A Novel Approach to Novelty Detection: Voronoi Tesselation

1. A Novel Approach to Novelty Detection: Voronoi Tesselation Jeffrey.D.Scargle@nasa.gov Space Science Division NASA Ames Research Center Collaborator: Nikunj Oza, NASA-Ames Research Center, IC PureSense, Inc. Machine Learning Seminar

2. The Basic Ideas • Nonparametric Density Estimation • Voronoi Tessellation • Voronoi Cells as Point Surrogates • 1/Area of cell ~ local point density • Cell geometry  local density gradient • Tessellate training points plus 1 test point • If the Voronoi cell assigned to the test point is an “edge” cell, the test point is an outlier; otherwise it is “normal”

3. Modes of Operation (1) • Static training data and test data

4. Modes of Operation (2) • Training data = all past data Test data = one new data point

5. Modes of Operation (2) • Training data = all past data Test data = one new data point

6. Modes of Operation (3) • Training data = past data of fixed size Test data = one new data point

7. Voronoi Tessellation of data in any dimension

8. Construct Voronoi cells to represent local photon density: density ~ 1 / cell area

12. Voronoi cells also represent local photon density gradients …

18. The Voronoi cells are a local representation of the data …

30. Selecting the smallest Voronoi cells yields the regions of highest photon density …

50. MatLab code % do abnormal data for id = 1: num_test data = [ train_data test_data( id ) ]; [ vertices, v_cells ] = voronoin( data ); vertices_last = v_cells{ num_use + 1 }; if find( vertices_last == 1 ) % “infinite vertex” = #1 count_correct = count_correct + 1; else count_error = count_error + 1; end end