Tables

Table 1: The 100 best ternary linear discrimination diagrams

rank	elements			resubstitution error (%)				# IAB	# MORB	# OIB
	1	2	3	overall	IAB	MORB	OIB	(/256)	(/241)	(/259)
1	Si	Sr	Ti	6.2	10.0	6.6	2.1	221	211	192
2	Ti	Sr	Al	6.5	10.0	7.6	2.1	220	211	194
3	Eu	Sr	Lu	6.6	10.5	6.0	3.3	124	117	120
4	Sr	Nb	Y	6.6	13.4	3.9	2.5	157	127	160
5	Ca	Nb	Sr	7.6	16.6	4.8	1.4	157	126	142
6	Ti	Sr	V	7.7	9.5	7.2	6.4	158	180	156
7	Eu	Y	Sr	7.8	16.1	4.7	2.5	124	106	121
8	Ti	Sr	Ca	7.8	12.3	9.0	2.1	220	211	194
9	Ti	Sr	Sc	7.9	12.6	7.1	3.9	119	155	128
10	Al	Nb	Sr	8.1	20.4	3.2	0.7	157	126	142
11	Ti	Sr	Mn	8.1	11.9	8.3	4.2	219	204	191
12	Ti	Y	Sr	8.4	12.9	3.9	8.5	202	153	177
13	Eu	Sr	Yb	8.4	15.2	5.1	5.0	138	157	141
14	Si	Nb	Sr	8.8	19.5	4.8	2.1	159	126	142
15	Ti	Sr	Na	8.8	13.6	6.1	6.7	220	213	194
16	Na	Nb	Sr	9.0	22.3	4.0	0.7	157	126	142
17	Tb	Sr	Lu	9.2	11.0	9.8	6.7	100	102	105
18	Ti	Nb	Sr	9.3	10.1	14.3	3.4	158	126	149
19	Mn	Nb	Sr	9.4	19.7	6.3	2.1	157	126	140
20	Nd	Y	Sr	9.5	19.6	6.7	2.4	138	135	127
21	Ti	Ba	Al	9.5	11.1	16.0	1.6	217	144	192
22	Na	Zr	Sr	9.6	18.8	5.5	4.5	208	165	177
23	Ti	Sr	Lu	9.6	11.5	6.2	11.1	113	113	108
24	Al	Sr	Nd	10.1	20.9	4.5	4.8	139	177	125
25	Al	Zr	Sr	10.1	20.2	5.5	4.5	208	163	177
26	V	Nb	Sr	10.2	18.9	9.4	2.4	122	117	124
27	Tb	Sr	Yb	10.3	14.7	6.4	9.9	102	125	111
28	Ti	V	Sc	10.4	15.2	10.1	5.8	105	148	121
29	Ti	Ba	Na	10.4	9.7	15.8	5.7	217	146	192
30	V	Nb	Rb	10.4	10.7	14.2	6.5	122	113	123
31	K	Nb	V	10.6	10.7	14.0	7.0	121	129	114
32	Ti	V	Sm	10.6	17.3	6.8	7.6	104	162	105
33	Sr	Zr	Y	10.6	21.6	3.9	6.4	204	155	203
34	Ti	Sr	Yb	10.6	13.4	6.7	11.8	127	150	127
35	Na	Sr	Nd	10.7	22.3	7.3	2.4	139	179	125
36	Si	Ba	Ti	10.8	12.0	17.4	3.2	217	144	190
37	Ca	Sr	Nd	10.9	20.9	6.2	5.6	139	177	125
38	Nd	Sr	Yb	10.9	19.4	9.7	3.8	134	145	133
39	Sm	Y	Sr	11.0	21.9	5.1	5.9	128	137	119
40	Al	Sr	Eu	11.0	20.9	7.1	5.0	129	154	120
41	Yb	Zr	Sr	11.0	19.8	6.5	6.7	126	107	134
42	Ti	Ba	Sc	11.2	13.1	16.5	3.9	122	115	129
43	Sc	Zr	Sr	11.2	21.0	6.8	5.7	119	118	122
44	Si	Sr	Nd	11.3	21.9	6.2	5.6	146	177	124
45	Si	Sr	Eu	11.3	18.5	7.8	7.6	135	154	118
46	Sm	Sr	Lu	11.3	23.0	6.0	5.0	122	116	119
47	Ti	Ba	Mn	11.4	11.1	18.2	4.8	216	137	189
48	Mn	Zr	Sr	11.4	21.7	5.0	7.5	207	160	174
