Soft PLS-DA

Predizione immagini

library(tidyverse)
library(kableExtra)
library(ggplot2)
library(mdatools)
#library(ggbiplot)
library(plotly)
library(stringr)

df_detrend = read.csv('Predizione_immagini_detrend.csv', sep = ';')
df_derivata = read.csv('Predizione_immagini_derivata.csv', sep = ';')


df_detrend$perc_Adulterant = 1-df_detrend$perc_origano

Conteggio campioni

colnames(df_detrend) = c('ID', 'Adulterant', 'Predicted_Oregano', 'NA', 'Contaminant', 'Type', 'Actual_oregano', 'Actual_adulterant')

df_detrend$Type = str_replace(df_detrend$Type, 'Miscela', 'Mix')
df_detrend$Type = str_replace(df_detrend$Type, 'Adulterante', 'Adulterant')
df_detrend$Type = str_replace(df_detrend$Type, 'Origano', 'Oregano')

p = ggplot(df_detrend, aes(Type, fill = Contaminant))+geom_bar()+
  theme_minimal()+
  ylab('')+
  xlab('')

ggplotly(p)

Detrend

kable(df_detrend, row.names = T) %>% kable_styling('striped', fixed_thead = T, full_width = FALSE) %>%scroll_box( height = "500px")

