jmlr jmlr2013 jmlr2013-lda knowledge-graph by maker-knowledge-mining
topicId: wordWeight*wordName (topN-words)
topic #0: 0.006*posterior + 0.004*fv + 0.004*bi + 0.004*si + 0.004*prior + 0.004*vi + 0.003*dt + 0.003*ei + 0.003*dual + 0.002*partial
topic #1: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #2: 0.001*sift + 0.001*shot + 0.000*hauptmann + 0.000*malima + 0.000*rez + 0.000*ldi + 0.000*gao + 0.000*emosift + 0.000*mosift + 0.000*lit
topic #3: 0.000*completion + 0.000*davenport + 0.000*mmax + 0.000*kmax + 0.000*srebro + 0.000*jt + 0.000*ompletion + 0.000*ds + 0.000*hou + 0.000*rs
topic #4: 0.006*divvy + 0.001*plugin + 0.001*visualizer + 0.001*plugins + 0.001*laurens + 0.001*baseball + 0.001*threads + 0.001*joshua + 0.001*ayasdi + 0.000*researcher
topic #5: 0.005*policy + 0.004*lemma + 0.004*kernel + 0.004*classi + 0.003*equation + 0.003*bayesian + 0.003*sup + 0.003*matrix + 0.003*theorem + 0.003*yi
topic #6: 0.008*graph + 0.004*nodes + 0.004*tree + 0.004*node + 0.004*wi + 0.004*time + 0.003*network + 0.003*greedy + 0.003*likelihood + 0.003*ak
topic #7: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #8: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #9: 0.004*string + 0.003*ui + 0.003*pac + 0.003*clause + 0.003*subsequence + 0.002*modeb + 0.002*literal + 0.002*candidate + 0.002*strings + 0.002*shuf
topic #10: 0.005*manifold + 0.004*clustering + 0.004*rn + 0.003*principal + 0.003*ds + 0.003*sampling + 0.003*error + 0.003*hang + 0.003*projection + 0.003*curve
topic #11: 0.003*herbster + 0.003*cutsize + 0.002*spanning + 0.001*dw + 0.001*rwj + 0.001*mistakes + 0.001*perceptron + 0.001*resistance + 0.001*unweighted + 0.001*diameter
topic #12: 0.004*egl + 0.003*gestures + 0.002*isax + 0.002*gesture + 0.002*magic + 0.001*sax + 0.001*recognizer + 0.001*hits + 0.001*summoning + 0.001*kohlsdorf
topic #13: 0.004*privacy + 0.003*ppca + 0.002*private + 0.002*differentially + 0.001*qf + 0.001*dwork + 0.001*mcsherry + 0.001*doi + 0.001*omponents + 0.001*sulq
topic #14: 0.005*sc + 0.003*permanent + 0.003*ri + 0.003*perr + 0.003*bp + 0.002*chertkov + 0.002*nn + 0.002*equations + 0.002*ls + 0.002*omp
topic #15: 0.004*sfa + 0.002*pvf + 0.002*lstd + 0.001*lspi + 0.001*diffusion + 0.001*steady + 0.001*pproximation + 0.001*usial + 0.001*unew + 0.001*ohmer
topic #16: 0.004*bh + 0.003*fdr + 0.002*sto + 0.001*hm + 0.001*mhm + 0.001*student + 0.001*neuvial + 0.001*rocedures + 0.001*symptotics + 0.001*euvial
topic #17: 0.003*adaboost + 0.002*mf + 0.002*margins + 0.001*onvergence + 0.001*rudin + 0.001*oost + 0.001*utp + 0.001*rt + 0.001*ker + 0.001*poly
topic #18: 0.003*fuzzy + 0.003*register + 0.002*buffer + 0.002*memory + 0.002*shift + 0.001*nmax + 0.001*redundancy + 0.001*tot + 0.001*oward + 0.001*hankar
topic #19: 0.005*intervention + 0.002*unordered + 0.002*causal + 0.002*sosmp + 0.002*bp + 0.002*atv + 0.001*mv + 0.001*antichain + 0.001*pv + 0.001*mtv
topic #20: 0.004*activity + 0.004*grasp + 0.004*attributes + 0.003*rule + 0.003*video + 0.002*accuracy + 0.002*visual + 0.002*rules + 0.002*mining + 0.002*activities
topic #21: 0.003*ep + 0.002*group + 0.002*wg + 0.002*andez + 0.002*obato + 0.002*ern + 0.001*horseshoe + 0.001*xnew + 0.001*reconstruction + 0.001*gss
