Issues of Inconsistency

We can observe two issues of inconsistency

•  Strict (Issue 1): Two views are rated similar bad/good, but one view has low/high class consistency (confirmed by visual inspection)
•  Practical (Issue 2): View is rated bad/good using a particular measure while the remaining measures rate that view good/bad

We define a view as good according to a particular measure iff score > 0.7
We define a view as bad according to a particular measure iff score < 0.5

 

Fisher's Iris Data (Real World)

    Brief Description
         

Dimensions	Data Points	Classes
4	150	3

   

    Scatterplot Matrix



    View Scores
   

View	Clumpiness	Distance Consistency	Global Class Consistency	Local Class Consistency	Pairwise Squared Distance	Weighted Squared Distance
0,1	15.4	81.3	67.5	63.6	19.6	17.4
0,2	64.1	88.6	84.6	90.2	85	85
0,3	28.1	84.6	88.2	93	28.4	27.2
1,2	34.3	94	83.9	87.6	74	74.5
1,3	16.6	94	87.9	92.1	17.2	16.7
2,3	63	96	90.6	95.4	82.7	84.2

 

    View Scores

View	General Class Consistency	General Consistency
0,1	26.9	72.7
0,2	83.4	79.2
0,3	88.4	69.1
1,2	78.4	73.6
1,3	83.4	53.4
2,3	90	53.1

    Dimension Scores (based distance consistency evaluation)
   

Class	Important Dimensions for class	Impact to consistent view
Red	0,1,2,3	284.2
Green	0,1	21.4
Blue	1,2,3	16.1

Dimension	Importance for Consistency
0	-0.87
1	0.34
2	-0.27
4	-0.39

     The weighting is based on the consistency matrix and a factor analysis based on SVD
      (Note, if the weight of a particular class converges to 0, then it becomes more difficult         to find a consistent view)

 Description

	Top 3 Views
	Inconsistent
	Bad Score but still consistent
	Scale: bad=0....100=good

   
    Analysis (what can we learn)

• Some views are rated as bad but are still consistent; and showing a good separation of clusters confirmed by visual inspection
• In practice many consistent view would be filtered out using Clumpiness and Distance Measures as a preprocessing step
  
• Clumpiness and Distance Measures are partially correlated
• Distance Measure are highly correlated

• Clumpiness Inconsistent case is caused by low local density
  

Olive Data (Real World)

    Brief Description

Dimensions	Data Points	Classes
8	572	3

    Scatterplot Matrix


  
    View Scores

View	Clumpiness	Distance Consistency	Global Class Consistency	Local Class Consistency	Pairwise Squared Distance	Weighted Squared Distance
0,1	4.6	75.4	56.2	53.4	12.3	11.8
0,2	3.2	71.9	52.4	48.7	11.8	11.2
0,3	38.1	81.6	70.1	79.8	76.2	76.6
0,4	23	80.4	75.1	83.6	34.5	33.6
0,5	1.2	72.6	63.6	66.6	11.3	10.9
0,6	2	78.1	63	68.4	11.4	11
0,7	1.6	72.4	81.1	53.7	11.3	11
1,2	1	72.6	51.5	48.5	1.6	1.4
1,3	11.5	74.7	64.3	68.9	66.1	66.8
1,4	6.9	52	71	75.8	24.4	23.8
1,5	0.4	72.7	69.3	75.4	1.2	1.1
1,6	0.6	76.4	62.8	60.4	1.3	1.2
1,7	0.5	74.3	82.6	56.4	1.2	1.1
2,3	8	74.3	60.6	65.2	65.6	66.2
2,4	4.7	48.4	50.4	50.1	23.9	23.2
2,5	0.2	54	42.7	34.8	0.6	0.5
2,6	0.3	59.1	41.5	35.2	0.7	0.6
2,7	0.3	72.4	82.2	59.3	0.6	0.5
3,4	58.2	88.3	72.8	82.3	88.3	88.6
3,5	3.8	74.3	71.9	80.2	65.1	65.9
3,6	4.7	74.7	64.4	65.2	65.2	66
3,7	3.7	74.3	95	93.5	65.1	65.9
4,5	1.7	48.6	65.5	62.1	23.3	22.9
4,6	2.7	48.6	64.2	65	23.5	23
4,7	2.2	48.8	97.1	97.2	23.5	23
5,6	0.2	76.2	51.7	57.6	0.3	0.3
5,7	0.1	78.7	85.6	72.8	0.1	0.2
6,7	0.2	88.1	88	84.3	0.3	0.3

 Description

	Top 3 Views
	Inconsistent
	Bad Score but still consistent
	Scale: bad=0....100=good

    Analysis (what can we learn)

Wine (Real World)