	ID	Adulterant	Predicted_Oregano	NA	Contaminant	Type	Actual_oregano	Actual_adulterant
1	P_A_01_R1	0.0748	0.9241	0.0011	Sumac	Mix	0.950	0.050
2	P_A_01_R2	0.0459	0.9530	0.0011	Sumac	Mix	0.950	0.050
3	P_A_01_R3	0.0543	0.9457	0.0000	Sumac	Mix	0.950	0.050
4	P_A_02_R1	0.1219	0.8765	0.0016	Sumac	Mix	0.900	0.100
5	P_A_02_R2	0.1173	0.8816	0.0011	Sumac	Mix	0.900	0.100
6	P_A_02_R3	0.1208	0.8782	0.0010	Sumac	Mix	0.900	0.100
7	P_A_03_R1	0.0820	0.9174	0.0006	Sumac	Mix	0.950	0.050
8	P_A_03_R2	0.0532	0.9454	0.0014	Sumac	Mix	0.950	0.050
9	P_A_03_R3	0.0617	0.9379	0.0004	Sumac	Mix	0.950	0.050
10	P_A_04_R1	0.1392	0.8595	0.0013	Sumac	Mix	0.900	0.100
11	P_A_04_R2	0.1176	0.8803	0.0021	Sumac	Mix	0.900	0.100
12	P_A_04_R3	0.1177	0.8798	0.0025	Sumac	Mix	0.900	0.100
13	P_A_05_R1	0.8759	0.1236	0.0004	Myrtle	Adulterant	0.000	1.000
14	P_A_05_R2	0.8561	0.1437	0.0003	Myrtle	Adulterant	0.000	1.000
15	P_A_05_R3	0.8522	0.1450	0.0029	Myrtle	Adulterant	0.000	1.000
16	P_A_06_R1	0.9539	0.0448	0.0013	Olive	Adulterant	0.000	1.000
17	P_A_06_R2	0.9250	0.0671	0.0079	Olive	Adulterant	0.000	1.000
18	P_A_06_R3	0.9124	0.0808	0.0068	Olive	Adulterant	0.000	1.000
19	P_A_07_R1	0.9850	0.0132	0.0018	Strawberry	Adulterant	0.000	1.000
20	P_A_07_R2	0.9912	0.0054	0.0035	Strawberry	Adulterant	0.000	1.000
21	P_A_07_R3	0.9926	0.0073	0.0002	Strawberry	Adulterant	0.000	1.000
22	P_A_08_R1	0.9831	0.0142	0.0027	Sumac	Adulterant	0.000	1.000
23	P_A_08_R2	0.9713	0.0243	0.0044	Sumac	Adulterant	0.000	1.000
24	P_A_08_R3	0.9753	0.0154	0.0093	Sumac	Adulterant	0.000	1.000
25	P_A_09_R1	0.0681	0.9319	0.0000	Infiorescenze	Oregano	1.000	0.000
26	P_A_09_R2	0.0792	0.9203	0.0005	Infiorescenze	Oregano	1.000	0.000
27	P_A_09_R3	0.0662	0.9330	0.0008	Infiorescenze	Oregano	1.000	0.000
28	P_A_10_R1	0.0052	0.9943	0.0005	Not Refined	Oregano	1.000	0.000
29	P_A_10_R2	0.0126	0.9863	0.0011	Not Refined	Oregano	1.000	0.000
30	P_A_10_R3	0.0063	0.9937	0.0000	Not Refined	Oregano	1.000	0.000
31	P_M_48_01_R1	0.1686	0.8314	0.0000	Strawberry	Mix	0.800	0.200
32	P_M_48_01_R2	0.1507	0.8493	0.0000	Strawberry	Mix	0.800	0.200
33	P_M_48_01_R3	0.1577	0.8421	0.0001	Strawberry	Mix	0.800	0.200
34	P_M_48_02_R1	0.3291	0.6709	0.0000	Strawberry	Mix	0.700	0.300
35	P_M_48_02_R2	0.3836	0.6164	0.0000	Strawberry	Mix	0.700	0.300
36	P_M_48_02_R3	0.3549	0.6425	0.0026	Strawberry	Mix	0.700	0.300
37	P_M_48_03_R1	0.0906	0.9064	0.0030	Sumac	Mix	0.800	0.200
38	P_M_48_03_R2	0.1026	0.8949	0.0025	Sumac	Mix	0.800	0.200
39	P_M_48_03_R3	0.0901	0.9073	0.0026	Sumac	Mix	0.800	0.200
40	P_M_48_04_R1	0.4463	0.5537	0.0000	Myrtle	Mix	0.400	0.600
41	P_M_48_04_R2	0.4244	0.5756	0.0000	Myrtle	Mix	0.400	0.600
42	P_M_48_04_R3	0.4252	0.5748	0.0000	Myrtle	Mix	0.400	0.600
43	P_M_48_05_R1	0.1061	0.8930	0.0010	Olive	Mix	0.700	0.300
44	P_M_48_05_R2	0.0939	0.9060	0.0002	Olive	Mix	0.700	0.300
45	P_M_48_05_R3	0.1186	0.8814	0.0000	Olive	Mix	0.700	0.300
46	P_M_48_06_R1	0.1912	0.8088	0.0000	Strawberry	Mix	0.800	0.200
47	P_M_48_06_R2	0.1942	0.8058	0.0000	Strawberry	Mix	0.800	0.200
48	P_M_48_06_R3	0.1593	0.8404	0.0003	Strawberry	Mix	0.800	0.200
49	P_M_48_07_R1	0.3606	0.6385	0.0009	Strawberry	Mix	0.600	0.400
50	P_M_48_07_R2	0.2927	0.7057	0.0016	Strawberry	Mix	0.600	0.400
51	P_M_48_07_R3	0.3677	0.6304	0.0019	Strawberry	Mix	0.600	0.400
52	P_M_48_08_R1	0.3597	0.6390	0.0013	Olive	Mix	0.600	0.400
53	P_M_48_08_R2	0.3171	0.6827	0.0001	Olive	Mix	0.600	0.400
54	P_M_48_08_R3	0.3045	0.6955	0.0000	Olive	Mix	0.600	0.400
55	P_M_48_14_R1	0.2169	0.7830	0.0001	Olive	Mix	0.800	0.200
56	P_M_48_14_R2	0.2159	0.7839	0.0001	Olive	Mix	0.800	0.200
57	P_M_48_14_R3	0.2377	0.7594	0.0030	Olive	Mix	0.800	0.200
58	P_M_48_16_R1	0.0045	0.9951	0.0004	Other	Mix	0.940	0.060
59	P_M_48_16_R2	0.0016	0.9984	0.0000	Other	Mix	0.940	0.060
60	P_M_48_16_R3	0.0068	0.9909	0.0023	Other	Mix	0.940	0.060
61	P_M_48_17_R1	0.0026	0.9973	0.0002	Other	Mix	0.985	0.015
62	P_M_48_17_R2	0.0038	0.9947	0.0015	Other	Mix	0.985	0.015
63	P_M_48_17_R3	0.0014	0.9981	0.0004	Other	Mix	0.985	0.015
64	P_M_48_29_R1	0.0915	0.9085	0.0000	Myrtle	Mix	0.900	0.100
65	P_M_48_29_R2	0.0970	0.9030	0.0000	Myrtle	Mix	0.900	0.100
66	P_M_48_29_R3	0.0940	0.9060	0.0000	Myrtle	Mix	0.900	0.100
67	P_M_48_36_R1	0.1236	0.8750	0.0015	Sumac	Mix	0.900	0.100
68	P_M_48_36_R2	0.1696	0.8298	0.0006	Sumac	Mix	0.900	0.100
69	P_M_48_36_R3	0.1705	0.8294	0.0001	Sumac	Mix	0.900	0.100
70	P_O_47_01_R1	0.0231	0.9769	0.0000	Oregano	Oregano	1.000	0.000
71	P_O_47_01_R2	0.0324	0.9676	0.0000	Oregano	Oregano	1.000	0.000
72	P_O_47_01_R3	0.0390	0.9600	0.0010	Oregano	Oregano	1.000	0.000