49	Si	Zr	Sr	11.4	21.8	6.1	6.3	211	163	175
50	Ti	K	Al	11.5	13.6	15.4	5.4	228	228	203
51	Nd	Sr	Lu	11.5	20.7	9.5	4.5	121	105	112
52	Ti	Y	V	11.6	19.6	8.4	6.8	153	155	147
53	Ti	Sc	K	11.6	10.7	15.4	8.7	122	162	126
54	Ti	Rb	Al	11.6	12.4	18.2	4.2	209	187	189
55	Ti	Ba	Ca	11.6	12.0	20.8	2.1	217	144	192
56	Si	K	Ti	11.7	14.0	14.0	7.0	229	228	201
57	Ti	Ba	V	11.7	10.8	16.0	8.4	158	125	155
58	Ti	Sr	Zn	11.7	12.8	11.9	10.6	149	109	142
59	Ti	V	Nd	11.9	16.8	9.0	9.7	113	155	113
60	Na	Sr	Ce	11.9	26.1	6.7	2.9	165	119	140
61	Ca	Zr	Sr	11.9	24.0	6.1	5.6	208	163	177
62	Eu	Sr	V	12.0	18.8	7.6	9.4	101	131	106
63	Ca	Nb	K	12.0	14.6	14.5	7.0	157	138	143
64	Mn	Sr	Nd	12.1	21.6	10.6	4.1	139	170	123
65	K	Nb	Y	12.2	14.2	16.2	6.1	155	136	147
66	Al	Sr	Ce	12.3	24.2	6.8	5.7	165	117	140
67	Ti	V	K	12.3	9.4	14.2	13.2	159	197	151
68	Si	Rb	Ti	12.3	12.4	19.3	5.3	210	187	189
69	Ti	V	Na	12.3	14.5	15.2	7.3	159	197	151
70	Al	Nb	K	12.4	16.6	13.8	7.0	157	138	143
71	Al	Nb	Rb	12.5	14.7	16.4	6.3	156	122	142
72	Ti	K	Mn	12.5	12.3	17.6	7.5	227	221	200
73	Mg	Nb	Sr	12.6	19.0	7.1	11.6	158	126	147
74	Sr	Nb	Zr	12.7	15.6	20.5	1.9	160	132	157
75	Ca	Sr	Ce	12.7	23.0	8.5	6.4	165	117	140
76	Nd	Sr	V	12.7	22.8	9.8	5.4	114	153	111
77	K	Nb	Na	12.7	16.6	15.2	6.3	157	138	143
78	Mn	Sr	Eu	12.8	18.6	9.5	10.2	129	147	118
79	Eu	Sr	Tb	12.8	23.6	7.6	7.1	106	131	113
80	Si	Sr	Ce	12.8	24.7	8.5	5.1	170	117	138
81	Na	Sr	P	12.8	27.3	6.4	4.7	220	202	192
82	K	Zr	Yb	12.8	18.4	11.3	8.7	125	106	115
83	Al	Sr	P	12.8	27.3	5.4	5.7	220	202	192
84	K	Lu	Eu	12.8	16.8	17.2	4.5	119	116	112
85	Ce	Sr	Lu	12.8	24.2	6.0	8.3	124	100	120
86	Ti	Y	Al	12.9	12.9	18.3	7.4	201	164	175
87	Si	Nb	K	12.9	15.7	15.9	7.0	159	138	143
88	Ti	V	Eu	13.0	21.0	9.6	8.3	100	146	108
89	Ca	Nb	Rb	13.0	14.7	17.2	7.0	156	122	142
90	Ce	Sr	Yb	13.0	23.2	8.7	7.1	138	126	141
91	Zn	Zr	Sr	13.1	21.8	8.3	9.2	147	109	152
92	P	Sr	Sc	13.1	26.1	6.6	6.7	119	151	120
93	Ti	V	Ce	13.1	13.5	14.4	11.5	126	104	122
94	Ti	Nd	Mn	13.2	21.1	13.8	4.6	142	174	131
95	Sm	Sr	Yb	13.3	25.0	7.7	7.3	136	156	137
96	Ca	Sr	Eu	13.3	23.3	8.4	8.3	129	154	120
97	V	Zr	Sr	13.4	21.7	8.2	10.3	157	147	156
98	Ti	Ce	Mn	13.4	19.9	14.9	5.5	171	114	145
99	Mn	Nb	K	13.5	15.3	17.4	7.8	157	138	141
100	Ti	Cu	V	13.5	13.1	15.7	11.7	107	108	120

