Overview

The following tables list spectrally optimal weights for predicting one unknown sample, indicated by a question mark '?', as a weighted combination of known samples in a 3-by-3 grid. Unknown samples correspond to gray squares, while negative, zero, and positive weights for known samples are on a blue, green, and red background, respectively. Weights for chosen vertex (corner), edge (border), and face (center) points are shown; weights for the remaining 6 samples can be obtained via symmetry.

Weights for vertex points



?



?	1



?		1



?	2	-1


1
?


1/2
?	1/2


4/5
?		1/5


0
?	2	-1


	1
?


	0
?	1


	1
?		0


	0
?	2	-1


1	0
?


1	-1
?	1


2	-2
?		1


0	0
?	2	-1


		1
?


		-1/2
?	3/2


		0
?		1


		0
?	2	-1


1		0
?


1/2		-1/2
?	1


1		-1
?		1


0		0
?	2	-1


	2	-1
?


	1	-1
?	1


	2	-2
?		1


	0	0
?	2	-1


1	0	0
?


1	-1	0
?	1


1	0	-1
?		1


1	-2	1
?	2	-1

1

?

1/5

?	4/5

1/2

?		1/2

0

?	2	-1

-1
2
?

-1
2
?	0

-1
2
?		0

-1/2
1
?	1	-1/2

0
	1
?

1
	-2
?	2

-1/2
	2
?		-1/2

0
	0
?	2	-1

-1
2	0
?

-1
2	0
?	0

-1
2	0
?		0

-1/2
1	0
?	1	-1/2

3/5
		2/5
?

1/3
		-2/3
?	4/3

1
		-2
?		2

0
		0
?	2	-1

-1
2		0
?

-1
2		0
?	0

-1
2		0
?		0

-1/2
1		0
?	1	-1/2

-1
	4	-2
?

-1
	4	-2
?	0

-1
	4	-2
?		0

1/2
	-2	1
?	3	-3/2

-1
2	0	0
?

-1
2	0	0
?	0

-1
2	0	0
?		0

0
1	-2	1
?	2	-1

	1

?

	0

?	1

	2/5

?		3/5

	0

?	2	-1

	-1/2
3/2
?

	-1/2
1
?	1/2

	-2/3
4/3
?		1/3

	0
0
?	2	-1

	-1
	2
?

	0
	0
?	1

	-2
	4
?		-1

	0
	0
?	2	-1

	-1
1	1
?

	0
1	-1
?	1

	-2
0	4
?		-1

	0
0	0
?	2	-1

	1/2
		1/2
?

	1/2
		-1
?	3/2

	2
		-4
?		3

	0
		0
?	2	-1

	-1
3/2		1/2
?

	-1/4
3/4		-1/4
?	3/4

	-2
2		2
?		-1

	-1/2
1/2		1/2
?	3/2	-1

	-1
	3	-1
?

	0
	1	-1
?	1

	-2
	4	0
?		-1

	0
	0	0
?	2	-1

	-1
1	1	0
?

	0
1	-1	0
?	1

	-2
1	2	1
?		-1

	0
1	-2	1
?	2	-1

1	0

?

1	-1

?	1

2	-2

?		1

0	0

?	2	-1

-1	0
2
?

-1	0
2
?	0

-1	0
2
?		0

-1/2	0
1
?	1	-1/2

1	-2
	2
?

1	-1
	0
?	1

0	-2
	4
?		-1

0	0
	0
?	2	-1

-1	0
2	0
?

-1	1
2	-2
?	1

-3/2	1
3	-2
?		1/2

-1	1
2	-2
?	1	0

3	-4
		2
?

-1	2
		-2
?	2

3/2	-1
		-1
?		3/2

1/2	-1
		1
?	2	-3/2

-1	0
2		0
?

-1	1/2
3/2		-1/2
?	1/2

-3/2	1
2		-1
?		1/2

-1/2	0
1		0
?	1	-1/2

-1	0
	4	-2
?

-1	1
	2	-2
?	1

-1/2	-1
	4	-1
?		-1/2

1	-1
	-2	2
?	3	-2

-1	0
2	0	0
?

-1	1
2	-2	0
?	1

-2	2
3	-2	-1
?		1

-1/2	1/2
3/2	-2	1/2
?	3/2	-1/2

		1

?

		-1/5

?	6/5

		0

?		1

		0

?	2	-1

		-1/5
6/5
?

		-1/3
2/3
?	2/3

		-1/2
1
?		1/2

		0
0
?	2	-1

		-1
	2
?

		-1
	2
?	0

		-1
	2
?		0

		0
	0
?	2	-1

		-1
0	2
?

		1
2	-4
?	2

		-2/5
6/5	-2/5
?		3/5

		2/5
4/5	-8/5
?	2	-3/5

		-1
		2
?

		1
		-2
?	2

		0
		0
?		1

		0
		0
?	2	-1

		-1
1		1
?

		1
0		-2
?	2

		0
1		-1
?		1

		0
0		0
?	2	-1

		-1
	2	0
?

		1
	0	-2
?	2

		0
	2	-2
?		1

		0
	0	0
?	2	-1

		-1
1	0	1
?

		1
1	-2	-1
?	2

		0
1	0	-1
?		1

		0
1	-2	1
?	2	-1

1		0

?

1/2		-1/2

?	1

1		-1

?		1

0		0

?	2	-1

-1		0
2
?

-1		0
2
?	0

-1		0
2
?		0

-1/2		0
1
?	1	-1/2

0		-1
	2
?

3/5		-2/5
	-2/5
?	6/5

-1		-1
	4
?		-1

1/5		1/5
	-4/5
?	12/5	-1

-1		0
2	0
?

-3/5		2/5
2	-8/5
?	4/5

-1		1/5
12/5	-4/5
?		1/5

-1/3		1/3
4/3	-4/3
?	4/3	-1/3

1		-2
		2
?

0		1
		-2
?	2

1		-1
		0
?		1

0		0
		0
?	2	-1

-1		0
2		0
?

-3/5