Skyline

A skyline is set of points which is not dominated by any other point.

This implementation uses a block nested loop. Identical observations are all part of the skyline if applicable.

Parameters

• minimize (list) – defaults to None

  A list of features for which the values need to be minimized. Can be omitted as long as maximize is specified.

• maximize (list) – defaults to None

  A list of features for which the values need to be maximized. Can be omitted as long as minimize is specified.

Examples

Here is an example taken from this blog post.

>>> import random
>>> from river import misc

>>> city_prices = {
...     'Bordeaux': 4045,
...     'Lyon': 4547,
...     'Toulouse': 3278
... }

>>> def random_house():
...     city = random.choice(['Bordeaux', 'Lyon', 'Toulouse'])
...     size = round(random.gauss(200, 50))
...     price = round(random.uniform(0.8, 1.2) * city_prices[city] * size)
...     return {'city': city, 'size': size, 'price': price}

>>> skyline = misc.Skyline(minimize=['price'], maximize=['size'])

>>> random.seed(42)

>>> for _ in range(100):
...     house = random_house()
...     skyline = skyline.update(house)

>>> print(len(skyline))
13

>>> print(skyline[0])
{'city': 'Toulouse', 'size': 280, 'price': 763202}

Here is another example using the kart data from Mario Kart: Double Dash!!.

>>> import collections
>>> from river import misc

>>> Kart = collections.namedtuple(
...      'Kart',
...      'name speed off_road acceleration weight turbo'
... )

>>> karts = [
...     Kart('Red Fire', 5, 4, 4, 5, 2),
...     Kart('Green Fire', 7, 3, 3, 4, 2),
...     Kart('Heart Coach', 4, 6, 6, 5, 2),
...     Kart('Bloom Coach', 6, 4, 5, 3, 2),
...     Kart('Turbo Yoshi', 4, 5, 6, 6, 2),
...     Kart('Turbo Birdo', 6, 4, 4, 7, 2),
...     Kart('Goo-Goo Buggy', 1, 9, 9, 2, 3),
...     Kart('Rattle Buggy', 2, 9, 8, 2, 3),
...     Kart('Toad Kart', 3, 9, 7, 2, 3),
...     Kart('Toadette Kart', 1, 9, 9, 2, 3),
...     Kart('Koopa Dasher', 2, 8, 8, 3, 3),
...     Kart('Para-Wing', 1, 8, 9, 3, 3),
...     Kart('DK Jumbo', 8, 2, 2, 8, 1),
...     Kart('Barrel Train', 8, 7, 3, 5, 3),
...     Kart('Koopa King', 9, 1, 1, 9, 1),
...     Kart('Bullet Blaster', 8, 1, 4, 1, 3),
...     Kart('Wario Car', 7, 3, 3, 7, 1),
...     Kart('Waluigi Racer', 5, 9, 5, 6, 2),
...     Kart('Piranha Pipes', 8, 7, 2, 9, 1),
...     Kart('Boo Pipes', 2, 9, 8, 9, 1),
...     Kart('Parade Kart', 7, 3, 4, 7, 3)
... ]

>>> skyline = misc.Skyline(
...     maximize=['speed', 'off_road', 'acceleration', 'turbo'],
...     minimize=['weight']
... )

>>> for kart in karts:
...     skyline = skyline.update(kart._asdict())

>>> best_cart_names = [kart['name'] for kart in skyline]
>>> for name in best_cart_names:
...     print(f'- {name}')
- Green Fire
- Heart Coach
- Bloom Coach
- Goo-Goo Buggy
- Rattle Buggy
- Toad Kart
- Toadette Kart
- Barrel Train
- Koopa King
- Bullet Blaster
- Waluigi Racer
- Parade Kart

>>> for name in sorted(set(kart.name for kart in karts) - set(best_cart_names)):
...     print(f'- {name}')
- Boo Pipes
- DK Jumbo
- Koopa Dasher
- Para-Wing
- Piranha Pipes
- Red Fire
- Turbo Birdo
- Turbo Yoshi
- Wario Car

Methods

append

S.append(value) -- append value to the end of the sequence

Parameters

• item

clear

S.clear() -> None -- remove all items from S

copy

count

S.count(value) -> integer -- return number of occurrences of value

Parameters

• item

extend

S.extend(iterable) -- extend sequence by appending elements from the iterable

Parameters

• other

index

S.index(value, [start, [stop]]) -> integer -- return first index of value. Raises ValueError if the value is not present.

Supporting start and stop arguments is optional, but recommended.

Parameters

• item
• args

insert

S.insert(index, value) -- insert value before index

Parameters

• i
• item

pop

S.pop([index]) -> item -- remove and return item at index (default last). Raise IndexError if list is empty or index is out of range.

Parameters

• i – defaults to -1

remove

S.remove(value) -- remove first occurrence of value. Raise ValueError if the value is not present.

Parameters

• item

reverse

S.reverse() -- reverse IN PLACE

sort

update

References

---

1. Skyline queries in Python ↩

2. Borzsony, S., Kossmann, D. and Stocker, K., 2001, April. The skyline operator. In Proceedings 17th international conference on data engineering (pp. 421-430). IEEE. ↩

3. Tao, Y. and Papadias, D., 2006. Maintaining sliding window skylines on data streams. IEEE Transactions on Knowledge and Data Engineering, 18(3), pp.377-391. ↩