73	P_O_47_02_R1	0.0148	0.9852	0.0000	Oregano	Oregano	1.000	0.000
74	P_O_47_02_R2	0.0105	0.9894	0.0001	Oregano	Oregano	1.000	0.000
75	P_O_47_02_R3	0.0107	0.9893	0.0000	Oregano	Oregano	1.000	0.000
76	P_O_47_03_R1	0.0254	0.9746	0.0000	Oregano	Oregano	1.000	0.000
77	P_O_47_03_R2	0.0184	0.9815	0.0002	Oregano	Oregano	1.000	0.000
78	P_O_47_03_R3	0.0147	0.9853	0.0000	Oregano	Oregano	1.000	0.000
79	P_O_47_04_R1	0.0476	0.9524	0.0000	Oregano	Oregano	1.000	0.000
80	P_O_47_04_R2	0.0648	0.9348	0.0004	Oregano	Oregano	1.000	0.000
81	P_O_47_04_R3	0.0731	0.9269	0.0000	Oregano	Oregano	1.000	0.000
82	P_O_47_05_R1	0.0073	0.9927	0.0000	Oregano	Oregano	1.000	0.000
83	P_O_47_05_R2	0.0123	0.9877	0.0000	Oregano	Oregano	1.000	0.000
84	P_O_47_05_R3	0.0132	0.9868	0.0000	Oregano	Oregano	1.000	0.000
85	P_O_47_06_R1	0.0612	0.9388	0.0000	Oregano	Oregano	1.000	0.000
86	P_O_47_06_R2	0.0519	0.9481	0.0000	Oregano	Oregano	1.000	0.000
87	P_O_47_06_R3	0.0608	0.9392	0.0000	Oregano	Oregano	1.000	0.000
88	P_O_47_07_R1	0.0224	0.9773	0.0003	Oregano	Oregano	1.000	0.000
89	P_O_47_07_R2	0.0163	0.9837	0.0000	Oregano	Oregano	1.000	0.000
90	P_O_47_07_R3	0.0145	0.9855	0.0000	Oregano	Oregano	1.000	0.000
91	P_O_47_08_R1	0.0811	0.9189	0.0000	Oregano	Oregano	1.000	0.000
92	P_O_47_08_R2	0.0904	0.9096	0.0000	Oregano	Oregano	1.000	0.000
93	P_O_47_08_R3	0.0700	0.9300	0.0000	Oregano	Oregano	1.000	0.000
94	P_O_47_09_R1	0.0155	0.9840	0.0004	Oregano	Oregano	1.000	0.000
95	P_O_47_09_R2	0.0195	0.9805	0.0000	Oregano	Oregano	1.000	0.000
96	P_O_47_09_R3	0.0143	0.9848	0.0010	Oregano	Oregano	1.000	0.000
97	P_O_47_10_R1	0.0361	0.9639	0.0000	Oregano	Oregano	1.000	0.000
98	P_O_47_10_R2	0.0521	0.9479	0.0000	Oregano	Oregano	1.000	0.000
99	P_O_47_10_R3	0.0502	0.9498	0.0000	Oregano	Oregano	1.000	0.000
100	P_O_47_11_R1	0.0665	0.9335	0.0000	Oregano	Oregano	1.000	0.000
101	P_O_47_11_R2	0.0734	0.9266	0.0000	Oregano	Oregano	1.000	0.000
102	P_O_47_11_R3	0.0765	0.9235	0.0000	Oregano	Oregano	1.000	0.000
103	P_O_47_12_R1	0.0415	0.9585	0.0000	Oregano	Oregano	1.000	0.000
104	P_O_47_12_R2	0.0476	0.9524	0.0000	Oregano	Oregano	1.000	0.000
105	P_O_47_12_R3	0.0466	0.9534	0.0000	Oregano	Oregano	1.000	0.000
106	P_O_47_13_R1	0.0117	0.9883	0.0000	Oregano	Oregano	1.000	0.000
107	P_O_47_13_R2	0.0161	0.9839	0.0000	Oregano	Oregano	1.000	0.000
108	P_O_47_13_R3	0.0136	0.9864	0.0000	Oregano	Oregano	1.000	0.000
109	P_O_47_14_R1	0.0036	0.9964	0.0000	Oregano	Oregano	1.000	0.000
110	P_O_47_14_R2	0.0037	0.9963	0.0000	Oregano	Oregano	1.000	0.000
111	P_O_47_14_R3	0.0037	0.9963	0.0000	Oregano	Oregano	1.000	0.000
112	P_O_47_15_R1	0.3579	0.6408	0.0013	Infiorescenze	Oregano	1.000	0.000
113	P_O_47_15_R2	0.3463	0.6536	0.0002	Infiorescenze	Oregano	1.000	0.000
114	P_O_47_15_R3	0.3283	0.6708	0.0009	Infiorescenze	Oregano	1.000	0.000
115	P_O_47_16_R1	0.0437	0.9563	0.0000	Oregano	Oregano	1.000	0.000
116	P_O_47_16_R2	0.0189	0.9811	0.0000	Oregano	Oregano	1.000	0.000
117	P_O_47_16_R3	0.0297	0.9703	0.0000	Oregano	Oregano	1.000	0.000
118	P_O_47_17_R1	0.0434	0.9566	0.0000	Oregano	Oregano	1.000	0.000
119	P_O_47_17_R2	0.0903	0.9097	0.0000	Oregano	Oregano	1.000	0.000
120	P_O_47_17_R3	0.0632	0.9367	0.0001	Oregano	Oregano	1.000	0.000
121	P_O_47_18_R1	0.0259	0.9741	0.0000	Oregano	Oregano	1.000	0.000
122	P_O_47_18_R2	0.0242	0.9758	0.0000	Oregano	Oregano	1.000	0.000
123	P_O_47_18_R3	0.0197	0.9803	0.0000	Oregano	Oregano	1.000	0.000
124	P_O_47_19_R1	0.0602	0.9392	0.0006	Oregano	Oregano	1.000	0.000
125	P_O_47_19_R2	0.0465	0.9531	0.0004	Oregano	Oregano	1.000	0.000
126	P_O_47_19_R3	0.0822	0.9178	0.0000	Oregano	Oregano	1.000	0.000
127	P_O_47_20_R1	0.0140	0.9772	0.0088	Oregano	Oregano	1.000	0.000
128	P_O_47_20_R2	0.0172	0.9826	0.0002	Oregano	Oregano	1.000	0.000
129	P_O_47_20_R3	0.0114	0.9886	0.0000	Oregano	Oregano	1.000	0.000
130	P_O_47_21_R1	0.0219	0.9781	0.0000	Oregano	Oregano	1.000	0.000
131	P_O_47_21_R2	0.0244	0.9756	0.0000	Oregano	Oregano	1.000	0.000
132	P_O_47_21_R3	0.0397	0.9603	0.0000	Oregano	Oregano	1.000	0.000
133	P_O_47_22_R1	0.0373	0.9626	0.0001	Oregano	Oregano	1.000	0.000
134	P_O_47_22_R2	0.0236	0.9764	0.0000	Oregano	Oregano	1.000	0.000
135	P_O_47_22_R3	0.0251	0.9748	0.0001	Oregano	Oregano	1.000	0.000
136	P_O_47_23_R1	0.0014	0.9986	0.0000	Oregano	Oregano	1.000	0.000
137	P_O_47_23_R2	0.0018	0.9973	0.0010	Oregano	Oregano	1.000	0.000
138	P_O_47_23_R3	0.0019	0.9978	0.0003	Oregano	Oregano	1.000	0.000
139	P_O_47_24_R1	0.0413	0.9587	0.0000	Oregano	Oregano	1.000	0.000
140	P_O_47_24_R2	0.0339	0.9659	0.0003	Oregano	Oregano	1.000	0.000
141	P_O_47_24_R3	0.0359	0.9638	0.0003	Oregano	Oregano	1.000	0.000

