def create(dataset,
label=None,
features=None,
distance=None,
method='auto',
verbose=True,
**kwargs):
"""
Create a nearest neighbor model, which can be searched efficiently and
quickly for the nearest neighbors of a query observation. If the `method`
argument is specified as `auto`, the type of model is chosen automatically
based on the type of data in `dataset`.
.. warning::
The 'dot_product' distance is deprecated and will be removed in future
versions of Turi Create. Please use 'transformed_dot_product'
distance instead, although note that this is more than a name change;
it is a *different* transformation of the dot product of two vectors.
Please see the distances module documentation for more details.
Parameters
----------
dataset : SFrame
Reference data. If the features for each observation are numeric, they
may be in separate columns of 'dataset' or a single column with lists
of values. The features may also be in the form of a column of sparse
vectors (i.e. dictionaries), with string keys and numeric values.
label : string, optional
Name of the SFrame column with row labels. If 'label' is not specified,
row numbers are used to identify reference dataset rows when the model
is queried.
features : list[string], optional
Name of the columns with features to use in computing distances between
observations and the query points. 'None' (the default) indicates that
all columns except the label should be used as features. Each column
can be one of the following types:
- *Numeric*: values of numeric type integer or float.
- *Array*: list of numeric (integer or float) values. Each list element
is treated as a separate variable in the model.
- *Dictionary*: key-value pairs with numeric (integer or float) values.
Each key indicates a separate variable in the model.
- *List*: list of integer or string values. Each element is treated as
a separate variable in the model.
- *String*: string values.
Please note: if a composite distance is also specified, this parameter
is ignored.
distance : string, function, or list[list], optional
Function to measure the distance between any two input data rows. This
may be one of three types:
- *String*: the name of a standard distance function. One of
'euclidean', 'squared_euclidean', 'manhattan', 'levenshtein',
'jaccard', 'weighted_jaccard', 'cosine', 'dot_product' (deprecated),
or 'transformed_dot_product'.
- *Function*: a function handle from the
:mod:`~turicreate.toolkits.distances` module.
- *Composite distance*: the weighted sum of several standard distance
functions applied to various features. This is specified as a list of
distance components, each of which is itself a list containing three
items:
1. list or tuple of feature names (strings)
2. standard distance name (string)
3. scaling factor (int or float)
For more information about Turi Create distance functions, please
see the :py:mod:`~turicreate.toolkits.distances` module.
If 'distance' is left unspecified or set to 'auto', a composite
distance is constructed automatically based on feature types.
method : {'auto', 'ball_tree', 'brute_force', 'lsh'}, optional
Method for computing nearest neighbors. The options are:
- *auto* (default): the method is chosen automatically, based on the
type of data and the distance. If the distance is 'manhattan' or
'euclidean' and the features are numeric or vectors of numeric
values, then the 'ball_tree' method is used. Otherwise, the
'brute_force' method is used.
- *ball_tree*: use a tree structure to find the k-closest neighbors to
each query point. The ball tree model is slower to construct than the
brute force model, but queries are faster than linear time. This
method is not applicable for the cosine and dot product distances.
See `Liu, et al (2004)
<http://papers.nips.cc/paper/2666-an-investigation-of-p
ractical-approximat e-nearest-neighbor-algorithms>`_ for
implementation details.
- *brute_force*: compute the distance from a query point to all
reference observations. There is no computation time for model
creation with the brute force method (although the reference data is
held in the model, but each query takes linear time.
- *lsh*: use Locality Sensitive Hashing (LSH) to find approximate
nearest neighbors efficiently. The LSH model supports 'euclidean',
'squared_euclidean', 'manhattan', 'cosine', 'jaccard', 'dot_product'
(deprecated), and 'transformed_dot_product' distances. Two options
are provided for LSH -- ``num_tables`` and
``num_projections_per_table``. See the notes below for details.
verbose: bool, optional
If True, print progress updates and model details.
**kwargs : optional
Options for the distance function and query method.
- *leaf_size*: for the ball tree method, the number of points in each
leaf of the tree. The default is to use the max of 1,000 and
n/(2^11), which ensures a maximum tree depth of 12.