Table 2: The best ternary linear discrimination diagrams using only incompatible elements

rank	elements			resubstitution error (%)				# IAB	# MORB	# OIB
	1	2	3	overall	IAB	MORB	OIB	(/256)	(/241)	(/259)
28	Ti	V	Sc	10.4	15.2	10.1	5.8	105	148	121
32	Ti	V	Sm	10.6	17.3	6.8	7.6	104	162	105
52	Ti	Y	V	11.6	19.6	8.4	6.8	153	155	147
59	Ti	V	Nd	11.9	16.8	9.0	9.7	113	155	113
93	Ti	V	Ce	13.1	13.5	14.4	11.5	126	104	122
101	Ti	V	La	13.5	13.6	17.5	9.5	125	143	116
108	Ti	Zr	V	13.9	19.2	11.7	10.8	156	162	148
159	V	Zr	Y	15.3	26.8	9.7	9.4	153	155	149
182	Ti	Nb	V	15.9	23.1	17.1	7.4	121	129	121
189	Ti	Cr	Sc	15.9	26.4	16.7	4.7	121	162	127
208	Ti	Cr	V	16.2	23.4	14.3	11.0	158	182	154
249	La	Nb	Zr	17.1	21.4	19.8	9.9	140	101	131
251	Nd	Nb	Y	17.1	35.7	11.5	4.1	129	113	123
252	Ti	Zr	Sc	17.1	22.9	22.5	5.9	118	120	119
267	V	Nb	Y	17.3	30.8	18.6	2.4	120	129	124
277	Nd	Y	V	17.5	38.1	9.6	4.9	113	125	103
324	Sm	Nb	Y	18.2	35.2	15.0	4.3	122	113	115
380	La	Y	V	19.1	31.5	16.0	9.8	124	106	112
385	La	Zr	V	19.2	32.0	17.3	8.2	125	110	110
393	Ti	Y	Sc	19.3	28.6	25.9	3.4	112	112	118
423	Ti	Sc	La	19.8	28.3	26.5	4.5	113	117	112
426	Nd	Zr	V	19.8	35.4	15.2	8.7	113	125	103
538	Sc	Zr	V	21.5	32.4	23.5	8.7	105	115	115
543	Ti	Y	Nd	21.6	42.6	16.4	5.7	136	134	122
551	Ti	Y	Sm	21.7	42.9	16.2	6.1	126	136	114
584	Ce	V	Yb	22.2	43.0	19.0	4.6	100	105	108
587	Sm	Zr	Y	22.3	50.4	8.7	7.8	127	138	116
591	Sc	Zr	Y	22.3	33.0	27.0	7.0	112	115	115
612	La	Zr	Yb	22.6	38.9	21.0	7.9	126	105	127
624	Ti	Y	La	22.7	38.6	25.0	4.5	153	116	134
633	Nd	Zr	Yb	22.8	48.0	13.9	6.6	123	101	122
639	Ti	Nb	Nd	22.9	34.1	25.9	8.7	129	112	115
646	Sc	Zr	Cr	23.0	35.5	23.4	10.1	121	124	119
658	Nd	Zr	Y	23.1	48.9	14.0	6.5	137	136	124
659	Sc	Y	V	23.1	28.2	19.8	21.4	103	111	117
679	Nd	Cr	Sc	23.4	43.0	22.2	4.9	100	135	103
766	La	Zr	Y	24.3	41.9	23.7	7.3	155	118	150
777	La	V	Yb	24.5	44.0	22.6	6.8	100	124	103
787	Ti	Cr	Lu	24.6	40.9	25.2	7.7	110	115	104
791	Ce	Cr	V	24.7	37.3	21.9	14.8	126	105	122
806	Nd	Nb	Zr	24.9	37.4	29.7	7.6	131	118	119
817	V	Zr	Cr	25.0	32.7	24.2	18.2	156	149	154
836	La	Cr	V	25.3	41.6	21.4	12.8	125	131	117
861	Ti	Nb	Sm	25.5	35.0	33.0	8.4	123	112	107
869	Ti	Cr	Yb	25.6	42.5	26.0	8.3	120	131	121
894	Ti	Yb	Ce	25.8	47.4	26.2	3.8	133	122	130
899	La	Cr	Sc	25.9	42.1	23.8	11.7	121	122	111
900	V	Nb	Zr	25.9	39.3	33.3	5.0	122	129	120
908	Sm	Zr	Yb	26.0	64.6	5.6	7.9	127	108	126
957	Sc	Y	Cr	26.6	27.7	24.1	28.0	112	116	118
966	Ti	Yb	Nd	26.6	53.2	22.7	4.1	126	141	123
976	Ti	Yb	La	26.8	44.6	30.2	5.6	130	149	126
977	Nd	Cr	V	26.8	41.6	25.4	13.5	113	142	111
984	Sm	Cr	Lu	26.9	56.6	20.2	3.8	113	114	104

