9  PCA Plots

9.1 Introduction

This tutorial is based on a nice blog post by Claus Wilke: https://clauswilke.com/blog/2020/09/07/pca-tidyverse-style/

Functions from the Tidyverse packages (dplyr , tidyr, ggplot2) and broom will be used in this tutorial. As example data a lipidomics dataset is imported that contains the lipid concentrations as columns and with one additional column indicating the experimental group

d_long <- read_csv(here("data/Metabolites-1614644-supplementary.csv"))
Table 9.1: Test dataset in tidy format
SubjectID Group CE 16:0 CE 17:0 CE 17:1 CE 18:0 CE 18:1 CE 18:2 CE 20:1 CE 20:2 CE 20:3 CE 20:4 CE 20:5 CE 22:4 CE 22:6 CE 24:4 Cer d18:0/16:0 Cer d18:0/18:0 Cer d18:0/20:0 Cer d18:0/22:0 Cer d18:0/24:1 Cer d18:1/16:0 Cer d18:1/18:0 Cer d18:1/20:0 Cer d18:1/22:0 Cer d18:1/24:0 Cer d18:1/24:1 Cer d18:1/25:0 Cer d18:1/26:0 Cer d18:2/22:0 Cer d18:2/24:1 DG 14:0_18:1 DG 16:0_16:0 DG 16:0_16:1 DG 16:0_20:3 DG 16:0_20:4 DG 16:0_22:6 DG 16:1_18:1 DG 18:0_18:1 DG 18:0_18:2 DG 18:0_20:4 DG 18:1_18:1 DG 18:1_18:2 DG 18:1_18:3 DG 18:1_20:3 DG 18:1_20:4 DG 18:2_18:2 DG 18:2_20:3 DG 18:2_20:4 GM3 d18:1/16:0 GM3 d18:1/18:0 GM3 d18:1/20:0 GM3 d18:1/22:0 Hex2Cer d18:1/16:0 Hex2Cer d18:1/18:0 Hex2Cer d18:1/22:0 Hex2Cer d18:1/24:0 Hex2Cer d18:1/24:1 Hex3Cer d18:1/16:0 HexCer d18:1/18:0 HexCer d18:1/20:0 HexCer d18:1/22:0 HexCer d18:1/24:0 HexCer d18:1/24:1 LPC 14:0 LPC 15:0 LPC 16:1 LPC 17:0 LPC 17:1 LPC 18:0 LPC 18:1 LPC 18:2 LPC 18:3 LPC 19:0 LPC 19:1 LPC 20:0 LPC 20:1 LPC 20:2 LPC 20:3 LPC 20:4 LPC 20:5 LPC 22:0 LPC 22:1 LPC 22:5 LPC 22:6 LPC 24:0 LPC O-16:0 LPC O-18:0 LPC O-18:1 LPC O-20:0 LPC O-20:1 LPC O-22:0 LPC O-22:1 LPC P-16:0 LPC P-18:0 LPC P-18:1 LPC P-20:0 LPE 16:0 LPE 18:0 LPE 18:1 LPE 18:2 LPE 20:4 LPE 22:6 LPE P-16:0 LPE P-18:0 LPE P-18:1 LPI 20:4 LPS 16:0 LPS 18:0 LPS 18:1 LPS 18:2 PC 31:0 PC 31:1 PC 32:0 PC 32:1 PC 32:2 PC 32:3 PC 33:1 PC 33:2 PC 34:0 PC 34:2 PC 34:3 PC 34:4 PC 34:5 PC 35:1 PC 35:2 PC 35:3 PC 35:4 PC 35:5 PC 36:1 PC 36:2 PC 36:3 PC 36:4 a PC 36:4 b PC 36:5 PC 36:6 PC 36:7 PC 37:4 PC 37:5 PC 37:6 PC 38:3 PC 38:6 PC 38:7 PC 38:8 PC 39:5 PC 39:6 PC 39:7 PC 40:6 PC 40:7 PC 40:8 PC O-32:0 PC O-32:1 PC O-32:2 PC O-34:1 PC O-34:2 PC O-36:1 PC