- *num_tables*: For the LSH method, the number of hash tables
constructed. The default value is 20. We recommend choosing values
from 10 to 30.
- *num_projections_per_table*: For the LSH method, the number of
projections/hash functions for each hash table. The default value is
4 for 'jaccard' distance, 16 for 'cosine' distance and 8 for other
distances. We recommend using number 2 ~ 6 for 'jaccard' distance, 8
~ 20 for 'cosine' distance and 4 ~ 12 for other distances.
Returns
-------
out : NearestNeighborsModel
A structure for efficiently computing the nearest neighbors in 'dataset'
of new query points.
See Also
--------
NearestNeighborsModel.query, turicreate.toolkits.distances
Notes
-----
- Missing data is not allowed in the 'dataset' provided to this function.
Please use the :func:`turicreate.SFrame.fillna` and
:func:`turicreate.SFrame.dropna` utilities to handle missing data before
creating a nearest neighbors model.
- Missing keys in sparse vectors are assumed to have value 0.
- The `composite_params` parameter was removed as of Turi Create
version 1.5. The `distance` parameter now accepts either standard or
composite distances. Please see the :mod:`~turicreate.toolkits.distances`
module documentation for more information on composite distances.
- If the features should be weighted equally in the distance calculations
but are measured on different scales, it is important to standardize the
features. One way to do this is to subtract the mean of each column and
divide by the standard deviation.
**Locality Sensitive Hashing (LSH)**
There are several efficient nearest neighbors search algorithms that work
well for data with low dimensions :math:`d` (approximately 50). However,
most of the solutions suffer from either space or query time that is
exponential in :math:`d`. For large :math:`d`, they often provide little,
if any, improvement over the 'brute_force' method. This is a well-known
consequence of the phenomenon called `The Curse of Dimensionality`.
`Locality Sensitive Hashing (LSH)
<https://en.wikipedia.org/wiki/Locality-sensitive_hashing>`_ is an approach
that is designed to efficiently solve the *approximate* nearest neighbor
search problem for high dimensional data. The key idea of LSH is to hash
the data points using several hash functions, so that the probability of
collision is much higher for data points which are close to each other than
those which are far apart.
An LSH family is a family of functions :math:`h` which map points from the
metric space to a bucket, so that
- if :math:`d(p, q) \\leq R`, then :math:`h(p) = h(q)` with at least probability :math:`p_1`.
- if :math:`d(p, q) \\geq cR`, then :math:`h(p) = h(q)` with probability at most :math:`p_2`.
LSH for efficient approximate nearest neighbor search:
- We define a new family of hash functions :math:`g`, where each
function :math:`g` is obtained by concatenating :math:`k` functions
:math:`h_1, ..., h_k`, i.e., :math:`g(p)=[h_1(p),...,h_k(p)]`.
The algorithm constructs :math:`L` hash tables, each of which
corresponds to a different randomly chosen hash function :math:`g`.
There are :math:`k \\cdot L` hash functions used in total.
- In the preprocessing step, we hash all :math:`n` reference points
into each of the :math:`L` hash tables.
- Given a query point :math:`q`, the algorithm iterates over the
:math:`L` hash functions :math:`g`. For each :math:`g` considered, it
retrieves the data points that are hashed into the same bucket as q.
These data points from all the :math:`L` hash tables are considered as
candidates that are then re-ranked by their real distances with the query
data.
**Note** that the number of tables :math:`L` and the number of hash
functions per table :math:`k` are two main parameters. They can be set
using the options ``num_tables`` and ``num_projections_per_table``
respectively.
Hash functions for different distances:
- `euclidean` and `squared_euclidean`:
:math:`h(q) = \\lfloor \\frac{a \\cdot q + b}{w} \\rfloor` where
:math:`a` is a vector, of which the elements are independently
sampled from normal distribution, and :math:`b` is a number
uniformly sampled from :math:`[0, r]`. :math:`r` is a parameter for the
bucket width. We set :math:`r` using the average all-pair `euclidean`
distances from a small randomly sampled subset of the reference data.