topic #22: 0.004*ep + 0.004*qda + 0.003*iep + 0.002*ldg + 0.002*reliability + 0.002*classification + 0.002*incomplete + 0.001*fixed + 0.001*parrish + 0.001*tilted
topic #23: 0.009*log + 0.005*gesture + 0.004*features + 0.004*probability + 0.004*inf + 0.003*motion + 0.003*action + 0.003*recognition + 0.003*parse + 0.003*svm
topic #24: 0.004*wbic + 0.003*nln + 0.002*watanabe + 0.001*nkn + 0.001*bic + 0.001*kn + 0.001*rlcts + 0.001*dw + 0.001*rlct + 0.001*parity
topic #25: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #26: 0.003*ka + 0.003*yt + 0.002*ep + 0.002*cumulants + 0.002*xt + 0.002*dalalyan + 0.002*correction + 0.002*seqsew + 0.002*cumulant + 0.002*bt
topic #27: 0.004*efs + 0.003*subspaces + 0.002*omp + 0.002*subspace + 0.001*unions + 0.001*dyer + 0.001*coherence + 0.001*elhamifar + 0.001*vidal + 0.001*ankaranarayanan
topic #28: 0.005*cap + 0.001*magnani + 0.001*ck + 0.001*weekly + 0.001*hyperplanes + 0.001*unson + 0.001*annah + 0.001*ultivariate + 0.001*daptive + 0.001*partitioning
topic #29: 0.004*sfa + 0.004*gsfa + 0.002*planted + 0.002*clique + 0.002*subgraph + 0.001*lov + 0.001*sz + 0.001*def + 0.001*kp + 0.001*wiskott
topic #30: 0.003*coda + 0.003*discriminant + 0.002*nonparanormal + 0.002*copula + 0.001*spearman + 0.001*rns + 0.001*rho + 0.001*han + 0.001*fj + 0.001*tau
topic #31: 0.000*sod + 0.000*fitc + 0.000*gpr + 0.000*ifgt + 0.000*synth + 0.000*smse + 0.000*hybrid + 0.000*hyperparameter + 0.000*msll + 0.000*sarcos
topic #32: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #33: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #34: 0.005*mlum + 0.003*cur + 0.003*nystr + 0.003*modified + 0.002*multicategory + 0.002*tuned + 0.001*soft + 0.001*ar + 0.001*lum + 0.001*drineas
topic #35: 0.006*gurls + 0.001*bgurls + 0.001*tacchetti + 0.001*rls + 0.001*matteo + 0.001*santoro + 0.001*optdigit + 0.001*pavan + 0.001*pendigit + 0.001*pipelines
topic #36: 0.004*sod + 0.003*fitc + 0.002*gpr + 0.002*synth + 0.001*smse + 0.001*ifgt + 0.001*mvm + 0.001*hybrid + 0.001*msll + 0.001*sarcos
topic #37: 0.002*ocl + 0.002*hs + 0.002*expert + 0.002*items + 0.002*qi + 0.002*macroscopic + 0.002*contingencies + 0.001*niu + 0.001*tucb + 0.001*requests
topic #38: 0.005*sdca + 0.004*anomalous + 0.003*records + 0.003*fgss + 0.003*sgd + 0.001*perm + 0.001*agd + 0.001*apd + 0.001*dca + 0.001*scan
topic #39: 0.002*rabanter + 0.002*derivative + 0.002*jd + 0.001*derivatives + 0.001*bimodal + 0.001*olynomial + 0.001*ijbels + 0.001*equispaced + 0.001*wj + 0.001*brabanter
topic #40: 0.000*ka + 0.000*ep + 0.000*correction + 0.000*xa + 0.000*cumulants + 0.000*qa + 0.000*kn + 0.000*ising + 0.000*cumulant + 0.000*ec
topic #41: 0.003*pruning + 0.003*query + 0.003*orange + 0.002*fri + 0.002*lj + 0.002*automaton + 0.002*python + 0.002*null + 0.002*qs + 0.002*queries
topic #42: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #43: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #44: 0.005*mlpack + 0.004*mjp + 0.002*skew + 0.002*pw + 0.002*ica + 0.002*tr + 0.002*connections + 0.002*lingam + 0.002*pairwise + 0.002*tanh
topic #45: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #46: 0.004*isometry + 0.003*fsc + 0.003*co + 0.003*csr + 0.002*pfe + 0.002*isometric + 0.002*tangent + 0.002*parallel + 0.002*ber + 0.001*elds