O-36:2 PC O-36:4 PC O-36:5 PC O-38:4 PC O-38:5 PC O-38:6 PC O-40:5 PC O-40:7 PC P-32:0 PC P-32:1 PC P-34:1 PC P-34:2 PC P-36:2 PC P-36:4 PC P-36:5 PC P-38:4 PC P-38:5 PC P-40:5 PC P-40:6 PE 32:1 PE 34:0 PE 34:1 PE 34:2 PE 34:3 PE 35:1 PE 35:2 PE 36:1 PE 36:2 PE 36:4 a PE 36:4 b PE 36:5 PE 38:3 PE 38:4 PE 38:5 PE 38:6 PE 40:4 PE 40:6 PE 40:7 PE O-34:1 PE O-34:2 PE O-36:2 PE O-36:3 PE O-38:4 PE O-38:5 PE O-40:5 PE O-40:7 PE P-16:0/18:1 PE P-16:0/18:2 PE P-16:0/20:4 PE P-16:0/22:5 PE P-16:0/22:6 PE P-18:0/18:1 PE P-18:0/18:2 PE P-18:0/20:4 PE P-18:0/22:5 PE P-18:0/22:6 PE P-20:0/20:4 PG 34:1 PG 36:1 PG 36:2 PI 32:0 PI 32:1 PI 34:1 PI 34:2 PI 35:1 PI 35:2 PI 36:2 PI 36:4 PI 36:5 PI 37:4 PI 38:4 PI 38:5 PI 38:6 PI 40:6 S1P d16:1 S1P d17:1 S1P d18:0 S1P d18:1 S1P d18:2 S1P d19:1 S1P d20:1 SM 30:1 SM 31:1 SM 32:0 SM 32:1 SM 32:2 SM 33:1 SM 34:1 SM 34:2 SM 34:3 SM 35:1 SM 35:2 SM 36:1 SM 36:2 SM 36:3 SM 38:1 SM 38:2 SM 38:3 SM 39:1 SM 40:1 SM 40:2 SM 41:1 SM 42:1 SM 42:2 SM 43:1 SM 44:1 SM 44:2 TG 48:0 TG 48:1 TG 48:2 TG 48:3 TG 49:1 TG 50:0 TG 50:1 TG 50:2 TG 50:3 TG 50:4 TG 51:0 TG 51:1 TG 51:2 TG 52:1 TG 52:2 TG 52:3 TG 52:4 TG 53:2 TG 54:1 TG 54:2 TG 54:3 TG 54:4 TG 54:5 TG 54:6 TG 56:6 TG 56:8 TG 58:8
HB_01 Healthy 36.82 1.02 1.34 12.34 573.83 4783.39 0.38 5.82 116.52 4123.15 44.71 12.74 33.72 0.30 0.02 0.03 0.02 0.05 0.85 0.20 0.29 0.21 1.44 2.38 2.00 0.07 0.03 0.12 0.17 0.49 1.11 1.27 0.69 3.83 0.12 5.70 2.05 4.96 3.19 30.36 34.52 3.43 1.56 6.97 12.12 1.47 5.26 2.39 1.07 0.20 0.11 4.76 0.20 0.13 0.10 0.21 0.74 0.07 0.04 0.09 0.11 0.09 0.80 1.85 6.25 2.50 0.30 197.98 52.83 105.47 0.79 0.84 0.12 0.24 0.69 0.83 5.45 94.90 0.60 0.06 0.03 6.66 1.87 0.07 1.62 0.58 1.62 0.04 0.04 0.00 0.01 0.30 0.04 0.04 0.04 1.99 4.55 2.43 2.46 1.53 0.16 0.31 0.47 0.13 0.33 0.27 0.31 0.07 0.15 0.69 0.14 18.23 20.27 4.94 0.11 3.07 8.96 6.35 725.25 56.00 2.07 0.13 10.78 17.68 4.78 3.34 0.02 140.27 397.37 195.86 63.39 347.22 21.84 0.36 0.03 36.10 5.71 0.20 75.69 83.26 1.73 0.01 8.12 0.95 0.10 31.54 7.50 4.86 5.60 2.73 0.59 15.95 5.95 0.83 4.54 61.03 2.69 26.80 44.17 2.25 7.63 1.42 2.32 0.46 4.77 8.37 2.37 16.51 0.79 9.47 7.78 1.65 0.16 5.00 0.05 0.68 1.27 0.19 0.05 0.10 0.51 3.16 0.90 2.22 0.11 0.22 