- `manhattan`: The hash function of `manhattan` is similar with that of
`euclidean`. The only difference is that the elements of `a` are sampled
from Cauchy distribution, instead of normal distribution.
- `cosine`: Random Projection is designed to approximate the cosine
distance between vectors. The hash function is :math:`h(q) = sgn(a \\cdot
q)`, where :math:`a` is randomly sampled normal unit vector.
- `jaccard`: We use a recently proposed method one permutation hashing by
Shrivastava and Li. See the paper `[Shrivastava and Li, UAI 2014]
<http://www.auai.org/uai2014/proceedings/individuals/225.pdf>`_ for
details.
- `dot_product`: The reference data points are first transformed to
fixed-norm vectors, and then the minimum `dot_product` distance search
problem can be solved via finding the reference data with smallest
`cosine` distances. See the paper `[Neyshabur and Srebro, ICML 2015]
<http://proceedings.mlr.press/v37/neyshabur15.html>`_ for details.
References
----------
- `Wikipedia - nearest neighbor
search <http://en.wikipedia.org/wiki/Nearest_neighbor_search>`_
- `Wikipedia - ball tree <http://en.wikipedia.org/wiki/Ball_tree>`_
- Ball tree implementation: Liu, T., et al. (2004) `An Investigation of
Practical Approximate Nearest Neighbor Algorithms
<http://papers.nips.cc/paper/2666-an-investigation-of-p
ractical-approximat e-nearest-neighbor-algorithms>`_. Advances in Neural
Information Processing Systems pp. 825-832.
- `Wikipedia - Jaccard distance
<http://en.wikipedia.org/wiki/Jaccard_index>`_
- Weighted Jaccard distance: Chierichetti, F., et al. (2010) `Finding the
Jaccard Median
<http://theory.stanford.edu/~sergei/papers/soda10-jaccard.pdf>`_.
Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete
Algorithms. Society for Industrial and Applied Mathematics.
- `Wikipedia - Cosine distance
<http://en.wikipedia.org/wiki/Cosine_similarity>`_
- `Wikipedia - Levenshtein distance
<http://en.wikipedia.org/wiki/Levenshtein_distance>`_
- Locality Sensitive Hashing : Chapter 3 of the book `Mining Massive
Datasets <http://infolab.stanford.edu/~ullman/mmds/ch3.pdf>`_.
Examples
--------
Construct a nearest neighbors model with automatically determined method
and distance:
>>> sf = turicreate.SFrame({'X1': [0.98, 0.62, 0.11],
... 'X2': [0.69, 0.58, 0.36],
... 'str_feature': ['cat', 'dog', 'fossa']})
>>> model = turicreate.nearest_neighbors.create(sf, features=['X1', 'X2'])
For datasets with a large number of rows and up to about 100 variables, the
ball tree method often leads to much faster queries.
>>> model = turicreate.nearest_neighbors.create(sf, features=['X1', 'X2'],
... method='ball_tree')
Often the final determination of a neighbor is based on several distance
computations over different sets of features. Each part of this composite
distance may have a different relative weight.
>>> my_dist = [[['X1', 'X2'], 'euclidean', 2.],
... [['str_feature'], 'levenshtein', 3.]]
...
>>> model = turicreate.nearest_neighbors.create(sf, distance=my_dist)
"""
## Validate the 'dataset' input
_tkutl._raise_error_if_not_sframe(dataset, "dataset")
_tkutl._raise_error_if_sframe_empty(dataset, "dataset")
## Basic validation of the features input
if features is not None and not isinstance(features, list):
raise TypeError("If specified, input 'features' must be a list of " +
"strings.")
## Clean the method options and create the options dictionary
allowed_kwargs = ['leaf_size', 'num_tables', 'num_projections_per_table']
_method_options = {}
for k, v in kwargs.items():
if k in allowed_kwargs:
_method_options[k] = v
else:
raise _ToolkitError(
"'{}' is not a valid keyword argument".format(k) +
" for the nearest neighbors model. Please " +
"check for capitalization and other typos.")