topic #47: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #48: 0.005*fd + 0.003*kappa + 0.003*privacy + 0.003*cp + 0.003*scad + 0.002*lasso + 0.002*differential + 0.002*bic + 0.002*pd + 0.001*ada
topic #49: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #50: 0.004*aluma + 0.002*pool + 0.002*optmax + 0.002*mellow + 0.001*cal + 0.001*favg + 0.001*queries + 0.001*aggressive + 0.001*qbc + 0.001*alfspaces
topic #51: 0.003*lasso + 0.002*pred + 0.002*scaled + 0.002*clime + 0.001*kk + 0.001*glasso + 0.001*spectrum + 0.001*nversion + 0.001*asso + 0.001*caled
topic #52: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #53: 0.004*px + 0.003*topic + 0.003*zi + 0.003*variational + 0.003*dirichlet + 0.002*manifold + 0.002*document + 0.002*dn + 0.002*documents + 0.002*spaces
topic #54: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #55: 0.002*mmax + 0.002*davenport + 0.002*completion + 0.002*kmax + 0.002*jt + 0.002*ompletion + 0.001*srebro + 0.001*rs + 0.001*foygel + 0.001*hou
topic #56: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #57: 0.004*suu + 0.003*vf + 0.002*tangent + 0.002*harmonic + 0.002*wll + 0.002*slu + 0.002*sul + 0.002*uu + 0.002*fx + 0.002*cos
topic #58: 0.004*budgetedsvm + 0.002*amm + 0.001*bsgd + 0.001*budgeted + 0.001*svm + 0.001*vucetic + 0.001*pegasos + 0.001*libsvm + 0.001*toolbox + 0.001*crammer
topic #59: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #60: 0.004*ryabko + 0.003*dh + 0.002*ergodic + 0.002*telescope + 0.002*hk + 0.001*homogeneity + 0.001*ary + 0.001*khaleghi + 0.001*distributional + 0.001*ighly
topic #61: 0.003*icm + 0.003*normalised + 0.003*cavity + 0.002*vb + 0.002*nakajima + 0.002*normalisation + 0.002*cbh + 0.002*walk + 0.002*vbmf + 0.002*cah
topic #62: 0.004*handshape + 0.002*signer + 0.002*skin + 0.001*eatures + 0.001*roussos + 0.001*sam + 0.001*color + 0.001*wp + 0.001*occlusion + 0.001*ffine
topic #63: 0.004*lx + 0.002*ly + 0.002*rmls + 0.002*lxu + 0.002*nx + 0.002*pls + 0.002*lyv + 0.001*queries + 0.001*vec + 0.001*dy
topic #64: 0.000*cebm + 0.000*rebm + 0.000*convolutional + 0.000*dtbm + 0.000*recurrent + 0.000*rbm + 0.000*missing + 0.000*energy + 0.000*chrauwen + 0.000*troobandt
topic #65: 0.003*poly + 0.003*parallel + 0.002*halfspace + 0.001*processors + 0.001*ervedio + 0.001*stages + 0.001*nesterov + 0.001*perceptron + 0.001*vitter + 0.001*servedio
topic #66: 0.000*ivm + 0.000*girolami + 0.000*contour + 0.000*ep + 0.000*iep + 0.000*vb + 0.000*la + 0.000*damping + 0.000*tilted + 0.000*mc
topic #67: 0.004*nystr + 0.002*jkernelmachines + 0.002*kernels + 0.002*svd + 0.002*thome + 0.002*picard + 0.002*matthieu + 0.001*talwalkar + 0.001*singular + 0.001*etc
topic #68: 0.005*markov + 0.004*convex + 0.004*penalty + 0.004*proposition + 0.003*ow + 0.003*sparsity + 0.003*solution + 0.003*vertices + 0.003*variables + 0.003*penalties
topic #69: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #70: 0.005*regret + 0.005*pr + 0.004*vy + 0.003*inequality + 0.003*bounds + 0.003*rate + 0.003*bandit + 0.003*dence + 0.003*process + 0.003*un
topic #71: 0.005*lsd + 0.005*kn + 0.003*lmm + 0.003*bn + 0.002*fdn + 0.002*skeleton + 0.002*cpi + 0.002*fd + 0.001*edges + 0.001*fpn
