_uncertainty_vs_expression.png" width="32%" /> + <img src="/assets/drosophila/nb_1_uncertainty_vs_expression.png" width="32%" /> + <img src="/assets/drosophila/nb_2_uncertainty_vs_expression.png" width="32%" /> + <img src="/assets/drosophila/nb_3_uncertainty_vs_expression.png" width="32%" /> <figurecaption> Each point is a gene (row). Color of point determined by mean expression of gene. </figurecaption> @@ -240,8 +240,8 @@ The right figure displays the cumulative density function for the filtered genes ```@raw html <p align="center"> <figure> - <img src="/assets/nb_total_uncertainty_vs_expression.png" width="49%" /> - <img src="/assets/nb_badfits.png" width="49%" /> + <img src="/assets/drosophila/nb_total_uncertainty_vs_expression.png" width="49%" /> + <img src="/assets/drosophila/nb_badfits.png" width="49%" /> <figurecaption> Filter genes with bad fits. Genes with high uncertainty are determined to be lowly expressed. </figurecaption> @@ -255,8 +255,8 @@ This phenomenon persists across all gene expression levels. ```@raw html <p align="center"> <figure> - <img src="/assets/nb_param2.png" width="49%" /> - <img src="/assets/nb_param3.png" width="49%" /> + <img src="/assets/drosophila/nb_param2.png" width="49%" /> + <img src="/assets/drosophila/nb_param3.png" width="49%" /> <figurecaption> Parameter distributions </figurecaption> @@ -274,9 +274,9 @@ As shown below, we find great quantitative agreement between the empirical estim ```@raw html <p align="center"> <figure> - <img src="/assets/bootstrap_1.png" width="60%" /> - <img src="/assets/bootstrap_2.png" width="60%" /> - <img src="/assets/bootstrap_3.png" width="60%" /> + <img src="/assets/drosophila/bootstrap_1.png" width="60%" /> + <img src="/assets/drosophila/bootstrap_2.png" width="60%" /> + <img src="/assets/drosophila/bootstrap_3.png" width="60%" /> </figure> </p> ``` @@ -288,8 +288,8 @@ As shown below, we find there are ``\sim 30`` **statistically significant** line Interestingly, while not fully delocalized as seen by the participation ratio of the "noise" components, we see that roughly ``\sim 1000`` genes contribute significantly to each component suggesting these are coarse "pathways" discovered. ```@raw html <p align="center"> -<img src="/assets/rank_estimate.png" width="49%" class="center"/> -<img src="/assets/participation_ratio.png" width="49%" class="center"/> +<img src="/assets/drosophila/rank_estimate.png" width="49%" class="center"/> +<img src="/assets/drosophila/participation_ratio.png" width="49%" class="center"/> </p> ``` To ensure element-wise positivity, the estimated ``\tilde{\mu}_{i\alpha}`` is obtained by performing non-negative matrix factorization on the rescaled ``\tilde{n}_{i\alpha}`` with rank ``35``. @@ -311,7 +311,7 @@ This was determined to be an excellent stochastic model for the computed ``\tild ```@raw html <p align="center"> -<img src="/assets/gamma_qq.png" width="49%" class="center"/> +<img src="/assets/drosophila/gamma_qq.png" width="49%" class="center"/> </p> ``` |