## Exclude inappropriate combinations of method an distance
if method == 'ball_tree' and (
distance == 'cosine' or distance == _turicreate.distances.cosine
or distance == 'dot_product'
or distance == _turicreate.distances.dot_product
or distance == 'transformed_dot_product'
or distance == _turicreate.distances.transformed_dot_product):
raise TypeError(
"The ball tree method does not work with 'cosine' " +
"'dot_product', or 'transformed_dot_product' distance." +
"Please use the 'brute_force' method for these distances.")
if method == 'lsh' and ('num_projections_per_table'
not in _method_options):
if distance == 'jaccard' or distance == _turicreate.distances.jaccard:
_method_options['num_projections_per_table'] = 4
elif distance == 'cosine' or distance == _turicreate.distances.cosine:
_method_options['num_projections_per_table'] = 16
else:
_method_options['num_projections_per_table'] = 8
## Initial validation and processing of the label
if label is None:
_label = _robust_column_name('__id', dataset.column_names())
_dataset = dataset.add_row_number(_label)
else:
_label = label
_dataset = _copy.copy(dataset)
col_type_map = {c: _dataset[c].dtype for c in _dataset.column_names()}
_validate_row_label(_label, col_type_map)
ref_labels = _dataset[_label]
## Determine the internal list of available feature names (may still include
# the row label name).
if features is None:
_features = _dataset.column_names()
else:
_features = _copy.deepcopy(features)
## Check if there's only one feature and it's the same as the row label.
# This would also be trapped by the composite distance validation, but the
# error message is not very informative for the user.
free_features = set(_features).difference([_label])
if len(free_features) < 1:
raise _ToolkitError("The only available feature is the same as the " +
"row label column. Please specify features " +
"that are not also row labels.")
### Validate and preprocess the distance function
### ---------------------------------------------
# - The form of the 'distance' controls how we interact with the 'features'
# parameter as well.
# - At this point, the row label 'label' may still be in the list(s) of
# features.
## Convert any distance function input into a single composite distance.
# distance is already a composite distance
if isinstance(distance, list):
distance = _copy.deepcopy(distance)
# distance is a single name (except 'auto') or function handle.
elif (hasattr(distance, '__call__')
or (isinstance(distance, str) and not distance == 'auto')):
distance = [[_features, distance, 1]]
# distance is unspecified and needs to be constructed.
elif distance is None or distance == 'auto':
sample = _dataset.head()
distance = _construct_auto_distance(_features, _dataset.column_names(),
_dataset.column_types(), sample)
else:
raise TypeError("Input 'distance' not understood. The 'distance' "
" argument must be a string, function handle, or " +
"composite distance.")
## Basic composite distance validation, remove the row label from all
# feature lists, and convert string distance names into distance functions.
distance = _scrub_composite_distance_features(distance, [_label])
distance = _convert_distance_names_to_functions(distance)
_validate_composite_distance(distance)
## Raise an error if any distances are used with non-lists
list_features_to_check = []
sparse_distances = [
'jaccard', 'weighted_jaccard', 'cosine', 'dot_product',
'transformed_dot_product'
]
sparse_distances = [
getattr(_turicreate.distances, k) for k in sparse_distances
]
for d in distance:
feature_names, dist, _ = d
list_features = [f for f in feature_names if _dataset[f].dtype == list]
for f in list_features:
if dist in sparse_distances:
list_features_to_check.append(f)
else:
raise TypeError(
"The chosen distance cannot currently be used " +
"on list-typed columns.")
for f in list_features_to_check:
only_str_lists = _validate_lists(_dataset[f], [str])
if not only_str_lists:
raise TypeError("Distances for sparse data, such as jaccard " +
"and weighted_jaccard, can only be used on " +
"lists containing only strings. Please modify " +
"any list features accordingly before creating " +
"the nearest neighbors model.")
## Raise an error if any component has string features are in single columns
for d in distance:
feature_names, dist, _ = d
if (len(feature_names) > 1) and (dist
== _turicreate.distances.levenshtein):
raise ValueError(
"Levenshtein distance cannot be used with multiple " +
"columns. Please concatenate strings into a single " +
"column before creating the nearest neighbors model.")
