InformationGainSegmentation#
- class InformationGainSegmentation(k_max: int = 10, step: int = 5)[source]#
Information Gain based Temporal Segmentation (IGTS) Estimator.
IGTS is a n unsupervised method for segmenting multivariate time series into non-overlapping segments by locating change points that for which the information gain is maximized.
Information gain (IG) is defined as the amount of entropy lost by the segmentation. The aim is to find the segmentation that have the maximum information gain for a specified number of segments.
IGTS uses top-down search method to greedily find the next change point location that creates the maximum information gain. Once this is found, it repeats the process until it finds
k_max
splits of the time series.Note
IGTS does not work very well for univariate series but it can still be used if the original univariate series are augmented by an extra feature dimensions. A technique proposed in the paper [1] us to subtract the series from it’s largest element and append to the series.
- Parameters:
- k_max: int, default=10
Maximum number of change points to find. The number of segments is thus k+1.
- step:int, default=5
Step size, or stride for selecting candidate locations of change points. Fox example a
step=5
would produce candidates [0, 5, 10, …]. Has the same meaning asstep
inrange
function.
- Attributes:
- change_points_: list of int
Locations of change points as integer indexes. By convention change points include the identity segmentation, i.e. first and last index + 1 values.
- intermediate_results_: list of ``ChangePointResult``
Intermediate segmentation results for each k value, where k=1, 2, …, k_max
Notes
Based on the work from [1]. - alt. py implementation: cruiseresearchgroup/IGTS-python - MATLAB version: cruiseresearchgroup/IGTS-matlab - paper available at:
References
[1] (1,2)Sadri, Amin, Yongli Ren, and Flora D. Salim. “Information gain-based metric for recognizing transitions in human activities.”, Pervasive and Mobile Computing, 38, 92-109, (2017). https://www.sciencedirect.com/science/article/abs/pii/S1574119217300081
Examples
>>> from sktime.annotation.datagen import piecewise_normal_multivariate >>> from sklearn.preprocessing import MinMaxScaler >>> X = piecewise_normal_multivariate( ... lengths=[10, 10, 10, 10], ... means=[[0.0, 1.0], [11.0, 10.0], [5.0, 3.0], [2.0, 2.0]], ... variances=0.5, ... ) >>> X_scaled = MinMaxScaler(feature_range=(0, 1)).fit_transform(X) >>> from sktime.annotation.igts import InformationGainSegmentation >>> igts = InformationGainSegmentation(k_max=3, step=2) >>> y = igts.fit_predict(X_scaled)
Methods
check_is_fitted
([method_name])Check if the estimator has been fitted.
clone
()Obtain a clone of the object with same hyper-parameters and config.
clone_tags
(estimator[, tag_names])Clone tags from another object as dynamic override.
create_test_instance
([parameter_set])Construct an instance of the class, using first test parameter set.
create_test_instances_and_names
([parameter_set])Create list of all test instances and a list of names for them.
fit
(X[, y])Fit method for compatibility with sklearn-type estimator interface.
fit_predict
(X[, y])Perform segmentation.
get_class_tag
(tag_name[, tag_value_default])Get class tag value from class, with tag level inheritance from parents.
Get class tags from class, with tag level inheritance from parent classes.
Get config flags for self.
get_fitted_params
([deep])Get fitted parameters.
Get object's parameter defaults.
get_param_names
([sort])Get object's parameter names.
get_params
([deep])Return initialization parameters.
get_tag
(tag_name[, tag_value_default, ...])Get tag value from instance, with tag level inheritance and overrides.
get_tags
()Get tags from instance, with tag level inheritance and overrides.
get_test_params
([parameter_set])Return testing parameter settings for the estimator.
Check if the object is composed of other BaseObjects.
load_from_path
(serial)Load object from file location.
load_from_serial
(serial)Load object from serialized memory container.
predict
(X[, y])Perform segmentation.
reset
()Reset the object to a clean post-init state.
save
([path, serialization_format])Save serialized self to bytes-like object or to (.zip) file.
set_config
(**config_dict)Set config flags to given values.
set_params
(**parameters)Set the parameters of this object.
set_random_state
([random_state, deep, ...])Set random_state pseudo-random seed parameters for self.
set_tags
(**tag_dict)Set instance level tag overrides to given values.
to_classification
(change_points)Convert change point locations to a classification vector.
to_clusters
(change_points)Convert change point locations to a clustering vector.
- fit(X: Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], y: Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] = None)[source]#
Fit method for compatibility with sklearn-type estimator interface.
It sets the internal state of the estimator and returns the initialized instance.