Table 3: The 100 best ternary quadratic discrimination diagrams

rank	elements			resubstitution error (%)				# IAB	# MORB	# OIB
	1	2	3	overall	IAB	MORB	OIB	(/256)	(/241)	(/259)
1	Na	Nb	Sr	5.0	8.3	4.0	2.8	157	126	142
2	Al	Nb	Sr	5.7	10.2	4.0	2.8	157	126	142
3	Si	Nb	Sr	5.9	10.1	4.0	3.5	159	126	142
4	Ca	Nb	Sr	6.0	9.6	5.6	2.8	157	126	142
5	Sr	Nb	Y	6.1	7.0	3.9	7.5	157	127	160
6	Eu	Sr	Lu	6.3	9.7	7.7	1.7	124	117	120
7	Ti	Sr	Al	6.7	10.0	8.1	2.1	220	211	194
8	Si	Sr	Ti	6.7	9.5	8.1	2.6	221	211	192
9	Mn	Nb	Sr	6.9	10.2	6.3	4.3	157	126	140
10	Ti	Sr	V	7.0	7.6	8.9	4.5	158	180	156
11	Ti	Sr	Na	7.9	10.9	6.6	6.2	220	213	194
12	Eu	Sr	Yb	7.9	13.0	5.7	5.0	138	157	141
13	Ti	Sr	Lu	8.0	11.5	8.0	4.6	113	113	108
14	Ti	Sr	Sc	8.0	12.6	8.4	3.1	119	155	128
15	Na	Zr	Sr	8.1	14.4	4.8	5.1	208	165	177
16	Ti	Sr	Ca	8.1	11.8	9.5	3.1	220	211	194
17	Ti	Sr	Mn	8.2	10.5	10.3	3.7	219	204	191
18	Eu	Y	Sr	8.4	16.9	5.7	2.5	124	106	121
19	Al	Sr	Eu	8.6	14.7	8.4	2.5	129	154	120
20	K	Nb	V	8.6	9.1	12.4	4.4	121	129	114
21	V	Nb	Rb	8.8	9.0	13.3	4.1	122	113	123
22	Ti	Y	Sr	8.9	11.9	5.2	9.6	202	153	177
23	Na	Sr	Eu	9.0	16.3	5.8	5.0	129	156	120
24	Al	Zr	Sr	9.1	14.9	6.7	5.6	208	163	177
25	V	Nb	Sr	9.2	12.3	12.0	3.2	122	117	124
26	Tb	Sr	Lu	9.2	13.0	9.8	4.8	100	102	105
27	Ti	Nb	Sr	9.2	5.7	15.9	6.0	158	126	149
28	Ti	Sr	Yb	9.2	13.4	8.0	6.3	127	150	127
29	Nd	Y	Sr	9.3	17.4	5.9	4.7	138	135	127
30	Al	Nb	K	10.0	12.7	10.9	6.3	157	138	143
31	K	Nb	Na	10.0	12.7	13.0	4.2	157	138	143
32	Ti	Ba	Al	10.0	10.6	13.2	6.3	217	144	192
33	Ti	V	Sm	10.0	12.5	6.2	11.4	104	162	105
34	Ti	V	Nd	10.1	12.4	9.0	8.8	113	155	113
35	Ti	Ba	Na	10.1	12.4	13.7	4.2	217	146	192
36	Mg	Nb	Sr	10.3	11.4	7.1	12.2	158	126	147
37	Si	Zr	Sr	10.4	17.5	6.7	6.9	211	163	175
38	Nd	Sr	Yb	10.4	19.4	9.7	2.3	134	145	133
39	Ca	Zr	Sr	10.5	20.2	6.1	5.1	208	163	177
40	Yb	Zr	Sr	10.5	18.3	6.5	6.7	126	107	134
41	Sr	Zr	Y	10.5	19.1	4.5	7.9	204	155	203
42	Si	Sr	Eu	10.5	15.6	8.4	7.6	135	154	118
43	Ca	Sr	Nd	10.5	20.9	6.8	4.0	139	177	125
44	Mn	Zr	Sr	10.6	19.3	6.3	6.3	207	160	174
45	Al	Sr	Nd	10.7	22.3	5.6	4.0	139	177	125
46	Ca	Sr	Eu	10.7	17.1	8.4	6.7	129	154	120
47	Ti	V	Sc	10.8	17.1	9.5	5.8	105	148	121
48	Al	Nb	Rb	10.8	11.5	13.9	7.0	156	122	142
49	Ca	Nb	K	10.9	12.1	13.0	7.7	157	138	143