## Get the union of feature names and make a clean dataset.
clean_features = _get_composite_distance_features(distance)
sf_clean = _tkutl._toolkits_select_columns(_dataset, clean_features)
## Decide which method to use
## - If more than one distance component (specified either directly or
# generated automatically because distance set to 'auto'), then do brute
# force.
if len(distance) > 1:
_method = 'brute_force'
if method != 'brute_force' and verbose is True:
print("Defaulting to brute force instead of ball tree because " +\
"there are multiple distance components.")
else:
if method == 'auto':
# get the total number of variables. Assume the number of elements in
# array type columns does not change
num_variables = sum([
len(x) if hasattr(x, '__iter__') else 1
for x in _six.itervalues(sf_clean[0])
])
# flag if all the features in the single composite are of numeric
# type.
numeric_type_flag = all([
x in [int, float, list, array.array]
for x in sf_clean.column_types()
])
## Conditions necessary for ball tree to work and be worth it
if ((distance[0][1] in [
'euclidean', 'manhattan', _turicreate.distances.euclidean,
_turicreate.distances.manhattan
]) and numeric_type_flag is True and num_variables <= 200):
_method = 'ball_tree'
else:
_method = 'brute_force'
else:
_method = method
## Pick the right model name for the method
if _method == 'ball_tree':
model_name = 'nearest_neighbors_ball_tree'
elif _method == 'brute_force':
model_name = 'nearest_neighbors_brute_force'
elif _method == 'lsh':
model_name = 'nearest_neighbors_lsh'
else:
raise ValueError(
"Method must be 'auto', 'ball_tree', 'brute_force', " +
"or 'lsh'.")
## Package the model options
opts = {}
opts.update(_method_options)
opts.update({
'model_name': model_name,
'ref_labels': ref_labels,
'label': label,
'sf_features': sf_clean,
'composite_params': distance
})
## Construct the nearest neighbors model
with QuietProgress(verbose):
result = _turicreate.extensions._nearest_neighbors.train(opts)
model_proxy = result['model']
model = NearestNeighborsModel(model_proxy)
return model
def create(dataset, num_clusters=None, features=None, label=None,
initial_centers=None, max_iterations=10, batch_size=None,
verbose=True):
"""
Create a k-means clustering model. The KmeansModel object contains the
computed cluster centers and the cluster assignment for each instance in
the input 'dataset'.
Given a number of clusters, k-means iteratively chooses the best cluster
centers and assigns nearby points to the best cluster. If no points change
cluster membership between iterations, the algorithm terminates.
Parameters
----------
dataset : SFrame
Each row in the SFrame is an observation.
num_clusters : int
Number of clusters. This is the 'k' in k-means.
features : list[str], optional
Names of feature columns to use in computing distances between
observations and cluster centers. 'None' (the default) indicates that
all columns should be used as features. Columns may be of the following
types:
- *Numeric*: values of numeric type integer or float.
- *Array*: list of numeric (int or float) values. Each list element
is treated as a distinct feature in the model.
- *Dict*: dictionary of keys mapped to numeric values. Each unique key
is treated as a distinct feature in the model.
Note that columns of type *list* are not supported. Convert them to
array columns if all entries in the list are of numeric types.
label : str, optional
Name of the column to use as row labels in the Kmeans output. The
values in this column must be integers or strings. If not specified,
row numbers are used by default.
initial_centers : SFrame, optional
Initial centers to use when starting the K-means algorithm. If
specified, this parameter overrides the *num_clusters* parameter. The
'initial_centers' SFrame must contain the same features used in the
input 'dataset'.
If not specified (the default), initial centers are chosen
intelligently with the K-means++ algorithm.
max_iterations : int, optional
The maximum number of iterations to run. Prints a warning if the
algorithm does not converge after max_iterations iterations. If set to
0, the model returns clusters defined by the initial centers and
assignments to those centers.
batch_size : int, optional
Number of randomly-chosen data points to use in each iteration. If
'None' (the default) or greater than the number of rows in 'dataset',
then this parameter is ignored: all rows of `dataset` are used in each
iteration and model training terminates once point assignments stop
changing or `max_iterations` is reached.
verbose : bool, optional
If True, print model training progress to the screen.
