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Abstract–Definitive screening designs permit the study of many quantitative factors in a few runs more than twice the number of factors. In practical applications, researchers often require a design for m quantitative factors, construct a definitive screening design for more than m factors and drop the superfluous columns. This is done when the number of runs in the standard m-factor definitive screening design is considered too limited or when no standard definitive screening design (sDSD) exists for m factors. In these cases, it is common practice to arbitrarily drop the last columns of the larger design. In this article, we show that certain statistical properties of the resulting experimental design depend on the exact columns dropped and that other properties are insensitive to these columns. We perform a complete search for the best sets of 1–8 columns to drop from sDSDs with up to 24 factors. We observed the largest differences in statistical properties when dropping four columns from 8- and 10-factor definitive screening designs. In other cases, the differences are small, or even nonexistent.
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#https://www.kaggle.com/c/facial-keypoints-detection/details/getting-started-with-r #################################
###Variables for downloaded files data.dir <- ' ' train.file <- paste0(data.dir, 'training.csv') test.file <- paste0(data.dir, 'test.csv') #################################
###Load csv -- creates a data.frame matrix where each column can have a different type. d.train <- read.csv(train.file, stringsAsFactors = F) d.test <- read.csv(test.file, stringsAsFactors = F)
###In training.csv, we have 7049 rows, each one with 31 columns. ###The first 30 columns are keypoint locations, which R correctly identified as numbers. ###The last one is a string representation of the image, identified as a string.
###To look at samples of the data, uncomment this line:
###Let's save the first column as another variable, and remove it from d.train: ###d.train is our dataframe, and we want the column called Image. ###Assigning NULL to a column removes it from the dataframe
im.train <- d.train$Image d.train$Image <- NULL #removes 'image' from the dataframe
im.test <- d.test$Image d.test$Image <- NULL #removes 'image' from the dataframe
################################# #The image is represented as a series of numbers, stored as a string #Convert these strings to integers by splitting them and converting the result to integer
#strsplit splits the string #unlist simplifies its output to a vector of strings #as.integer converts it to a vector of integers. as.integer(unlist(strsplit(im.train[1], " "))) as.integer(unlist(strsplit(im.test[1], " ")))
###Install and activate appropriate libraries ###The tutorial is meant for Linux and OSx, where they use a different library, so: ###Replace all instances of %dopar% with %do%.
library("foreach", lib.loc="~/R/win-library/3.3")
###implement parallelization im.train <- foreach(im = im.train, .combine=rbind) %do% { as.integer(unlist(strsplit(im, " "))) } im.test <- foreach(im = im.test, .combine=rbind) %do% { as.integer(unlist(strsplit(im, " "))) } #The foreach loop will evaluate the inner command for each row in im.train, and combine the results with rbind (combine by rows). #%do% instructs R to do all evaluations in parallel. #im.train is now a matrix with 7049 rows (one for each image) and 9216 columns (one for each pixel):
###Save all four variables in data.Rd file ###Can reload them at anytime with load('data.Rd')
#each image is a vector of 96*96 pixels (96*96 = 9216). #convert these 9216 integers into a 96x96 matrix: im <- matrix(data=rev(im.train[1,]), nrow=96, ncol=96)
#im.train[1,] returns the first row of im.train, which corresponds to the first training image. #rev reverse the resulting vector to match the interpretation of R's image function #(which expects the origin to be in the lower left corner).
#To visualize the image we use R's image function: image(1:96, 1:96, im, col=gray((0:255)/255))
#Let’s color the coordinates for the eyes and nose points(96-d.train$nose_tip_x[1], 96-d.train$nose_tip_y[1], col="red") points(96-d.train$left_eye_center_x[1], 96-d.train$left_eye_center_y[1], col="blue") points(96-d.train$right_eye_center_x[1], 96-d.train$right_eye_center_y[1], col="green")
#Another good check is to see how variable is our data. #For example, where are the centers of each nose in the 7049 images? (this takes a while to run): for(i in 1:nrow(d.train)) { points(96-d.train$nose_tip_x[i], 96-d.train$nose_tip_y[i], col="red") }
#there are quite a few outliers -- they could be labeling errors. Looking at one extreme example we get this: #In this case there's no labeling error, but this shows that not all faces are centralized idx <- which.max(d.train$nose_tip_x) im <- matrix(data=rev(im.train[idx,]), nrow=96, ncol=96) image(1:96, 1:96, im, col=gray((0:255)/255)) points(96-d.train$nose_tip_x[idx], 96-d.train$nose_tip_y[idx], col="red")
#One of the simplest things to try is to compute the mean of the coordinates of each keypoint in the training set and use that as a prediction for all images colMeans(d.train, na.rm=T)
#To build a submission file we need to apply these computed coordinates to the test instances: p <- matrix(data=colMeans(d.train, na.rm=T), nrow=nrow(d.test), ncol=ncol(d.train), byrow=T) colnames(p) <- names(d.train) predictions <- data.frame(ImageId = 1:nrow(d.test), p) head(predictions)
#The expected submission format has one one keypoint per row, but we can easily get that with the help of the reshape2 library:
library(...
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Discrete wavelength radiance measurements from the Deep Space Climate Observatory (DSCOVR) Earth Polychromatic Imaging Camera (EPIC) allows derivation of global synoptic maps of total and tropospheric ozone columns every hour during Northern Hemisphere (NH) Summer or 2 hours during Northern Hemisphere winter. In this study, we present version 3 retrieval of Earth Polychromatic Imaging Camera ozone that covers the period from June 2015 to the present with improved geolocation, calibration, and algorithmic updates. The accuracy of total and tropospheric ozone measurements from EPIC have been evaluated using correlative satellite and ground-based total and tropospheric ozone measurements at time scales from daily averages to monthly means. The comparisons show good agreement with increased differences at high latitudes. The agreement improves if we only accept retrievals derived from the EPIC 317 nm triplet and limit solar zenith and satellite looking angles to 70°. With such filtering in place, the comparisons of EPIC total column ozone retrievals with correlative satellite and ground-based data show mean differences within ±5-7 Dobson Units (or 1.5–2.5%). The biases with other satellite instruments tend to be mostly negative in the Southern Hemisphere while there are no clear latitudinal patterns in ground-based comparisons. Evaluation of the EPIC ozone time series at different ground-based stations with the correlative ground-based and satellite instruments and ozonesondes demonstrated good consistency in capturing ozone variations at daily, weekly and monthly scales with a persistently high correlation (r2 > 0.9) for total and tropospheric columns. We examined EPIC tropospheric ozone columns by comparing with ozonesondes at 12 stations and found that differences in tropospheric column ozone are within ±2.5 DU (or ∼±10%) after removing a constant 3 DU offset at all stations between EPIC and sondes. The analysis of the time series of zonally averaged EPIC tropospheric ozone revealed a statistically significant drop of ∼2–4 DU (∼5–10%) over the entire NH in spring and summer of 2020. This drop in tropospheric ozone is partially related to the unprecedented Arctic stratospheric ozone losses in winter-spring 2019/2020 and reductions in ozone precursor pollutants due to the COVID-19 pandemic.
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