topic #72: 0.003*vb + 0.002*bkl + 0.002*site + 0.002*pproximate + 0.002*parameterisations + 0.001*cholesky + 0.001*seeger + 0.001*optimisation + 0.001*nference + 0.001*barber
topic #73: 0.005*comparators + 0.003*cww + 0.003*cxx + 0.002*hx + 0.002*ky + 0.002*kbr + 0.002*hy + 0.002*comparator + 0.002*sorting + 0.001*kx
topic #74: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #75: 0.004*covariance + 0.004*training + 0.004*gp + 0.004*gradient + 0.003*gaussian + 0.003*depth + 0.003*dq + 0.003*gcv + 0.003*di + 0.003*models
topic #76: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #77: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #78: 0.003*kr + 0.003*shuf + 0.002*ztk + 0.002*disco + 0.002*sztk + 0.002*basket + 0.002*mapreduce + 0.001*minhash + 0.001*adjusted + 0.001*similarity
topic #79: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #80: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #81: 0.003*zs + 0.002*documents + 0.002*mab + 0.002*bandits + 0.002*contextual + 0.001*slot + 0.001*zooming + 0.001*document + 0.001*kleinberg + 0.001*radlinski
topic #82: 0.005*ell + 0.002*svm + 0.001*sang + 0.001*wok + 0.001*abeled + 0.001*eakly + 0.001*tsvm + 0.001*calable + 0.001*hou + 0.001*violated
topic #83: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #84: 0.003*ji + 0.003*msmtfl + 0.002*ulti + 0.002*dirtymtl + 0.001*gi + 0.001*wii + 0.001*tage + 0.001*wg + 0.001*gic + 0.001*jalali
topic #85: 0.008*ln + 0.006*rd + 0.005*xi + 0.004*margin + 0.004*exp + 0.004*ip + 0.004*let + 0.004*earning + 0.003*hypothesis + 0.003*dx
topic #86: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #87: 0.005*regression + 0.005*sparse + 0.005*xt + 0.005*pca + 0.004*estimator + 0.004*library + 0.004*tapkee + 0.004*tpower + 0.004*embedding + 0.003*risk
topic #88: 0.004*fz + 0.003*mee + 0.003*operational + 0.002*fh + 0.002*zhou + 0.002*rudin + 0.002*ch + 0.002*opcost + 0.002*optimistic + 0.002*bb
topic #89: 0.004*wanbia + 0.003*congruence + 0.003*entries + 0.003*mi + 0.003*onto + 0.003*projd + 0.003*sparseness + 0.003*nb + 0.003*language + 0.003*remark
topic #90: 0.004*rllib + 0.003*labeled + 0.003*ggmc + 0.002*unlabeled + 0.002*lgc + 0.002*typedef + 0.002*ssl + 0.002*reinforcement + 0.002*lapsvm + 0.002*rl
topic #91: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
topic #92: 0.006*avgm + 0.003*mosift + 0.002*emosift + 0.002*somp + 0.001*codebook + 0.001*mld + 0.001*vq + 0.001*pyramid + 0.001*wan + 0.001*uchi
topic #93: 0.007*variational + 0.004*laplace + 0.004*da + 0.003*inference + 0.003*nonconjugate + 0.002*regularized + 0.002*blei + 0.002*delta + 0.002*conjugate + 0.002*logistic
topic #94: 0.004*angles + 0.002*cos + 0.002*weakly + 0.002*packing + 0.002*cai + 0.002*sphere + 0.002*jiang + 0.002*angle + 0.002*iang + 0.001*pheres
topic #95: 0.005*scoring + 0.003*mk + 0.003*mn + 0.003*roc + 0.002*ranking + 0.002*mnn + 0.002*nearest + 0.002*cl + 0.002*mencon + 0.002*aggregation
topic #96: 0.004*xb + 0.003*xa + 0.002*bethe + 0.002*trw + 0.002*bp + 0.001*proximal + 0.001*ha + 0.001*ab + 0.001*hb + 0.001*hler
topic #97: 0.004*mo + 0.002*uncertainty + 0.002*mpm + 0.002*takeda + 0.001*uzuki + 0.001*anamori + 0.001*elation + 0.001*xo + 0.001*onjugate + 0.001*uo
