Dataset Housing MEDV>35

Basic characteristics Housing MEDV>35

48

target objects

The Boston Housing Database from the Statlib Library. To predict the housing prices in suburbs of Boston. The class of a median price of more than 35,000 dollar is used as target class. Download mat-file with Prtools dataset.

458

outlier objects

13

features

Unsupervised PCA Housing MEDV>35

On the left, the PCA scatterplot is shown, on the right the retained variance for varying number of features.
On the left, the PCA scatterplot is shown of data rescaled to unit variance, on the right the retained variance.

Supervised Fisher Housing MEDV>35

On the left, the Fisher scatterplot is shown, on the right the ROC curve along this direction.

Results Housing MEDV>35

The experiments are performed using dd_tools. A rudimentary explanation of the classifiers is given in the classifier section.

619, 0 outliers, AUC (x100) 5x strat. 10-fold
Classifiers Preproc
none unit var PCA 95\%
Gauss 79.3 ( 0.3) 88.0 ( 1.1) 52.5 ( 0.9)
Min.Cov.Determinant 81.0 ( 0.9) 81.0 ( 0.9) 57.5 ( 0.9)
Mixture of Gaussians 71.7 ( 0.9) 55.5 (10.4) 54.8 ( 1.9)
Naive Parzen 89.4 ( 1.1) 89.4 ( 1.1) 70.4 ( 1.4)
Parzen 52.7 ( 6.3) 54.9 ( 7.0) 59.8 ( 1.1)
k-means 64.8 ( 1.6) 87.2 ( 1.1) 49.2 ( 0.9)
1-Nearest Neighbors 82.8 ( 1.1) 88.3 ( 1.5) 69.2 ( 1.2)
k-Nearest Neighbors 82.8 ( 1.1) 88.3 ( 1.5) 69.2 ( 1.2)
knn, opt-AUC 82.8 ( 1.1) 88.1 ( 1.3) 68.7 ( 0.8)
Nearest-neighbor dist 71.3 ( 1.4) 73.8 ( 2.9) 68.2 ( 2.4)
Principal comp. 59.0 ( 1.0) 86.3 ( 1.7) 39.6 ( 0.6)
Self-Organ. Map 62.1 ( 0.5) 88.0 ( 0.8) 53.9 ( 1.3)
Auto-enc network 64.9 ( 3.0) 87.3 ( 1.5) 59.6 ( 3.8)
Spanning Tree 83.7 ( 1.8) 88.7 ( 1.4) 69.3 ( 2.1)
L_1-ball 50.9 ( 0.5) 62.8 ( 1.9) 47.3 ( 1.6)
k-center 77.3 ( 1.4) 88.0 ( 2.5) 63.8 ( 2.0)
Support vector DD 4.7 ( 2.6) 49.4 ( 8.5) 31.3 ( 7.9)
Minimax Prob. DD 78.6 ( 1.3) 88.5 ( 1.4) 68.9 ( 1.2)
LinProg DD 47.1 ( 2.7) 82.7 ( 4.4) 54.1 ( 3.7)

Classifier projection spaces The first classifier projection spaces are obtained by computing the classifier label disagreements (setting the threshold on 10% target error) and applying an MDS on the resulting distance matrix between classifiers:



Original



Unit variance



PCA mapped

Classifier projection spaces The second versions of the classifier projection spaces are obtained by computing the classifier ranking disagreements and applying an MDS on the resulting distance matrix between classifiers:



Original



Unit variance



PCA mapped