    Brief Description

Dimensions	Data Points	Classes
13	178	3

    View Scores

View	Clumpiness	Distance Consistency	Global Class Consistency	Local Class Consistency	Pairwise Squared Distance	Weighted Squared Distance
0,1	0	79.2	71.3	63.3	0	0
0,2	0	71.3	50.8	49.5	0	0
0,3	0	58.4	62	58.3	0	0
0,4	0.1	50	52.8	51.8	0.2	0.2
0,5	0	83.7	71.2	68.9	0	0
0,6	0	90.4	87.7	82.4	0	0
0,7	0	71.9	62.9	59.5	0	0
0,8	0	78.7	65.3	61.3	0	0
0,9	0	75.3	69.5	65	0	0
0,10	0	73	77.9	73.8	0	0
0,11	0	88.8	84.7	79.7	0	0
0,12	2.5	72.5	70.2	66.8	100	100
1,2	0	60.1	37.8	36.4	0	0
1,3	0	57.3	51	45.2	0	0
1,4	0.2	49.4	49	42.6	0.2	0.2
1,5	0	69.7	56.9	54.2	0	0
1,6	0	77.5	73.3	67.2	0	0
1,7	0	51.7	51	44.1	0	0
1,8	0	61.8	41.9	44.2	0	0
1,9	0	77	71.6	66.1	0	0
1,10	0	49.4	54.3	52.2	0	0
1,11	0	64	57.4	60.9	0	0
1,12	3.7	72.5	74.2	65.4	100	100
2,3	0	50	37.8	41.4	0	0
2,4	0	48.9	22.5	26.4	0.2	0.2
2,5	0	69.1	48	47.9	0	0
2,6	0	82	70.3	66.3	0	0
2,7	0	57.3	38	37.2	0	0
2,8	0	61.8	34.5	35.2	0	0
2,9	0	71.9	53.7	52.3	0	0
2,10	0	70.2	48.6	49	0	0
2,11	0	68.5	59.5	57.8	0	0
2,12	0.9	72.5	54.4	56	100	100
3,4	0.1	55.1	36.2	39.3	0	0.2
3,5	0	53.4	55.4	51.4	0	0
3,6	0	59	73.7	67.8	0	0
3,7	0	50	40.8	37.5	0	0
3,8	0	50.6	46.5	43.7	0	0
3,9	0	74.7	60.1	59.8	0	0
3,10	0	50	54.1	52.8356	0	0
3,11	0	53.9	63.6	63.5	0	0
3,12	11	72.5	52.6	57.3	100	100
4,5	0	48.9	50.8	51.7	0.2	0.2
4,6	0	50	77.7	73	0.2	0.2
4,7	0	49	49.7	41	0.2	0.2
4,8	0	49	42.7	41.7875	0.2	0.2
4,9	0	52.8	56.4	54	0.2	0.2
4,10	0	48.9	56.3	54	0.2	0.2
4,11	0	50	66.8	64.6516	0.2	0.2
4,12	0	72.5	57.3	58.3	100	100
5,6	0	78.1	65.1	61.8	0	0
5,7	0	65.2	53.9	50.3	0	0
5,8	0	63	48.8	46.6	0	0
5,9	0	74.2	80.5	76.2	0	0
5,10	0	70.8	67.1	62.9	0	0
5,11	0	74.7	64.5	59.6	0	0
5,12	2	72.5	66.2	67.8	0	0
6,7	0	79.2	68.3	65.8	0	0
6,8	0	78.7	69.6	62.8	0	0
6,9	0	83.7	84.9	81.6	0	0
6,10	0	79.8	81.3	73.9	0	0
6,11	0	83.7	70.8	67.2	0	0
6,12	0	72.5	81	77.9	100	100
7,8	0	54	40.7	39.7	0	0
7,9	0	71.9	66.3	61.1	0	0
7,10	0	68	54.3	53.7	0	0
7,11	0	62.4	58.9	54.8	0	0
7,12	0.4	72.5	66.3	58.3	100	100
8,9	0	71.9	70.2	67.5	0	0
8,10	0	61.2	57	53.6	0	0
8,11	0	67.4	60.2	57.6	0	0
8,12	1.8	72.5	64	63.2	100	100
9,10	0	71.9	68.6	67.1	0	0
9,11	0	74.7	80.9	76.4	0	0
9,12	7.1	72.5	82.8	77.2	100	100
10,11	0	65.2	63	59.9	0	0
10,12	0.8	72.5	77.6	76.1	100	100
11,12	2.3	72.5	82.6	78.8	100	100

Subspace Cluster (Synthetic)

    Brief Description

Dimensions	Data Points	Classes
3	500	3

Subspace Cluster 1	2 Cluster in x/y dimension
Subspace Cluster 2	1 Cluster in x/z dimension

    Scatterplot Matrix



    View Scores
   

View	Clumpiness	Distance Consistency	Global Class Consistency	Local Class Consistency	Pairwise Squared Distance	Weighted Squared Distance
0,1	38.3	82.6	79.7	73.7	97.4	62.3
0,2	41	88.2	100	100	90.1	100
1,2	20	69.4	76.2	57.5	33.4	21.5

Description

	Top 3 Views
	Inconsistent
	Bad Score but still consistent
	Scale: bad=0....100=good
	Label: x=0; y=1; z=2

    Analysis (what can we learn)

Subspace Cluster with Noisy Dimension (Synthetic; controversial case)

    Brief Description

Dimensions	Data Points	Classes
2	500	2

    Scatterplot Matrix




    View Scores

View	Clumpiness	Distance Consistency	Global Class Consistency	Local Class Consistency	Pairwise Squared Distance	Weighted Squared Distance
0,1	47.2	98.6	100	100	99.2	99.2
0,2	28	71	74.5	71	75.7	66.2
1,2	45.3	77.3	76	97.7	85.1	82.1

    Description

	Top 3 Views
	Inconsistent
	Bad Score but still consistent
	Scale: bad=0....100=good
	Label: x=0; y=1; z=2

    Analysis (what can we learn)