50	Sm	Y	Sr	11.0	23.4	4.4	5.0	128	137	119
51	Na	Nb	Rb	11.0	11.5	16.4	4.9	156	122	142
52	V	Zr	Sr	11.0	17.2	7.5	8.3	157	147	156
53	Si	Sr	Nd	11.1	21.9	7.3	4.0	146	177	124
54	Si	Nb	K	11.1	12.6	13.8	7.0	159	138	143
55	Sc	Zr	Sr	11.2	19.3	6.8	7.4	119	118	122
56	Ti	Cu	Al	11.2	10.7	16.8	6.0	121	107	134
57	Nd	Sr	Lu	11.3	19.8	11.4	2.7	121	105	112
58	Ti	Sc	K	11.4	11.5	15.4	7.1	122	162	126
59	Sm	Sr	Lu	11.4	20.5	7.8	5.9	122	116	119
60	Ti	K	Al	11.4	13.2	13.6	7.4	228	228	203
61	Eu	Sr	V	11.4	18.8	6.9	8.5	101	131	106
62	Ti	V	Na	11.4	12.6	13.7	7.9	159	197	151
63	Rb	Nb	Y	11.4	11.5	14.6	8.1	156	123	160
64	Si	Ba	Ti	11.4	11.5	16.0	6.8	217	144	190
65	Ti	Sr	Zn	11.5	11.4	11.0	12.0	149	109	142
66	K	Nb	Y	11.5	11.6	16.2	6.8	155	136	147
67	Ti	Ba	Sc	11.7	14.8	15.7	4.7	122	115	129
68	Mn	Nb	K	11.7	12.7	18.1	4.3	157	138	141
69	Zn	Zr	Sr	11.7	17.7	8.3	9.2	147	109	152
70	Ti	Lu	Mn	11.7	20.3	13.9	1.0	118	115	105
71	Tb	Sr	Yb	11.8	16.7	9.6	9.0	102	125	111
72	Ti	V	K	11.8	8.2	15.2	11.9	159	197	151
73	Na	Sr	Nd	11.8	24.5	7.8	3.2	139	179	125
74	Si	Nb	Rb	11.8	11.4	16.4	7.7	158	122	142
75	Na	Sr	Ce	11.9	23.0	7.6	5.0	165	119	140
76	Mn	Sr	Nd	11.9	21.6	10.0	4.1	139	170	123
77	Sr	Nb	Zr	11.9	8.1	21.2	6.4	160	132	157
78	Ti	K	Mn	11.9	11.5	16.3	8.0	227	221	200
79	Ti	Rb	Na	12.0	15.3	14.8	5.8	209	189	189
80	Ti	Y	V	12.0	19.6	12.3	4.1	153	155	147
81	Si	K	Ti	12.0	12.7	14.9	8.5	229	228	201
82	Si	Ni	Ti	12.0	24.2	10.2	1.7	211	205	180
83	P	Y	Sr	12.1	23.3	4.7	8.2	202	149	170
84	Ca	Nb	Rb	12.1	11.5	16.4	8.5	156	122	142
85	Ti	Ba	V	12.1	12.0	16.0	8.4	158	125	155
86	Ti	Rb	Al	12.1	12.4	17.6	6.3	209	187	189
87	Ti	Ba	Mn	12.2	12.0	19.7	4.8	216	137	189
88	K	Yb	Nd	12.2	22.8	11.3	2.5	127	141	121
89	Al	Sr	Ce	12.3	24.2	6.8	5.7	165	117	140
90	K	Lu	Nd	12.3	19.5	13.6	3.8	113	103	104
91	Ti	Ba	Ca	12.3	12.0	18.8	6.3	217	144	192
92	Mn	Sr	Eu	12.3	16.3	8.8	11.9	129	147	118
93	Ti	V	P	12.3	13.2	11.1	12.8	159	190	149
94	Mn	Nb	Rb	12.3	11.5	20.5	5.0	156	122	140
95	Sm	Sr	V	12.4	19.0	7.5	10.7	105	160	103
96	Ca	Sr	Ce	12.4	23.0	8.5	5.7	165	117	140
97	Ti	V	La	12.5	13.6	16.1	7.8	125	143	116
98	Ti	Sr	Cu	12.6	10.8	9.8	17.0	120	102	141
99	Nd	Sr	V	12.6	21.9	10.5	5.4	114	153	111
100	Ti	Rb	V	12.6	10.5	16.8	10.7	153	161	150