Percentuale di Oregano

df_detrend1 = df_detrend[df_detrend$Type != 'Adulterant',]


p = ggplot(df_detrend1, aes(Predicted_Oregano, fill = Type))+
  geom_histogram(bins = 40, position = position_dodge2())+
  scale_fill_manual(values = c('deepskyblue3', 'forestgreen'))+
  theme_bw()+
  xlab('Predicted oregano %')+
  ylab('')+
  scale_y_continuous(breaks=seq(0,24,2))+
  scale_x_continuous(breaks = seq(0.5,1,0.05))
 
ggplotly(p)

p = ggplot(df_detrend, aes(x = Contaminant,y= Predicted_Oregano, color = Type, text = ID))+geom_boxplot()+
  scale_color_manual(values = c('brown3','deepskyblue4', 'forestgreen'))+
  theme_bw()+
  xlab('')+
  ylab('Predicted % oregano')

ggplotly(p)

p = ggplot(df_detrend, aes(x = Actual_oregano,y = Predicted_Oregano, color = Type, class = Contaminant, text= ID))+
  scale_color_manual(values = c('brown3','deepskyblue4', 'forestgreen'))+
  geom_point()+
  theme_bw()+
  xlab('Actual % oregano')+
  ylab('Predicted % oregano')
  
ggplotly(p)

p = ggplot(df_detrend, aes(x = Actual_oregano,y = Predicted_Oregano, color = Contaminant, class = Type, text= ID))+
  geom_point()+
  theme_bw()+
  xlab('Actual % oregano')+
  ylab('Predicted % oregano')

ggplotly(p)

Ricerca di un valore soglia

Selezione delle immagini appartenenti alle repliche 1 e 2, ovvero quelle che hanno costuito il training set, escludendo i campioni di Adulterant, Oregano not refined, infiorescenze e other.

df1 = df_detrend[(df_detrend$Type == 'Oregano' & df_detrend$Contaminant == 'Oregano'),] 


dfO3 = df1[str_detect(df1$ID, 'R3'),]
df1 = df1[str_detect(df1$ID, 'R2') |str_detect(df1$ID, 'R1') ,]
dfmisc = df_detrend[(df_detrend$Type == 'Mix' & df_detrend$Contaminant != 'Other'),]




kable(df1, row.names = T) %>% kable_styling('striped', fixed_thead = T, full_width = FALSE) %>%
  scroll_box( height = "500px")

	ID	Adulterant	Predicted_Oregano	NA	Contaminant	Type	Actual_oregano	Actual_adulterant
70	P_O_47_01_R1	0.0231	0.9769	0.0000	Oregano	Oregano	1	0
71	P_O_47_01_R2	0.0324	0.9676	0.0000	Oregano	Oregano	1	0
73	P_O_47_02_R1	0.0148	0.9852	0.0000	Oregano	Oregano	1	0
74	P_O_47_02_R2	0.0105	0.9894	0.0001	Oregano	Oregano	1	0
76	P_O_47_03_R1	0.0254	0.9746	0.0000	Oregano	Oregano	1	0
77	P_O_47_03_R2	0.0184	0.9815	0.0002	Oregano	Oregano	1	0
79	P_O_47_04_R1	0.0476	0.9524	0.0000	Oregano	Oregano	1	0
80	P_O_47_04_R2	0.0648	0.9348	0.0004	Oregano	Oregano	1	0
82	P_O_47_05_R1	0.0073	0.9927	0.0000	Oregano	Oregano	1	0
83	P_O_47_05_R2	0.0123	0.9877	0.0000	Oregano	Oregano	1	0
85	P_O_47_06_R1	0.0612	0.9388	0.0000	Oregano	Oregano	1	0
86	P_O_47_06_R2	0.0519	0.9481	0.0000	Oregano	Oregano	1	0
88	P_O_47_07_R1	0.0224	0.9773	0.0003	Oregano	Oregano	1	0
89	P_O_47_07_R2	0.0163	0.9837	0.0000	Oregano	Oregano	1	0
91	P_O_47_08_R1	0.0811	0.9189	0.0000	Oregano	Oregano	1	0
92	P_O_47_08_R2	0.0904	0.9096	0.0000	Oregano	Oregano	1	0
94	P_O_47_09_R1	0.0155	0.9840	0.0004	Oregano	Oregano	1	0
95	P_O_47_09_R2	0.0195	0.9805	0.0000	Oregano	Oregano	1	0
97	P_O_47_10_R1	0.0361	0.9639	0.0000	Oregano	Oregano	1	0
98	P_O_47_10_R2	0.0521	0.9479	0.0000	Oregano	Oregano	1	0
100	P_O_47_11_R1	0.0665	0.9335	0.0000	Oregano	Oregano	1	0
101	P_O_47_11_R2	0.0734	0.9266	0.0000	Oregano	Oregano	1	0
103	P_O_47_12_R1	0.0415	0.9585	0.0000	Oregano	Oregano	1	0
104	P_O_47_12_R2	0.0476	0.9524	0.0000	Oregano	Oregano	1	0
106	P_O_47_13_R1	0.0117	0.9883	0.0000	Oregano	Oregano	1	0
107	P_O_47_13_R2	0.0161	0.9839	0.0000	Oregano	Oregano	1	0
109	P_O_47_14_R1	0.0036	0.9964	0.0000	Oregano	Oregano	1	0
110	P_O_47_14_R2	0.0037	0.9963	0.0000	Oregano	Oregano	1	0
115	P_O_47_16_R1	0.0437	0.9563	0.0000	Oregano	Oregano	1	0
116	P_O_47_16_R2	0.0189	0.9811	0.0000	Oregano	Oregano	1	0
118	P_O_47_17_R1	0.0434	0.9566	0.0000	Oregano	Oregano	1	0
119	P_O_47_17_R2	0.0903	0.9097	0.0000	Oregano	Oregano	1	0
121	P_O_47_18_R1	0.0259	0.9741	0.0000	Oregano	Oregano	1	0
122	P_O_47_18_R2	0.0242	0.9758	0.0000	Oregano	Oregano	1	0
124	P_O_47_19_R1	0.0602	0.9392	0.0006	Oregano	Oregano	1	0
125	P_O_47_19_R2	0.0465	0.9531	0.0004	Oregano	Oregano	1	0
127	P_O_47_20_R1	0.0140	0.9772	0.0088	Oregano	Oregano	1	0
128	P_O_47_20_R2	0.0172	0.9826	0.0002	Oregano	Oregano	1	0
130	P_O_47_21_R1	0.0219	0.9781	0.0000	Oregano	Oregano	1	0
131	P_O_47_21_R2	0.0244	0.9756	0.0000	Oregano	Oregano	1	0
133	P_O_47_22_R1	0.0373	0.9626	0.0001	Oregano	Oregano	1	0
134	P_O_47_22_R2	0.0236	0.9764	0.0000	Oregano	Oregano	1	0
136	P_O_47_23_R1	0.0014	0.9986	0.0000	Oregano	Oregano	1	0
137	P_O_47_23_R2	0.0018	0.9973	0.0010	Oregano	Oregano	1	0
139	P_O_47_24_R1	0.0413	0.9587	0.0000	Oregano	Oregano	1	0
140	P_O_47_24_R2	0.0339	0.9659	0.0003	Oregano	Oregano	1	0

