9 Linear Discriminant Analysis
Learning objectives:
- Purpose of classifiers
- What are generative classifiers
- Gaussian Discriminant Analysis lead to curved decision boundaries
- Linear Discriminant Analysis and linear decision boundaries
- ScikitLearn approaches for Linear / Gaussian Discriminant Analysis
- Explore Naive Bayes classification
- Discuss Fisher’s linear discriminant analysis
library("bayesrules")
library("dplyr")
library("e1071")
library("ggplot2")
library("ggtext")
library("gt")
library("janitor")
library("magrittr") #need for "." in pipe acts
# library("MASS") #carefully use lda() later to not overwrite select()
library("patchwork")
library("tidyr")
sessionInfo()## R version 4.4.0 (2024-04-24)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 22.04.4 LTS
##
## Matrix products: default
## BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so; LAPACK version 3.10.0
##
## locale:
## [1] LC_CTYPE=C.UTF-8 LC_NUMERIC=C LC_TIME=C.UTF-8
## [4] LC_COLLATE=C.UTF-8 LC_MONETARY=C.UTF-8 LC_MESSAGES=C.UTF-8
## [7] LC_PAPER=C.UTF-8 LC_NAME=C LC_ADDRESS=C
## [10] LC_TELEPHONE=C LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C
##
## time zone: UTC
## tzcode source: system (glibc)
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] tidyr_1.3.1 patchwork_1.2.0 magrittr_2.0.3 janitor_2.2.0
## [5] gt_0.10.1 ggtext_0.1.2 ggplot2_3.5.1 e1071_1.7-14
## [9] dplyr_1.1.4 bayesrules_0.0.2
##
## loaded via a namespace (and not attached):
## [1] gridExtra_2.3 inline_0.3.19 rlang_1.1.3
## [4] snakecase_0.11.1 matrixStats_1.3.0 compiler_4.4.0
## [7] loo_2.7.0 vctrs_0.6.5 reshape2_1.4.4
## [10] stringr_1.5.1 pkgconfig_2.0.3 fastmap_1.2.0
## [13] backports_1.5.0 utf8_1.2.4 threejs_0.3.3
## [16] promises_1.3.0 rmarkdown_2.27 markdown_1.12
## [19] nloptr_2.0.3 purrr_1.0.2 xfun_0.44
## [22] cachem_1.1.0 jsonlite_1.8.8 highr_0.11
## [25] later_1.3.2 parallel_4.4.0 R6_2.5.1
## [28] dygraphs_1.1.1.6 bslib_0.7.0 stringi_1.8.4
## [31] StanHeaders_2.32.9 boot_1.3-30 lubridate_1.9.3
## [34] jquerylib_0.1.4 Rcpp_1.0.12 bookdown_0.39
## [37] rstan_2.32.6 knitr_1.47 zoo_1.8-12
## [40] base64enc_0.1-3 bayesplot_1.11.1 httpuv_1.6.15
## [43] Matrix_1.7-0 splines_4.4.0 igraph_2.0.3
## [46] timechange_0.3.0 tidyselect_1.2.1 abind_1.4-5
## [49] yaml_2.3.8 codetools_0.2-20 miniUI_0.1.1.1
## [52] curl_5.2.1 pkgbuild_1.4.4 lattice_0.22-6
## [55] tibble_3.2.1 plyr_1.8.9 shiny_1.8.1.1
## [58] withr_3.0.0 groupdata2_2.0.3 posterior_1.5.0
## [61] evaluate_0.23 survival_3.5-8 proxy_0.4-27
## [64] RcppParallel_5.1.7 xml2_1.3.6 xts_0.13.2
## [67] pillar_1.9.0 tensorA_0.36.2.1 checkmate_2.3.1
## [70] DT_0.33 stats4_4.4.0 shinyjs_2.1.0
## [73] distributional_0.4.0 generics_0.1.3 rstantools_2.4.0
## [76] munsell_0.5.1 scales_1.3.0 minqa_1.2.7
## [79] gtools_3.9.5 xtable_1.8-4 class_7.3-22
## [82] glue_1.7.0 tools_4.4.0 shinystan_2.6.0
## [85] lme4_1.1-35.3 colourpicker_1.3.0 grid_4.4.0
## [88] QuickJSR_1.2.0 crosstalk_1.2.1 colorspace_2.1-0
## [91] nlme_3.1-164 cli_3.6.2 fansi_1.0.6
## [94] V8_4.4.2 gtable_0.3.5 sass_0.4.9
## [97] digest_0.6.35 htmlwidgets_1.6.4 htmltools_0.5.8.1
## [100] lifecycle_1.0.4 mime_0.12 rstanarm_2.32.1
## [103] gridtext_0.1.5 shinythemes_1.2.0 MASS_7.3-60.2