Table 4: The best ternary quadratic discrimination diagrams using only incompatible elements

rank	elements			resubstitution error (%)				# IAB	# MORB	# OIB
	1	2	3	overall	IAB	MORB	OIB	(/256)	(/241)	(/259)
33	Ti	V	Sm	10.0	12.5	6.2	11.4	104	162	105
34	Ti	V	Nd	10.1	12.4	9.0	8.8	113	155	113
47	Ti	V	Sc	10.8	17.1	9.5	5.8	105	148	121
80	Ti	Y	V	12.0	19.6	12.3	4.1	153	155	147
97	Ti	V	La	12.5	13.6	16.1	7.8	125	143	116
118	Ti	V	Ce	13.1	14.3	14.4	10.7	126	104	122
123	Nd	Nb	Y	13.3	28.7	7.1	4.1	129	113	123
163	Ti	Zr	V	14.4	18.6	11.7	12.8	156	162	148
182	Ti	Nb	V	14.8	23.1	16.3	5.0	121	129	121
202	V	Zr	Y	15.1	23.5	12.9	8.7	153	155	149
232	Ti	Cr	Sc	15.5	31.4	13.6	1.6	121	162	127
252	La	Nb	Zr	15.9	15.7	19.8	12.2	140	101	131
283	Ti	Cr	V	16.3	25.3	12.6	11.0	158	182	154
310	Ti	Nb	Nd	16.8	19.4	17.0	13.9	129	112	115
340	V	Nb	Y	17.3	29.2	17.8	4.8	120	129	124
353	Nd	Zr	V	17.5	31.9	12.8	7.8	113	125	103
365	Nd	Y	V	17.6	37.2	8.8	6.8	113	125	103
405	La	Zr	V	18.2	27.2	17.3	10.0	125	110	110
407	Sm	Nb	Y	18.2	36.1	9.7	8.7	122	113	115
408	Ti	Lu	Sm	18.2	44.8	7.0	2.7	116	114	113
443	Ti	Y	Nd	18.6	37.5	12.7	5.7	136	134	122
448	La	Y	V	18.7	32.3	14.2	9.8	124	106	112
461	Nd	Zr	Y	18.9	40.1	11.8	4.8	137	136	124
485	Ti	Sc	La	19.3	38.1	15.4	4.5	113	117	112
494	Sc	Zr	Y	19.4	36.6	19.1	2.6	112	115	115
506	Nd	Zr	Yb	19.6	43.9	10.9	4.1	123	101	122
536	Ti	Zr	Sc	20.0	39.0	14.2	6.7	118	120	119
548	Nd	Cr	Sc	20.1	43.0	13.3	3.9	100	135	103
568	Nd	Nb	Zr	20.3	30.5	21.2	9.2	131	118	119
571	Ti	Y	Sm	20.4	47.6	7.4	6.1	126	136	114
573	Nd	Nb	Sm	20.4	33.9	15.4	11.9	124	117	109
590	Ti	Y	Sc	20.5	42.0	17.9	1.7	112	112	118
591	Sc	Zr	V	20.5	38.1	13.0	10.4	105	115	115
593	Sc	Zr	Cr	20.6	38.0	16.9	6.7	121	124	119
610	Ti	Yb	Sm	20.8	51.1	7.2	3.9	131	152	127
620	La	Zr	Yb	20.9	38.9	14.3	9.4	126	105	127
633	Ti	Lu	Nd	21.0	44.6	15.5	2.8	112	103	106
656	Ti	Y	La	21.2	44.4	14.7	4.5	153	116	134
670	Ti	Cr	Lu	21.4	50.9	10.4	2.9	110	115	104
690	Ce	Cr	V	21.7	36.5	16.2	12.3	126	105	122
759	Sm	Zr	Y	22.3	50.4	8.0	8.6	127	138	116
773	Ti	Yb	Nd	22.6	52.4	12.1	3.3	126	141	123
791	Sc	Y	V	22.8	31.1	12.6	24.8	103	111	117
792	Ce	V	Yb	22.8	44.0	16.2	8.3	100	105	108
797	Ti	Lu	La	22.9	50.0	16.1	2.7	118	112	113
803	Ti	Zr	Yb	23.0	48.8	15.1	5.1	125	106	117
818	La	Cr	V	23.2	42.4	16.0	11.1	125	131	117
824	Ti	Zr	Y	23.2	51.7	11.6	6.4	201	164	173
829	La	Cr	Sc	23.3	46.3	16.4	7.2	121	122	111
838	Sm	Zr	Yb	23.4	52.0	11.1	7.1	127	108	126
858	V	Zr	Cr	23.6	35.9	16.1	18.8	156	149	154
865	Sm	Cr	Lu	23.7	54.9	12.3	3.8	113	114	104
867	Nd	Cr	V	23.7	41.6	16.9	12.6	113	142	111
930	La	V	Yb	24.3	47.0	16.1	9.7	100	124	103
932	Ti	Cr	Yb	24.3	55.0	13.7	4.1	120	131	121
936	Sc	Y	Cr	24.3	29.5	15.5	28.0	112	116	118
941	Sm	Cr	Yb	24.4	53.7	13.4	6.0	123	134	116
947	La	Zr	Y	24.5	47.1	16.9	9.3	155	118	150
958	Ti	Yb	Ce	24.5	54.1	16.4	3.1	133	122	130