dfperc = quantile(df1$Predicted_Oregano, probs = c(0, 0.03, 0.05 , 0.1 , 0.15, 0.2)) %>% data.frame()
colnames(dfperc) = 'Percentile'
dfperc = dfperc %>% data.frame()
dfperc %>% kable(row.names = T) %>% kable_paper('striped', fixed_thead = T, full_width = FALSE)

	Percentile
0%	0.909600
3%	0.912920
5%	0.920825
10%	0.934150
15%	0.939100
20%	0.948100

soglia0 = min(df1$Predicted_Oregano)
soglia05 = quantile(df1$Predicted_Oregano, probs = 0.05)
soglia10 = quantile(df1$Predicted_Oregano, probs = 0.10)

Relativamente alla percentuale di Oregano predetta dal modello, per la classe ‘Oregano’ il valore più basso è 0.9096.

Si valutano i dati relativi alle immagini del test set più quelli delle miscele.

soglia = soglia0

dftest = rbind(dfmisc, dfO3)
#write.csv(dftest, "dftest.csv", row.names=FALSE)

dftest$Oregano_test = with(dftest, ifelse(Type == 'Oregano' & Predicted_Oregano > soglia, 'TP',ifelse(Type == 'Mix' & Predicted_Oregano > soglia, 'FP', ifelse(Type == 'Oregano' & Predicted_Oregano < soglia, 'FN','TN'))))
dftest$misc_test = with(dftest, ifelse(Type == 'Mix' & Predicted_Oregano < soglia, 'TP',ifelse(Type == 'Oregano' & Predicted_Oregano < soglia, 'FP', ifelse(Type == 'Mix' & Predicted_Oregano > soglia, 'FN','TN'))))



kable(dftest, row.names = T) %>% kable_styling('striped', fixed_thead = T, full_width = FALSE) %>%
  scroll_box( height = "500px")

