1. Algebraic Topology Simplical Complex
Tsau Young (‘T. Y.’) Lin
Institute of Data Science and Computing
and
Computer Science Department,
San Jose State University ;

2. Formal Theory of Simplicial Complex
The mathematical Structure Ssimplex similar to R3
are used in algebraic topology
(U, Ssimplex)

3. Open Simplexes 
0- Simplex ( 1 point)

4. Open Simplexes -
  
1-simplex (no end points)

5. Open Simplexes 
  
2-simplex (no boundary)

6. Open Simplexes
3-simplex(no boundary)
Open tetrahedron

7. Data Mining Theorem 1: Isomorphic Information Tables 
Isomorphic Patterns
PAKDD 1999

8. BiT IT Tuple : What did a customer buy?)
Diaper
Beer
Milk
Pen …. 1

9. BiT Geometric IT
Instead of item names, we may use name of the “unit vector”
First item is A=(1, 0, 0, …)
The second item is B=(0, 1, 0, 0, ….)

10. BiT IT (IT=A Relation in Relational Database)C D …. 1

11. Closed 3-simplex : It summarizes all information of First tupleB A C

12. An Example of Bit IT A B C D E F G 1 #1 #2 #3 #4 #5 #6 #7 Pen Beer#1 #2 #3 #4 #5 #6 #7
Pen
Beer
Milk
Diaper
Paper
Tape
Knife

13. Its Simplicial Complex View
Open tetrahedron 2
d #3 d
Open tetrahedron 1
b #2 b
c #1 c
a #4
e #5
g # 7
f #6