Table 5: Misclassification estimates

true	predicted (training)			predicted (test)
affinity	IAB	MORB	OIB	IAB	MORB	OIB
linear Ti-V
IAB	130	24	5	19	8	0
MORB	34	153	10	2	39	12
OIB	0	14	144	0	0	36
quadratic Ti-V
IAB	127	27	5	19	8	0
MORB	26	161	10	4	37	12
OIB	0	14	144	0	0	36
linear Ti-Zr
IAB	176	28	6	36	10	1
MORB	34	125	22	0	7	4
OIB	0	17	170	0	2	29
quadratic Ti-Zr
IAB	167	37	6	32	14	1
MORB	20	148	13	3	5	3
OIB	5	18	164	0	4	27
linear Ti-Zr-Y
IAB	89	101	11	33	9	3
MORB	67	91	6	0	11	0
OIB	6	5	162	3	2	24
quadratic Ti-Zr-Y
IAB	97	93	11	20	22	3
MORB	11	145	8	6	5	0
OIB	8	3	162	3	2	24
linear Zr-Y-Nb
IAB	81	57	19	16	5	2
MORB	73	55	11	2	6	0
OIB	1	6	149	0	4	23
quadratic Zr-Y-Nb
IAB	60	79	18	6	17	0
MORB	12	115	12	0	8	0
OIB	5	5	146	2	2	23
linear Th-Ta-Hf
IAB	78	6	10	12	12	2
MORB	0	37	14	0	0	0
OIB	0	13	69	0	0	10
quadratic Th-Ta-Hf
IAB	81	3	10	14	10	2
MORB	1	38	12	0	0	0
OIB	4	12	66	0	0	10
linear discriminant function analysis of
SiO$_2$,Al$_2$O$_3$,TiO$_2$,CaO,MgO,MnO,K$_2$O and Na$_2$O
IAB	205	15	7	52	7	5
MORB	7	205	9	2	17	4
OIB	2	8	188	1	0	59
linear discriminant function analysis of Ti, Zr, Y and Sr
IAB	175	13	13	41	1	2
MORB	3	145	3	0	10	0
OIB	5	5	163	0	4	25
linear Si-Ti-Sr
IAB	199	15	7	45	9	7
MORB	7	197	7	0	45	1
OIB	0	4	188	0	0	57
linear Eu-Lu-Sr
IAB	111	9	4	31	7	3
MORB	3	110	4	0	35	0
OIB	1	3	116	0	0	27
linear Ti-V-Sc
IAB	89	11	5	19	0	0
MORB	10	133	5	9	28	4
OIB	0	7	114	0	0	12
quadratic Na-Nb-Sr
IAB	144	6	7	21	0	0
MORB	2	121	3	5	7	0
OIB	4	0	138	0	0	28
quadratic Ti-V-Sm
IAB	91	8	5	24	2	0
MORB	5	152	5	1	44	5
OIB	3	9	93	0	0	9