	ID	Adulterant	Predicted_Oregano	NA	Contaminant	Type	Actual_oregano	Actual_adulterant	Oregano_test	misc_test
1	P_A_01_R1	0.0748	0.9241	0.0011	Sumac	Mix	0.95	0.05	FP	FN
2	P_A_01_R2	0.0459	0.9530	0.0011	Sumac	Mix	0.95	0.05	FP	FN
3	P_A_01_R3	0.0543	0.9457	0.0000	Sumac	Mix	0.95	0.05	FP	FN
4	P_A_02_R1	0.1219	0.8765	0.0016	Sumac	Mix	0.90	0.10	TN	TP
5	P_A_02_R2	0.1173	0.8816	0.0011	Sumac	Mix	0.90	0.10	TN	TP
6	P_A_02_R3	0.1208	0.8782	0.0010	Sumac	Mix	0.90	0.10	TN	TP
7	P_A_03_R1	0.0820	0.9174	0.0006	Sumac	Mix	0.95	0.05	FP	FN
8	P_A_03_R2	0.0532	0.9454	0.0014	Sumac	Mix	0.95	0.05	FP	FN
9	P_A_03_R3	0.0617	0.9379	0.0004	Sumac	Mix	0.95	0.05	FP	FN
10	P_A_04_R1	0.1392	0.8595	0.0013	Sumac	Mix	0.90	0.10	TN	TP
11	P_A_04_R2	0.1176	0.8803	0.0021	Sumac	Mix	0.90	0.10	TN	TP
12	P_A_04_R3	0.1177	0.8798	0.0025	Sumac	Mix	0.90	0.10	TN	TP
31	P_M_48_01_R1	0.1686	0.8314	0.0000	Strawberry	Mix	0.80	0.20	TN	TP
32	P_M_48_01_R2	0.1507	0.8493	0.0000	Strawberry	Mix	0.80	0.20	TN	TP
33	P_M_48_01_R3	0.1577	0.8421	0.0001	Strawberry	Mix	0.80	0.20	TN	TP
34	P_M_48_02_R1	0.3291	0.6709	0.0000	Strawberry	Mix	0.70	0.30	TN	TP
35	P_M_48_02_R2	0.3836	0.6164	0.0000	Strawberry	Mix	0.70	0.30	TN	TP
36	P_M_48_02_R3	0.3549	0.6425	0.0026	Strawberry	Mix	0.70	0.30	TN	TP
37	P_M_48_03_R1	0.0906	0.9064	0.0030	Sumac	Mix	0.80	0.20	TN	TP
38	P_M_48_03_R2	0.1026	0.8949	0.0025	Sumac	Mix	0.80	0.20	TN	TP
39	P_M_48_03_R3	0.0901	0.9073	0.0026	Sumac	Mix	0.80	0.20	TN	TP
40	P_M_48_04_R1	0.4463	0.5537	0.0000	Myrtle	Mix	0.40	0.60	TN	TP
41	P_M_48_04_R2	0.4244	0.5756	0.0000	Myrtle	Mix	0.40	0.60	TN	TP
42	P_M_48_04_R3	0.4252	0.5748	0.0000	Myrtle	Mix	0.40	0.60	TN	TP
43	P_M_48_05_R1	0.1061	0.8930	0.0010	Olive	Mix	0.70	0.30	TN	TP
44	P_M_48_05_R2	0.0939	0.9060	0.0002	Olive	Mix	0.70	0.30	TN	TP
45	P_M_48_05_R3	0.1186	0.8814	0.0000	Olive	Mix	0.70	0.30	TN	TP
46	P_M_48_06_R1	0.1912	0.8088	0.0000	Strawberry	Mix	0.80	0.20	TN	TP
47	P_M_48_06_R2	0.1942	0.8058	0.0000	Strawberry	Mix	0.80	0.20	TN	TP
48	P_M_48_06_R3	0.1593	0.8404	0.0003	Strawberry	Mix	0.80	0.20	TN	TP
49	P_M_48_07_R1	0.3606	0.6385	0.0009	Strawberry	Mix	0.60	0.40	TN	TP
50	P_M_48_07_R2	0.2927	0.7057	0.0016	Strawberry	Mix	0.60	0.40	TN	TP
51	P_M_48_07_R3	0.3677	0.6304	0.0019	Strawberry	Mix	0.60	0.40	TN	TP
52	P_M_48_08_R1	0.3597	0.6390	0.0013	Olive	Mix	0.60	0.40	TN	TP
53	P_M_48_08_R2	0.3171	0.6827	0.0001	Olive	Mix	0.60	0.40	TN	TP
54	P_M_48_08_R3	0.3045	0.6955	0.0000	Olive	Mix	0.60	0.40	TN	TP
55	P_M_48_14_R1	0.2169	0.7830	0.0001	Olive	Mix	0.80	0.20	TN	TP
56	P_M_48_14_R2	0.2159	0.7839	0.0001	Olive	Mix	0.80	0.20	TN	TP
57	P_M_48_14_R3	0.2377	0.7594	0.0030	Olive	Mix	0.80	0.20	TN	TP
64	P_M_48_29_R1	0.0915	0.9085	0.0000	Myrtle	Mix	0.90	0.10	TN	TP
65	P_M_48_29_R2	0.0970	0.9030	0.0000	Myrtle	Mix	0.90	0.10	TN	TP
66	P_M_48_29_R3	0.0940	0.9060	0.0000	Myrtle	Mix	0.90	0.10	TN	TP
67	P_M_48_36_R1	0.1236	0.8750	0.0015	Sumac	Mix	0.90	0.10	TN	TP
68	P_M_48_36_R2	0.1696	0.8298	0.0006	Sumac	Mix	0.90	0.10	TN	TP
69	P_M_48_36_R3	0.1705	0.8294	0.0001	Sumac	Mix	0.90	0.10	TN	TP
72	P_O_47_01_R3	0.0390	0.9600	0.0010	Oregano	Oregano	1.00	0.00	TP	TN
75	P_O_47_02_R3	0.0107	0.9893	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
78	P_O_47_03_R3	0.0147	0.9853	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
81	P_O_47_04_R3	0.0731	0.9269	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
84	P_O_47_05_R3	0.0132	0.9868	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
87	P_O_47_06_R3	0.0608	0.9392	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
90	P_O_47_07_R3	0.0145	0.9855	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
93	P_O_47_08_R3	0.0700	0.9300	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
96	P_O_47_09_R3	0.0143	0.9848	0.0010	Oregano	Oregano	1.00	0.00	TP	TN
99	P_O_47_10_R3	0.0502	0.9498	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
102	P_O_47_11_R3	0.0765	0.9235	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
105	P_O_47_12_R3	0.0466	0.9534	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
108	P_O_47_13_R3	0.0136	0.9864	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
111	P_O_47_14_R3	0.0037	0.9963	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
117	P_O_47_16_R3	0.0297	0.9703	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
120	P_O_47_17_R3	0.0632	0.9367	0.0001	Oregano	Oregano	1.00	0.00	TP	TN
123	P_O_47_18_R3	0.0197	0.9803	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
126	P_O_47_19_R3	0.0822	0.9178	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
129	P_O_47_20_R3	0.0114	0.9886	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
132	P_O_47_21_R3	0.0397	0.9603	0.0000	Oregano	Oregano	1.00	0.00	TP	TN
135	P_O_47_22_R3	0.0251	0.9748	0.0001	Oregano	Oregano	1.00	0.00	TP	TN
138	P_O_47_23_R3	0.0019	0.9978	0.0003	Oregano	Oregano	1.00	0.00	TP	TN
141	P_O_47_24_R3	0.0359	0.9638	0.0003	Oregano	Oregano	1.00	0.00	TP	TN

