Random subspace selection constructs feature subsets by choosing dimensions randomly. In outlier detection, multiple small subspaces can efficiently expose strong outliers when domain knowledge is limited, though important outliers may be missed. section 10.1.2
Construct a diverse set of comparable subspaces by:
- Selecting the least-used feature as the starting point for each subspace. section 10.1.2
- Adding features that minimize overlap with features already selected, while choosing randomly among ties. section 10.1.2
- Keeping the feature count constant when simpler tuning and more comparable detector scores matter; varying counts can add diversity but complicate score combination. section 10.1.2
Listing 10.2 Algorithm to select random subspaces
import pandas as pd
import numpy as np
def get_random_subspaces(features_arr, num_base_detectors,
num_feats_per_detector):
num_feats = len(features_arr)
feat_sets_arr = []
ft_used_counts = np.zeros(num_feats)
ft_pair_mtx = np.zeros((num_feats, num_feats))
for _ in range(num_base_detectors):
min_count = ft_used_counts.min() #1
idxs = np.where(ft_used_counts == min_count)[0]
feat_set = [np.random.choice(idxs)] #2
while len(feat_set) < num_feats_per_detector: #3
mtx_with_set = ft_pair_mtx[:, feat_set]
sums = mtx_with_set.sum(axis=1)
min_sum = sums.min()
min_idxs = np.where(sums==min_sum)[0]
new_feat = np.random.choice(min_idxs)
feat_set.append(new_feat)
feat_set = list(set(feat_set))
for c in feat_set: #4
ft_pair_mtx[c][new_feat] += 1
ft_pair_mtx[new_feat][c] += 1
for c in feat_set: #5
ft_used_counts[c] += 1
feat_sets_arr.append(feat_set)
return feat_sets_arr
np.random.seed(0)
features_arr = ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H']
num_base_detectors = 4
num_feats_per_detector = 5
feat_sets_arr = get_random_subspaces(features_arr,
num_base_detectors, num_feats_per_detector)
for feat_set in feat_sets_arr:
print([features_arr[x] for x in feat_set])
Use the selection algorithm to generate multiple feature subsets while tracking feature usage and pairwise overlap. section 10.1.2
