Top-k Typicality Queries on Uncertain Data - Ranking Queries on Uncertain Data - page 76

Top-10 most representatively typical animals Top-10 most typical animals

Rank Animal Representative Category Rank Animal Simple Category

typicality score typicality score

1 Boar 0.0874661 Mammal 1 Boar 0.0855363 Mammal

2 Lark 0.135712 Bird 1 Cheetah 0.0855363 Mammal

3 Bass 0.176546 Fish 1 Leopard 0.0855363 Mammal

4 Gnat 0.198142 Insect 1 Lion 0.0855363 Mammal

5 Aardvark 0.213342 Mammal 1 Lynx 0.0855363 Mammal

6 wallaby 0.225642 Mammal 1 Mongoose 0.0855363 Mammal

7 starfish 0.236235 Invertebrate 1 Polecat 0.0855363 Mammal

8 Slug 0.246638 Invertebrate 1 Puma 0.0855363 Mammal

9 Dolphin 0.236347 Mammal 1 Raccoon 0.0855363 Mammal

10 frog 0.265012 Amphibian 1 Wolf 0.0855363 Mammal

Table 4.3 The most representatively typical and the most typical animals.

in category mammals , the most typical animals are more likely to be referred to as
a mammal than the most atypical one, platypuses , which are one of the very few
mammal species that lay eggs instead of giving birth to live young.
We apply discriminative typicality analysis on the Zoo Database to find the dis-
criminative typical animals for each category. The results are listed in Table 4.2 as
well. In some categories, the instances having the largest simple typicality value also
have the highest discriminative typicality value, such as categories mammals , birds ,
fish , invertebrates , and amphibians . In some categories such as insects and reptiles ,
the most typical animals are not the most discriminatively typical. For example, in
category reptiles , the most discriminatively typical animal is pitvipers in stead of
slowworm , because slowworm is also similar to some animals in other categories
besides reptiles , such as newts in category amphibians . On the other hand, pitvipers
are venomous. Very few animals in the other categories are venomous. The result
matches the above analysis.
In some situations, the results from the simple typicality queries may have a bias
on the most popular categories. Table 4.3 lists the top-10 most typical animals in
the Zoo Database. The 10 animals are all mammals, since mammals are the largest
category in the Zoo Database. As a result, the top-10 most typical animals as a whole
is not representative. The animals in other categories cannot be represented well.
Representative typicality queries avoid this problem. The top-10 most represen-
tatively typical animals are also listed in Table 4.3, which cover 6 out of the 7 cat-
egories in the Zoo Database. The only missed category is Reptile , which only con-
tains 5 animals. Boar is the first animal in the answer set of both queries, since it is
the most typical animal in the whole data set. Note that the representative typical-
ity score and the simple typicality score of boar are slightly different, because the
bandwidth parameter h is computed via sampling, and thus may have a small differ-
ence in each computation. The second most representatively typical animal is Lark ,
which is the most typical animal in the second most popular category Bird . Dolphin
is in the answer to the top-10 representative typicality query, since it represents a
set of aquatic mammal in the Zoo database, such as porpoise and mink. They are