p = ggplot(dftest, aes(Predicted_Oregano, fill = Type))+
  geom_histogram(bins = 40, position = position_dodge2())+
  scale_fill_manual(values = c('deepskyblue3', 'forestgreen'))+
  theme_bw()+
  xlab('Predicted % oregano')+
  ylab('')+
  scale_y_continuous(breaks=seq(0,8,1))+
  scale_x_continuous(breaks = seq(0.5,1,0.05))+
  geom_vline(xintercept = soglia0, linetype="dashed", color = "red", size=0.5)+
  annotate(geom="text", y=8.1, x= soglia0-0.017, label="Min", color="red")
ggplotly(p)

median = dftest %>%
  group_by(Type) %>%
  summarise(median=median(Predicted_Oregano))

p = ggplot(dftest, aes(Predicted_Oregano, fill = Type))+
  geom_density(alpha = 0.4, aes(y=..density..))+
  geom_vline(data = median, aes(xintercept = median, color = Type), linetype = 'dashed')+
  scale_fill_manual(values = c('deepskyblue3', 'forestgreen'))+
  scale_color_manual(values = c('deepskyblue4', 'darkgreen'))+
  theme_bw()+
  xlab('Predicted % oregano')+
  ylab('Density')+
  scale_x_continuous(breaks = seq(0.5,1,0.05))+
  ggtitle('Density plot')
 
ggplotly(p)

p = ggplot(dftest, aes(x = Contaminant,y= Predicted_Oregano, color = Type))+geom_boxplot()+
  scale_color_manual(values = c('deepskyblue4', 'forestgreen'))+
  theme_bw()+
  xlab('')+
  ylab('Predicted % oregano')+
  geom_hline(yintercept = soglia0, linetype="dashed", color = "red", size=0.5)+
  #geom_hline(yintercept = soglia10, linetype="dashed", color = "orange", size=0.5)+
  annotate(geom="text", x=0.55, y= soglia0+0.01, label="Min", color="red")
  #annotate(geom="text", x=0.7, y= soglia10+0.01, label="10%", color="orange")
  
ggplotly(p)

La percentuale di NA per tale campione è invece in linea con il resto del dataset.

p = ggplot(dftest, aes(x = Actual_oregano,y = Predicted_Oregano, color = Contaminant, class = Type, text= ID))+
  geom_point()+
  theme_bw()+
  xlab('Actual % oregano')+
  ylab('Predicted % oregano')+
  geom_hline(yintercept = soglia0, linetype="dashed", color = "red", size=0.5)+
  #geom_hline(yintercept = soglia10, linetype="dashed", color = "orange", size=0.5)+
  annotate(geom="text", x=0.4, y= soglia0+0.01, label="Min", color="red")
  #annotate(geom="text", x=0.42, y= soglia10+0.01, label="10%", color="orange")
  
ggplotly(p)

Sulla base dei dati appena trovati è possibile ricavare i valori di sensibilità e specificità per entrambe le classi.

otp = dftest[(dftest$Oregano_test == 'TP'),] %>% nrow()
otn = dftest[(dftest$Oregano_test == 'TN'),] %>% nrow()
ofp = dftest[(dftest$Oregano_test == 'FP'),] %>% nrow()
ofn = dftest[(dftest$Oregano_test == 'FN'),] %>% nrow()
mtp = dftest[(dftest$misc_test == 'TP'),] %>% nrow()
mtn = dftest[(dftest$misc_test == 'TN'),] %>% nrow()
mfp = dftest[(dftest$misc_test == 'FP'),] %>% nrow()
mfn = dftest[(dftest$misc_test == 'FN'),] %>% nrow()

oacc = ((otp+otn)/nrow(dftest))
macc = ((mtp+mtn)/nrow(dftest))

Oregano = c(otp,otn, ofp, ofn)
Mix = c(mtp, mtn, mfp, mfn)

dfconf = data.frame(Oregano, Mix) %>% t() %>% data.frame()
colnames(dfconf) = c('TP', 'TN', 'FP', 'FN')

Oregano_reale = c(otp, ofn)
Miscela_reale = c(ofp, otn)


dfconf2 = data.frame(Oregano_reale, Miscela_reale)
rownames(dfconf2) = c('Oregano predetto', 'Miscela predetta')
colnames(dfconf2) = c('Oregano reale', 'Miscela reale')


dfconf2 %>% kable(row.names = T) %>% kable_paper( 'hover', fixed_thead = T, full_width = FALSE)

	Oregano reale	Miscela reale
Oregano predetto	23	6
Miscela predetta	0	39

kable(dfconf, row.names = T) %>% kable_styling( 'hover', fixed_thead = T, full_width = FALSE)

	TP	TN	FP	FN
Oregano	23	39	6	0
Mix	39	23	0	6

senso = otp/(otp+ofn)
speco = otn/(otn+ofp)
sensm = mtp/(mtp+mfn)
specm = mtn/(mtn+mfp)
eff = sqrt(senso*speco)

Oregano = c(senso, speco, eff, oacc)
Mix = c(sensm, specm, eff, macc) 

dfconf2 = data.frame(Oregano, Mix)
dfconf2 = dfconf2 %>% t() %>% data.frame()
colnames(dfconf2) = c('SENS', 'SPEC', 'EFF', 'ACC')
dfconf2 = round(dfconf2, digits = 3)

kable(dfconf2, row.names = T) %>% kable_styling( 'hover', fixed_thead = T, full_width = FALSE)