Returns
-------
out : KmeansModel
A Model object containing a cluster id for each vertex, and the centers
of the clusters.
See Also
--------
KmeansModel
Notes
-----
- Integer features in the 'dataset' or 'initial_centers' inputs are
converted internally to float type, and the corresponding features in the
output centers are float-typed.
- It can be important for the K-means model to standardize the features so
they have the same scale. This function does *not* standardize
automatically.
References
----------
- `Wikipedia - k-means clustering
<http://en.wikipedia.org/wiki/K-means_clustering>`_
- Artuhur, D. and Vassilvitskii, S. (2007) `k-means++: The Advantages of
Careful Seeding <http://ilpubs.stanford.edu:8090/778/1/2006-13.pdf>`_. In
Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete
Algorithms. pp. 1027-1035.
- Elkan, C. (2003) `Using the triangle inequality to accelerate k-means
<http://www.aaai.org/Papers/ICML/2003/ICML03-022.pdf>`_. In Proceedings
of the Twentieth International Conference on Machine Learning, Volume 3,
pp. 147-153.
- Sculley, D. (2010) `Web Scale K-Means Clustering
<http://www.eecs.tufts.edu/~dsculley/papers/fastkmeans.pdf>`_. In
Proceedings of the 19th International Conference on World Wide Web. pp.
1177-1178
Examples
--------
>>> sf = turicreate.SFrame({
... 'x1': [0.6777, -9.391, 7.0385, 2.2657, 7.7864, -10.16, -8.162,
... 8.8817, -9.525, -9.153, 2.0860, 7.6619, 6.5511, 2.7020],
... 'x2': [5.6110, 8.5139, 5.3913, 5.4743, 8.3606, 7.8843, 2.7305,
... 5.1679, 6.7231, 3.7051, 1.7682, 7.4608, 3.1270, 6.5624]})
...
>>> model = turicreate.kmeans.create(sf, num_clusters=3)
"""
opts = {'model_name': 'kmeans',
'max_iterations': max_iterations,
}
## Validate the input dataset and initial centers.
_validate_dataset(dataset)
if initial_centers is not None:
_validate_initial_centers(initial_centers)
## Validate and determine the correct number of clusters.
opts['num_clusters'] = _validate_num_clusters(num_clusters,
initial_centers,
dataset.num_rows())
## Validate the row label
col_type_map = {c: dataset[c].dtype for c in dataset.column_names()}
if label is not None:
_validate_row_label(label, col_type_map)
if label in ['cluster_id', 'distance']:
raise ValueError("Row label column name cannot be 'cluster_id' " +
"or 'distance'; these are reserved for other " +
"columns in the Kmeans model's output.")
opts['row_labels'] = dataset[label]
opts['row_label_name'] = label
else:
opts['row_labels'] = _tc.SArray.from_sequence(dataset.num_rows())
opts['row_label_name'] = 'row_id'
## Validate the features relative to the input dataset.
if features is None:
features = dataset.column_names()
valid_features = _validate_features(features, col_type_map,
valid_types=[_array, dict, int, float],
label=label)
sf_features = dataset.select_columns(valid_features)
opts['features'] = sf_features
## Validate the features in the initial centers (if provided)
if initial_centers is not None:
try:
initial_centers = initial_centers.select_columns(valid_features)
except:
raise ValueError("Specified features cannot be extracted from " +
"the provided initial centers.")
if initial_centers.column_types() != sf_features.column_types():
raise TypeError("Feature types are different in the dataset and " +
"initial centers.")
else:
initial_centers = _tc.SFrame()
opts['initial_centers'] = initial_centers
## Validate the batch size and determine the training method.
if batch_size is None:
opts['method'] = 'elkan'
opts['batch_size'] = dataset.num_rows()
else:
opts['method'] = 'minibatch'
opts['batch_size'] = batch_size
## Create and return the model
params = _tc.toolkits._main.run('kmeans_train', opts, verbose)
return KmeansModel(params['model'])