5.39 2.22 2.81 0.30 0.37 0.29 0.34 0.19 1.12 0.27 7.36 3.21 3.68 0.42 0.17 0.25 0.94 1.07 0.44 0.28 0.71 3.51 0.75 0.28 0.07 0.08 0.05 0.37 0.13 0.32 3.01 5.30 0.12 0.26 9.29 11.66 0.18 0.95 74.62 6.87 0.43 0.26 0.04 0.02 0.06 0.58 0.17 0.01 0.00 0.05 0.11 0.05 1.93 0.16 4.68 389.77 8.08 0.05 4.82 0.91 24.57 31.56 0.48 8.62 3.38 0.80 6.89 17.32 10.78 10.35 7.62 33.19 0.48 0.08 0.23 5.97 7.81 21.94 6.19 1.93 3.95 28.19 53.31 54.20 1.48 0.41 1.54 4.84 16.46 70.45 29.21 95.72 1.88 1.98 23.87 113.44 24.18 48.59 16.26 10.51 7.99 0.17
HB_02 Healthy 45.57 1.11 1.28 10.16 712.27 6232.73 0.40 5.80 113.39 4415.84 57.05 14.15 42.67 0.33 0.01 0.02 0.02 0.05 1.11 0.21 0.25 0.20 1.73 2.91 2.38 0.09 0.04 0.10 0.15 0.02 0.59 0.32 0.26 1.68 0.01 1.12 1.62 3.38 1.42 5.61 6.70 0.89 0.70 5.31 2.72 0.67 3.25 3.08 1.20 0.20 0.11 7.48 0.36 0.19 0.10 0.24 0.78 0.04 0.03 0.08 0.10 0.08 1.05 1.75 6.59 2.05 0.26 153.57 52.02 108.45 0.84 0.67 0.10 0.26 0.61 0.75 3.77 74.98 0.87 0.07 0.04 5.97 1.21 0.07 1.62 0.67 1.54 0.05 0.05 0.01 0.01 0.32 0.06 0.04 0.05 2.59 4.80 2.78 3.02 1.72 0.17 0.28 0.68 0.14 0.39 0.30 0.31 0.09 0.15 0.74 0.15 17.55 30.93 6.98 0.17 3.69 8.16 6.54 614.49 71.32 2.64 0.14 11.14 15.42 4.79 4.09 0.04 115.08 457.87 190.02 53.79 333.31 31.97 0.48 0.03 28.79 6.26 0.24 57.56 88.95 2.00 0.02 10.74 0.88 0.14 23.68 7.56 4.78 4.38 2.84 0.63 16.71 6.73 1.37 6.63 65.08 3.61 31.57 55.85 2.63 10.20 1.47 2.56 0.39 5.54 9.06 3.26 23.47 1.07 9.15 11.27 1.91 0.15 4.60 0.03 0.75 1.08 0.15 0.02 0.10 0.70 2.65 0.77 2.05 0.11 0.18 7.22 1.89 1.96 0.27 0.26 0.20 0.60 0.27 2.16 0.34 9.41 4.07 5.37 0.32 0.15 0.36 1.14 2.00 0.51 0.47 1.20 4.53 1.22 0.29 0.10 0.06 0.02 0.22 0.45 0.68 4.86 8.59 0.24 0.36 19.72 11.50 0.30 1.16 85.63 6.94 0.55 0.34 0.04 0.02 0.06 0.50 0.14 0.01 0.00 0.05 0.11 0.08 2.31 0.21 4.98 397.57 9.34 0.04 4.50 0.71 23.48 41.21 0.45 9.93 2.83 0.68 6.72 15.78 10.63 10.42 8.15 33.41 0.59 0.07 0.20 5.00 1.77 5.04 1.26 1.07 2.30 12.19 15.12 9.56 0.61 0.24 0.70 1.93 11.54 29.36 8.07 16.65 0.54 1.39 16.94 33.20 5.63 7.21 2.76 9.31 3.98 0.06