	SENS	SPEC	EFF	ACC
Oregano	1.000	0.867	0.931	0.912
Mix	0.867	1.000	0.931	0.912

prob_prev = c(0.1, 0.2, 0.3, 0.4, 0.5, 0.6)
soglie = seq(0.8, 1, 0.01)
sensvec = c()
specvec = c()
probvec = c()
effvec = c()
accvec = c()

dftest1 = dftest

for (soglia in soglie) {
  
  for (prob in prob_prev) {
  
  dftest1$Oregano_test = with(dftest, ifelse(Type == 'Oregano' & Oregano > soglia, 'TP',ifelse(Type == 'Mix' & Predicted_Oregano > soglia, 'FP', ifelse(Type == 'Oregano' & Predicted_Oregano <   soglia, 'FN','TN'))))
  
  otp = dftest1[(dftest1$Oregano_test == 'TP'),] %>% nrow()
  otn = dftest1[(dftest1$Oregano_test == 'TN'),] %>% nrow()
  ofp = dftest1[(dftest1$Oregano_test == 'FP'),] %>% nrow()
  ofn = dftest1[(dftest1$Oregano_test == 'FN'),] %>% nrow() 
  
  senso = (otp/(otp+ofn))
  speco = (otn/(otn+ofp))
  oacc = ((otp+otn)/nrow(dftest))

  probvec = append(probvec, (senso*(1-prob))/(senso*(1-prob)+((1-speco)*(prob))))
  
  }
   
  sensvec = append(sensvec, (otp/(otp+ofn)))
  specvec = append(specvec, (otn/(otn+ofp)))
  effvec = append(effvec, sqrt(senso*speco))
  accvec = append(accvec, (otp+otn)/nrow(dftest))
  
}

dfsensspec = data.frame( 'Soglia' = soglie, 'SENS' = sensvec, 'SPEC' = specvec)
dfsensspec = pivot_longer(dfsensspec, cols = 2:3, names_to = 'SENS_SPEC', values_to = 'Valore')


P = ggplot(dfsensspec, aes(Soglia, Valore, color = SENS_SPEC))+ geom_line(size = 0.2)+ geom_point(size =1)+
  theme_bw()+scale_x_continuous(breaks = seq(0.8,1,0.01))+
  scale_y_continuous(breaks = seq(0,1,0.1))+
  ggtitle('Variazione SENS/SPEC')

ggplotly(P)

dfeff = data.frame('Soglia' = soglie, 'EFF' = effvec)


p = ggplot(dfeff, aes(Soglia, EFF))+ geom_line(size = 0.1)+ geom_point(size =1, color = 'blue3')+
  theme_bw()+scale_x_continuous(breaks = seq(0.8,1,0.01))+
  scale_y_continuous(breaks = seq(0,1,0.1))+
  ggtitle('Variazione efficienza')
ggplotly(p)

dfacc = data.frame('Soglia' = soglie, 'ACC' = accvec)


p = ggplot(dfacc, aes(Soglia, ACC))+ geom_line(size = 0.1)+ geom_point(size =1, color = 'green4')+
  theme_bw()+scale_x_continuous(breaks = seq(0.8,1,0.01))+
  scale_y_continuous(breaks = seq(0,1,0.1))+
  ggtitle('Variazione accuratezza')
ggplotly(p)

(Per vedere come cambiano sensibilità e specificità con un diverso valore soglia CLICCA QUI)

otp = dftest[(dftest$Oregano_test == 'TP'),] %>% nrow()
otn = dftest[(dftest$Oregano_test == 'TN'),] %>% nrow()
ofp = dftest[(dftest$Oregano_test == 'FP'),] %>% nrow()
ofn = dftest[(dftest$Oregano_test == 'FN'),] %>% nrow()
mtp = dftest[(dftest$misc_test == 'TP'),] %>% nrow()
mtn = dftest[(dftest$misc_test == 'TN'),] %>% nrow()
mfp = dftest[(dftest$misc_test == 'FP'),] %>% nrow()
mfn = dftest[(dftest$misc_test == 'FN'),] %>% nrow()

senso = (otp/(otp+ofn))
speco = (otn/(otn+ofp))

prob_prev05 = 0.52
prob = (senso*prob_prev05)/(senso*prob_prev05+((1-speco)*(1-prob_prev05)))*100

Alla luce di questi risultati, se si ipotizza un’incidenza sul mercato di campioni adulterati di circa il 52% è possibile stimare la probabilità che un campione incognito che viene classificato come Oregano sia effettivamente tale.

In altre parole, indicando con \(P(A)\) l’incidenza ipotizzata e con \(P(O)\) il suo complementare, si avrà che

\[ P(O|+) = \frac{P(+|O)P(O)}{P(+)} = \frac{P(+|O)P(O)}{P(+|O)P(O)+P(+|A)P(A)} \]

\(P(+|O)\) è ovviamente la sensibilità del modello è \(P(+|A)\) la specificità complementare.

In questo ipotetico scenario quindi, ogni qual volta viene rilevato un campione positivo, la probabilità che sia effettivamente un campione di Oregano puro sarà dell’89.04% !

prob_prevlong = rep(prob_prev, length(soglie))
soglielong = rep(soglie, each = length(prob_prev))


dfprob = data.frame('Soglia' = soglielong, 'perc_adulterazione' = factor(prob_prevlong), 'Prob_Oregano' = probvec)
dfprob = dfprob[dfprob$Soglia != 1,]

p= ggplot(dfprob, aes(Soglia, Prob_Oregano, color = perc_adulterazione))+ geom_line(size = 0.2)+ geom_point(size =1)+
  theme_bw()+scale_x_continuous(breaks = seq(0.8,1,0.01))+
  scale_y_continuous(breaks = seq(0,1,0.1))+
  ggtitle('Variazione probabilità')
ggplotly(p)