A Bi-level Individualized Adaptive Learning Recommendation System Based on Topic Modeling

Abstract

Adaptive learning offers real attention to individual students’ differences and fits different needs from students. This study proposes a bi-level recommendation system with topic models, gradient descent, and a content-based filtering algorithm. In the first level, the learning materials were analyzed by a topic model, and topic proportions to each short item in each learning material were yielded as representation features. The second level contains a measurement component and a recommendation strategy component which employ gradient descent and content-based filtering algorithm to analyze personal profile vectors and make an individualized recommendation. An empirical data consists of cumulative assessments that were used as a demonstration of the recommendation process. Results have suggested that the distribution to the estimated values in the person profile vectors were related to the ability estimation from the Rasch model, and students with similar profile vectors could be recommended with the same learning material.

Appendix

1.1 Data

Cumulative Assessments are aligned and assess a representation of the Georgia Standards of Excellence (GSE). These cumulative forms can help teachers to gather strong evidence on student learning toward the overall end-of-year expectations at each grade level. The sample assessment items were provided on this web site: https://www.lennections.com/assesslets-science

1.2 R Code

############################################################ ##########################read data######################### ############################################################ data<-read.csv(file='data.csv', header=T, sep=",", fill=T,       stringsAsFactors = F) #processing data2    <- udpipe(data, "english") biterms <- as.data.table(data2)[, cooccurrence(x = lemma,                                 relevant = upos %in%                                 c("NOUN",                                 "ADJ", "VERB") &                                 nchar(lemma) > 2 & !lemma                                 %in%                                 stopwords("en"),                                 skipgram = 3),                                 by = list(doc_id)] data3 <- data2[, c("doc_id", "lemma")] ############################################################ ####################decide optimal numbers################## ############################################################ cd_k<-seq(2,10) #JSD model=NULL for (i in cd_k) {     model[[i]]   <- BTM(data3, biterms = biterms,     k = i,     alpha = 1,     beta = 1,     window = 3,     iter = 5000, background = F,     trace = F,detailed = F) } # Compute Jensen-Shannon Divergence for each value in model scores <- predict(model[[1]], newdata = data3) colnames(scores)<-c("topic1","topic2","topic3","topic4") JSD <- function(p, q) { m <- 0.5 ∗ (p + q) divergence <-            0.5 ∗ (sum(p ∗ log(p / m)) + sum(q ∗ log(q / m))) return(divergence) } n <- dim(scores)[1] X <- matrix(rep(0, n∗n), nrow=n, ncol=n) indexes <- t(combn(1:nrow(scores), m=2)) for (r in 1:nrow(indexes)) { i <- indexes[r, ][1] j <- indexes[r, ][2] p <- scores[i, ] q <- scores[j, ] X[i, j] <- JSD(p,q) } ############################################################ ####################Estimation and predict################## ############################################################ #read students' response data student = read.csv(file='4_Cumulative_Assesslet.csv',                    header=T, sep=",",                    fill=T,stringsAsFactors = F) #M4 is feature matrix of 4th assessment M4 = read.csv(file='M4.csv', header=T, sep=",",                    fill=T,stringsAsFactors = F) X = as.matrix(M4) y= as.matrix(student) N= dim(y)[1]∗dim(y)[2] theta.init = matrix(rnorm(n=dim(X)[2]∗dim(y)[1],                     mean=0,sd = 1), nrow=dim(y)[1],ncol=dim(X)[2], byrow=T) e = y - theta.init%∗%t(X) grad.init = -(2/N)∗(e)%∗%X theta = theta.init - eta∗(1/N)∗grad.init l2loss = c() for(i in 1:iters){ myMatrix = y - theta%∗%t(X) # empty matrix for the results squaredMatrix = matrix(nrow=dim(myMatrix)[1],                                 ncol=dim(myMatrix)[2]) for(i in 1:nrow(myMatrix)) { for(j in 1:ncol(myMatrix)) { squaredMatrix[i,j] = myMatrix[i,j]ˆ2 } } l2loss = c(l2loss,sqrt(sum(squaredMatrix))) e = y - theta%∗%t(X) grad = -(2/N)∗e%∗%X theta = theta - eta∗(2/N)∗grad # empty matrix for the results squaredMatrix2 = matrix(nrow=dim(grad)[1],                                     ncol=dim(grad)[2]) for(i in 1:nrow(grad)) { for(j in 1:ncol(grad)) { squaredMatrix2[i,j] = grad[i,j]ˆ2 } } if(sqrt(sum(squaredMatrix2)) <= epsilon){ break } } values<-list("coef" = theta, "l2loss" = l2loss) h=sigmoid(X%∗%t(theta.init)) sum(diag(-y%∗%log(h)-(1-y)%∗%log(1-h)))/m #sigmoid function, inverse of logit sigmoid <- function(z){1/(1+exp(-z))} #initialize theta theta <- matrix(rnorm(n=dim(X)[2]∗dim(y)[1],                                       mean=0,sd = 1), nrow=dim(y)[1],ncol=dim(X)[2], byrow=T) #comput GD compCost<-function(para){ m <- dim(y)[1]∗dim(y)[2] j=0 for (i in seq(1,492∗4,by=4)) { k=match(i,seq(1,492∗4,by=4)) l1_1=sigmoid(colSums(para[i:(i+3)]∗t(X))) l1 <- log(l1_1) l2 <- log(1-l1_1) j=j+sum(y[k,]∗l1+(1-y[k,])∗l2) } J=-j/m }