topic #98: 0.000*jkernelmachines + 0.000*thome + 0.000*library + 0.000*kernels + 0.000*matthieu + 0.000*picard + 0.000*svm + 0.000*vision + 0.000*cord + 0.000*etc
topic #99: 0.000*tntn + 0.000*miss + 0.000*negatively + 0.000*neapolitan + 0.000*ndings + 0.000*ncmigs + 0.000*natsoulis + 0.000*nance + 0.000*multicategory + 0.000*mortality
Latent Dirichlet allocation
In natural language processing, latent Dirichlet allocation (LDA) is a generative model that allows sets of observations to be explained by unobserved groups that explain why some parts of the data are similar. For example, if observations are words collected into documents, it posits that each document is a mixture of a small number of topics and that each word's creation is attributable to one of the document's topics. LDA is an example of a topic model and was first presented as a graphical model for topic discovery by David Blei, Andrew Ng, and Michael Jordan in 2003.
Topics in LDA
In LDA, each document may be viewed as a mixture of various topics. This is similar to probabilistic latent semantic analysis (pLSA), except that in LDA the topic distribution is assumed to have a Dirichlet prior. In practice, this results in more reasonable mixtures of topics in a document. It has been noted, however, that the pLSA model is equivalent to the LDA model under a uniform Dirichlet prior distribution.
For example, an LDA model might have topics that can be classified as CAT_related and DOG_related. A topic has probabilities of generating various words, such as milk, meow, and kitten, which can be classified and interpreted by the viewer as "CAT_related". Naturally, the word cat itself will have high probability given this topic. The DOG_related topic likewise has probabilities of generating each word: puppy, bark, and bone might have high probability. Words without special relevance, such as the (see function word), will have roughly even probability between classes (or can be placed into a separate category). A topic is not strongly defined, neither semantically nor epistemologically. It is identified on the basis of supervised labeling and (manual) pruning on the basis of their likelihood of co-occurrence. A lexical word may occur in several topics with a different probability, however, with a different typical set of neighboring words in each topic.
Each document is assumed to be characterized by a particular set of topics. This is akin to the standard bag of words model assumption, and makes the individual words exchangeable.
Model
With plate notation, the dependencies among the many variables can be captured concisely. The boxes are “plates” representing replicates. The outer plate represents documents, while the inner plate represents the repeated choice of topics and words within a document. M denotes the number of documents, N the number of words in a document. Thus:
α is the parameter of the Dirichlet prior on the per-document topic distributions,
β is the parameter of the Dirichlet prior on the per-topic word distribution,
\theta_i is the topic distribution for document i,
\phi_k is the word distribution for topic k,
z_{ij} is the topic for the jth word in document i, and
w_{ij} is the specific word.