Table 6: Anchor points for selected linear discriminant analyses.

node	1	2	3	4
ld1 (Equation 7)	-12	-12.23	-18	-8
ld2 (Equation 7)	4	-1.37	-6.6	-6.45
ld1 (Equation 8)	5.02	12.17	15.9	11.85
ld2 (Equation 8)	-6.28	-12.23	-10.93	-16
log(Ti/(10$^6$-Ti-V))	-4.65	-6	-4.11	-5.22
log(V/(10$^6$-Ti-V))	7.36	10.5	7.36	10.5
log(Zr/(10$^6$-Ti-Zr))	-13	-7	-13	-7
log(Ti/(10$^6$-Ti-Zr))	-4.28	-4.45	-5.36	-4.72
log(100xZr/Ti)	-2.5	2	-2.5	2
log(300xY/Ti)	-0.48	0.53	-0.97	0.17
log(Zr/(8xNb))	-2	2	0.41	3
log(Y/(2xNb))	-1.49	2.92	0.19	1.81
log(3xTh/Hf)	-1.49	1.43	-0.07	2.81
log(3xTa/Hf)	-2.48	-1.5	-0.86	1
log(Si/(25xTi))	-1.26	-0.2	-0.05	2
log(40xSr/Ti)	-2.15	2.98	0.39	-0.77
log(Eu/(5xLu))	-1.23	0.5	0.03	-0.61
log(Sr/(500xLu))	-1	2.33	1	-5
log(50xV/Ti)	-2	1.1	0.57	2
log(250xSc/Ti)	-0.54	2	-0.39	-1.41

Table 7: Comparison between old and new decision boundaries using the test data.

Ti-Zr
true	Pearce and Cann (1973)			LDA		QDA
affinity	IAB	MORB	out of bounds	IAB	MORB	IAB	MORB
IAB	18	22	2	36	11	32	15
MORB	0	5	6	0	11	3	8

Ti-V
true	Shervais (1982)				LDA			QDA
affinity	IAB	MORB	OIB	out of bounds	IAB	MORB	OIB	IAB	MORB	OIB
IAB	17	10	0	0	19	8	0	19	8	0
MORB	0	47	2	3	2	39	12	4	37	12
OIB	0	2	28	6	0	0	36	0	0	36

Ti-Zr-Y
true	Pearce and Cann (1973)			LDA		QDA
affinity	IAB & MORB	OIB	out of bounds	IAB & MORB	OIB	IAB & MORB	OIB
IAB	36	3	6	42	3	42	3
MORB	8	0	3	11	0	11	0
OIB	3	24	2	5	24	5	24

Zr-Y-Nb
true	Meschede (1986)			LDA		QDA
affinity	IAB & MORB	OIB	out of bounds	IAB & MORB	OIB	IAB & MORB	OIB
IAB	22	0	1	21	2	23	0
MORB	8	0	0	8	0	8	0
OIB	3	23	1	4	23	4	23

Th-Ta-Hf
true	Wood (1980)			LDA		QDA
affinity	IAB	MORB & OIB	out of bounds	IAB	MORB & OIB	IAB	MORB & OIB
IAB	12	14	0	12	14	14	12
MORB	0	0	0	0	0	0	0
OIB	0	10	0	0	10	0	10