HB_03 Healthy 40.64 0.87 1.58 8.20 632.30 4920.22 0.42 5.55 149.03 4034.94 51.56 17.97 61.90 0.23 0.01 0.02 0.02 0.05 1.25 0.35 0.38 0.40 2.35 3.50 3.35 0.10 0.03 0.23 0.39 0.22 0.66 0.40 0.46 2.40 0.07 1.72 0.45 0.92 1.41 9.97 11.02 1.84 1.27 8.05 4.35 1.21 5.71 2.24 0.77 0.16 0.09 3.04 0.21 0.20 0.13 0.24 0.27 0.05 0.02 0.10 0.13 0.08 1.25 1.98 8.58 2.25 0.37 156.16 54.13 91.03 0.77 0.70 0.12 0.21 0.68 0.79 5.48 77.70 0.72 0.07 0.04 9.10 1.94 0.08 1.28 0.46 1.19 0.05 0.04 0.01 0.01 0.21 0.04 0.03 0.03 2.96 5.81 2.89 3.30 1.88 0.33 0.25 0.36 0.09 0.35 0.28 0.31 0.09 0.13 0.90 0.30 13.22 31.86 9.69 0.16 4.72 8.71 5.66 635.28 84.25 3.62 0.14 11.14 14.28 5.11 4.06 0.04 119.70 446.95 186.15 53.95 314.50 31.73 0.59 0.03 29.70 6.63 0.38 85.55 112.37 2.33 0.01 8.95 1.28 0.15 39.94 11.01 5.10 4.83 2.57 0.39 13.05 4.45 0.81 3.49 44.28 2.28 22.80 45.42 1.86 6.43 1.17 1.48 0.38 4.42 5.46 2.03 14.87 0.70 6.68 7.25 1.45 0.14 11.04 0.02 1.18 2.50 0.35 0.07 0.24 1.25 4.16 1.31 3.84 0.29 0.60 11.94 3.70 6.99 0.97 0.65 0.57 0.42 0.20 0.87 0.26 6.56 3.44 4.77 0.27 0.15 0.21 1.21 1.17 0.40 0.24 0.59 3.02 0.95 0.27 0.05 0.19 0.02 0.41 0.37 0.56 3.83 6.32 0.12 0.39 17.17 12.34 0.24 1.09 85.66 9.06 0.56 0.46 0.04 0.02 0.04 0.40 0.13 0.01 0.00 0.07 0.10 0.09 2.13 0.30 4.63 292.70 9.98 0.05 5.17 0.77 20.74 38.90 0.42 8.09 4.05 0.53 6.77 14.45 13.00 8.36 6.67 30.75 0.44 0.08 0.22 2.83 3.37 9.93 2.45 1.33 1.29 10.49 23.88 20.14 0.73 0.10 0.60 2.49 2.85 35.66 11.39 34.76 0.71 0.40 4.44 43.24 8.51 14.60 6.08 10.63 6.20 0.10
HB_04 Healthy 27.80 0.67 1.67 10.33 827.38 7627.41 0.46 5.26 95.88 5715.39 90.64 18.29 92.51 0.32 0.01 0.03 0.02 0.07 1.11 0.23 0.47 0.26 2.19 2.98 3.11 0.08 0.04 0.17 0.29 0.14 0.77 0.28 0.19 1.35 0.12 1.03 1.29 3.46 1.71 5.38 5.12 1.01 0.65 5.63 2.68 0.67 3.69 5.37 1.94 0.39 0.16 7.76 0.50 0.35 0.19 0.38 0.97 0.04 0.03 0.06 0.07 0.06 0.89 1.83 8.08 2.44 0.36 214.99 67.15 130.13 0.88 0.82 0.13 0.33 0.79 0.99 5.22 116.75 1.12 0.07 0.04 9.42 2.47 0.07 1.53 0.57 1.47 0.05 0.05 0.00 0.01 0.33 0.05 0.05 0.04 2.38 5.69 2.70 3.04 1.72 0.24 0.31 0.48 0.12 0.42 0.29 0.33 0.11 0.15 0.67 0.13 14.22 34.91 8.03 0.13 3.93 10.61 6.30 557.16 103.25 2.55 0.14 13.23 16.80 5.34 3.82 0.05 171.93 522.99 207.60 66.00 363.21 34.35 0.48 0.03 32.86 6.23 0.35 69.09 117.99 2.01 0.01 10.81 1.19 0.17 32.95 8.40 5.50 5.22 2.56 0.50 17.63 6.22 1.20 5.27 53.45 3.06 