The w_{ij} are the only observable variables, and the other variables are latent variables. Mostly, the basic LDA model will be extended to a smoothed version to gain better results .[citation needed] The plate notation is shown on the right, where K denotes the number of topics considered in the model and:
\phi is a K*V (V is the dimension of the vocabulary) Markov matrix each row of which denotes the word distribution of a topic.
The generative process behind is that documents are represented as random mixtures over latent topics, where each topic is characterized by a distribution over words. LDA assumes the following generative process for a corpus D consisting of M documents each of length N_i:
1. Choose \theta_i \, \sim \, \mathrm{Dir}(\alpha) , where i \in \{ 1,\dots,M \} and \mathrm{Dir}(\alpha) is the Dirichlet distribution for parameter \alpha
2. Choose \phi_k \, \sim \, \mathrm{Dir}(\beta) , where k \in \{ 1,\dots,K \}
3. For each of the word positions i, j, where j \in \{ 1,\dots,N_i \} , and i \in \{ 1,\dots,M \}
(a) Choose a topic z_{i,j} \,\sim\, \mathrm{Multinomial}(\theta_i).
(b) Choose a word w_{i,j} \,\sim\, \mathrm{Multinomial}( \phi_{z_{i,j}}) .
(Note that the Multinomial distribution here refers to the Multinomial with only one trial. It is formally equivalent to the categorical distribution.)
The lengths N_i are treated as independent of all the other data generating variables (q and z). The subscript is often dropped, as in the plate diagrams shown here.
Inference
Learning the various distributions (the set of topics, their associated word probabilities, the topic of each word, and the particular topic mixture of each document) is a problem of Bayesian inference. The original paper used a variational Bayes approximation of the posterior distribution;[1] alternative inference techniques use Gibbs sampling and expectation propagation.
Following is the derivation of the equations for collapsed Gibbs sampling, which means \varphis and \thetas will be integrated out. For simplicity, in this derivation the documents are all assumed to have the same length N_{}. The derivation is equally valid if the document lengths vary.
Applications, extensions and similar techniques
Topic modeling is a classic problem in information retrieval. Related models and techniques are, among others, latent semantic indexing, independent component analysis, probabilistic latent semantic indexing, non-negative matrix factorization, and Gamma-Poisson distribution.
The LDA model is highly modular and can therefore be easily extended. The main field of interest is modeling relations between topics. This is achieved by using another distribution on the simplex instead of the Dirichlet. The Correlated Topic Model follows this approach, inducing a correlation structure between topics by using the logistic normal distribution instead of the Dirichlet. Another extension is the hierarchical LDA (hLDA), where topics are joined together in a hierarchy by using the nested Chinese restaurant process. LDA can also be extended to a corpus in which a document includes two types of information (e.g., words and names), as in the LDA-dual model. Nonparametric extensions of LDA include the Hierarchical Dirichlet process mixture model, which allows the number of topics to be unbounded and learnt from data and the Nested Chinese Restaurant Process which allows topics to be arranged in a hierarchy whose structure is learnt from data.
As noted earlier, PLSA is similar to LDA. The LDA model is essentially the Bayesian version of PLSA model. The Bayesian formulation tends to perform better on small datasets because Bayesian methods can avoid overfitting the data. In a very large dataset, the results are probably the same. One difference is that PLSA uses a variable d to represent a document in the training set. So in PLSA, when presented with a document the model hasn't seen before, we fix \Pr(w \mid z)—the probability of words under topics—to be that learned from the training set and use the same EM algorithm to infer \Pr(z \mid d)—the topic distribution under d. Blei argues that this step is cheating because you are essentially refitting the model to the new data.
Variations on LDA have been used to automatically put natural images into categories, such as "bedroom" or "forest", by treating an image as a document, and small patches of the image as words; one of the variations is called Spatial Latent Dirichlet Allocation.
from wiki http://en.wikipedia.org/wiki/Latent_Dirichlet_allocation