29.12 46.48 3.13 10.19 1.46 2.26 0.52 5.97 10.43 2.99 20.05 1.07 7.20 11.13 2.25 0.18 7.77 0.03 0.81 1.51 0.25 0.03 0.11 0.82 3.68 0.59 2.81 0.24 0.25 7.22 2.58 3.71 0.38 0.33 0.26 0.36 0.20 1.69 0.28 7.16 4.41 4.89 0.49 0.19 0.25 1.09 1.63 0.71 0.37 1.13 3.66 1.07 0.32 0.06 0.07 0.04 0.29 0.39 0.71 5.53 9.38 0.28 0.46 21.22 12.41 0.29 1.24 90.67 7.83 0.57 0.37 0.05 0.03 0.08 0.66 0.21 0.01 0.00 0.07 0.12 0.10 2.70 0.29 4.76 388.18 12.54 0.06 5.41 0.96 30.81 37.74 0.73 9.26 4.11 0.76 9.15 23.51 13.42 13.23 9.49 43.24 0.53 0.07 0.24 4.28 1.64 5.08 1.40 0.99 2.54 8.91 15.50 9.56 0.57 0.21 0.52 1.46 6.30 22.70 6.94 16.75 0.33 1.00 7.73 21.32 3.60 5.73 2.87 6.65 3.65 0.06
HB_05 Healthy 26.21 0.93 1.76 14.02 810.18 7811.54 0.66 7.01 171.48 6238.77 50.53 18.38 90.20 0.38 0.01 0.05 0.03 0.08 1.20 0.27 0.45 0.31 2.10 3.20 3.18 0.08 0.05 0.16 0.28 0.22 0.30 0.45 0.41 2.25 0.14 1.96 2.44 4.89 2.62 10.06 11.91 1.16 0.83 4.09 3.93 0.89 3.62 4.02 1.68 0.27 0.19 4.46 0.22 0.19 0.16 0.23 0.64 0.05 0.04 0.07 0.07 0.06 0.99 1.99 8.16 2.70 0.37 205.91 69.11 137.94 0.87 0.94 0.13 0.29 0.88 1.02 7.43 126.11 0.66 0.08 0.05 8.38 2.86 0.08 2.24 0.83 2.24 0.06 0.07 0.01 0.01 0.42 0.08 0.05 0.06 2.67 6.05 2.91 3.24 1.94 0.31 0.36 0.52 0.13 0.37 0.28 0.36 0.12 0.16 0.89 0.14 17.78 27.54 6.63 0.13 3.33 6.94 6.83 618.59 73.62 2.73 0.18 12.30 16.99 4.61 4.29 0.02 143.72 456.82 205.75 71.45 360.53 30.82 0.46 0.04 31.51 7.47 0.28 100.62 115.45 1.85 0.01 13.82 1.10 0.18 34.54 9.81 5.17 9.44 4.89 0.87 20.90 6.71 1.23 7.44 81.86 5.04 40.85 62.77 3.74 13.21 2.76 3.13 0.61 8.88 10.04 4.59 24.90 0.98 10.79 12.49 2.29 0.18 4.78 0.03 0.80 1.88 0.26 0.06 0.15 0.67 3.40 0.91 2.47 0.15 0.43 7.32 2.52 5.30 0.45 0.59 0.30 0.38 0.26 1.37 0.28 9.33 4.17 5.38 0.42 0.19 0.30 1.32 1.71 0.74 0.25 0.70 4.64 0.92 0.37 0.10 0.08 0.03 0.30 0.26 0.47 3.90 5.02 0.21 0.24 8.84 10.95 0.17 0.81 86.83 7.34 0.50 0.38 0.10 0.05 0.14 1.06 0.19 0.03 0.01 0.05 0.11 0.09 2.35 0.21 5.19 437.15 11.51 0.04 5.71 1.00 36.85 50.71 0.58 12.44 4.38 0.76 8.01 23.70 15.01 11.84 10.08 47.27 0.56 0.09 0.31 7.09 3.50 9.80 2.95 1.31 3.72 16.68 29.82 19.00 1.04 0.36 0.94 2.27 13.69 40.87 11.75 25.68 0.75 2.67 14.56 36.97 7.93 9.55 3.99 6.75 3.22 0.11

9.2 Transform and Scale the Data

pca_res <- d_long %>% 
  select(where(is.numeric)) %>% # retain only numeric columns
  log2() |> 
  prcomp(scale = TRUE)

Compare this to plotting non-normalized concentrations

# Use broom to make the data ggplot ready and include annotations
pca_annot <- pca_res |> broom::augment(d_long)

pca_contrib <- pca_res |> tidy(matrix = "eigenvalues")

ggplot(data = pca_annot, aes(.fittedPC1, .fittedPC2, color = Group)) + 
geom_point(size = 1.5) + 
stat_ellipse(level = 0.95) +
theme_light() +
theme(aspect.ratio=1)

# Use broom to make the data ggplot ready and include annotations
pca_annot <- pca_res |> broom::augment(d_long)

pca_12 <- ggplot(data = pca_annot, aes(.fittedPC1, .fittedPC2, color = Group)) + 
  geom_point(size = 1.5) + 
  stat_ellipse(level = 0.95)+
  theme_light() +
  theme(legend.position = "none")


pca_34 <- ggplot(data = pca_annot, aes(.fittedPC3, .fittedPC4, color = Group)) + 
  geom_point(size = 1.5) + 
  stat_ellipse(level = 0.95) +
  theme_light() +
theme(legend.position = "none")

cowplot::plot_grid(pca_12, pca_34, nrow = 1, 
                   rel_widths = c(1,1), 
                   labels = c("A","B"))

# PCA plot of merged


 
m_log <- d_long  |> 
  dplyr::select(-Group) |> 
  dplyr::select(where(~!any(is.na(.)))) |> 
  column_to_rownames("SubjectID") |> 
  log2() 

d_annot <- d_long |> 
  select(SubjectID, Group)|> 
  column_to_rownames("SubjectID")

d_annot$Group <- factor(d_annot$Group)


# get pca result with annotation
pca_res <- PCAtools::pca(mat = m_log, center = TRUE, 
                         metadata = d_annot , 
                         scale = TRUE, 
                         transposed = TRUE)
  p_PCA <- PCAtools::biplot(
    pca_res,
    x = 1,
    y = 2 ,
    colby = "Group",
    #colkey = colby_color,
    legendPosition = 'right',
    pointSize = 3,
    lengthLoadingsArrowsFactor = 1.5,
    lab = NULL,
    sizeLoadingsNames = 2.5,
    alphaLoadingsArrow = 0.1,
    colLoadingsNames = "grey35",
    showLoadings = TRUE,
    ntopLoadings = 20,
    drawConnectorsLoadings = T,
    boxedLoadingsNames = T,
    widthLoadingsArrows = 0.5,
    widthConnectorsLoadings = 0.001,
    max.overlaps = 33,
    ellipseType = "t",
    # xlim = c(-22, 25),
    # ylim = c(-21, 20),
    ellipse = TRUE,
    ellipseLevel = 0.95,
    ellipseLineSize = 1,
    ellipseFill = TRUE,
    ellipseAlpha = .05,
    gridlines.minor = FALSE,
  )

p_PCA
    # theme(
    #   aspect.ratio = 1,
    #   panel.grid.major = element_line(size = .5),
    #   legend.position = c(.91, .93),
    #   legend.title = element_blank(),
    #   legend.background = element_rect(fill = alpha("white", 0.0), inherit.blank = TRUE)
    # )