- Parameters:
- X: array_like
2D
array_like
representing time series with sequence index along the first dimension and value series as columns.- y: array_like
Placeholder for compatibility with sklearn-api, not used, default=None.
- predict(X: Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], y: Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] = None) Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] [source]#
Perform segmentation.
- Parameters:
- X: array_like
2D
array_like
representing time series with sequence index along the first dimension and value series as columns.- y: array_like
Placeholder for compatibility with sklearn-api, not used, default=None.
- Returns:
- y_predarray_like
1D array with predicted segmentation of the same size as the first dimension of X. The numerical values represent distinct segments labels for each of the data points.
- fit_predict(X: Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], y: Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] = None) Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] [source]#
Perform segmentation.
A convenience method for compatibility with sklearn-like api.
- Parameters:
- X: array_like
2D
array_like
representing time series with sequence index along the first dimension and value series as columns.- y: array_like
Placeholder for compatibility with sklearn-api, not used, default=None.
- Returns:
- y_predarray_like
1D array with predicted segmentation of the same size as the first dimension of X. The numerical values represent distinct segments labels for each of the data points.
- get_params(deep: bool = True) dict [source]#
Return initialization parameters.
- Parameters:
- deep: bool
Dummy argument for compatibility with sklearn-api, not used.
- Returns:
- params: dict
Dictionary with the estimator’s initialization parameters, with keys being argument names and values being argument values.
- set_params(**parameters)[source]#
Set the parameters of this object.
- Parameters:
- parametersdict
Initialization parameters for th estimator.
- Returns:
- selfreference to self (after parameters have been set)
- classmethod get_test_params(parameter_set='default')[source]#
Return testing parameter settings for the estimator.
- Parameters:
- parameter_setstr, default=”default”
Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return
"default"
set.
- Returns:
- paramsdict or list of dict
- check_is_fitted(method_name=None)[source]#
Check if the estimator has been fitted.
Check if
_is_fitted
attribute is present andTrue
. Theis_fitted
attribute should be set toTrue
in calls to an object’sfit
method.If not, raises a
NotFittedError
.- Parameters:
- method_namestr, optional
Name of the method that called this function. If provided, the error message will include this information.
- Raises:
- NotFittedError
If the estimator has not been fitted yet.
- clone()[source]#
Obtain a clone of the object with same hyper-parameters and config.
A clone is a different object without shared references, in post-init state. This function is equivalent to returning
sklearn.clone
ofself
.Equivalent to constructing a new instance of
type(self)
, with parameters ofself
, that is,type(self)(**self.get_params(deep=False))
.If configs were set on
self
, the clone will also have the same configs as the original, equivalent to callingcloned_self.set_config(**self.get_config())
.Also equivalent in value to a call of
self.reset
, with the exception thatclone
returns a new object, instead of mutatingself
likereset
.- Raises:
- RuntimeError if the clone is non-conforming, due to faulty
__init__
.
- RuntimeError if the clone is non-conforming, due to faulty
- clone_tags(estimator, tag_names=None)[source]#
Clone tags from another object as dynamic override.
Every
scikit-base
compatible object has a dictionary of tags. Tags may be used to store metadata about the object, or to control behaviour of the object.Tags are key-value pairs specific to an instance
self
, they are static flags that are not changed after construction of the object.clone_tags
sets dynamic tag overrides from another object,estimator
.The
clone_tags
method should be called only in the__init__
method of an object, during construction, or directly after construction via__init__
.The dynamic tags are set to the values of the tags in
estimator
, with the names specified intag_names
.The default of
tag_names
writes all tags fromestimator
toself
.Current tag values can be inspected by
get_tags
orget_tag
.- Parameters:
- estimatorAn instance of :class:BaseObject or derived class
- tag_namesstr or list of str, default = None
Names of tags to clone. The default (
None
) clones all tags fromestimator
.
- Returns:
- self
Reference to
self
.
- classmethod create_test_instance(parameter_set='default')[source]#
Construct an instance of the class, using first test parameter set.
- Parameters:
- parameter_setstr, default=”default”
Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.
- Returns:
- instanceinstance of the class with default parameters
- classmethod create_test_instances_and_names(parameter_set='default')[source]#
Create list of all test instances and a list of names for them.
- Parameters:
- parameter_setstr, default=”default”
Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.
- Returns:
- objslist of instances of cls
i-th instance is
cls(**cls.get_test_params()[i])
- nameslist of str, same length as objs
i-th element is name of i-th instance of obj in tests. The naming convention is
{cls.__name__}-{i}
if more than one instance, otherwise{cls.__name__}
- classmethod get_class_tag(tag_name, tag_value_default=None)[source]#
Get class tag value from class, with tag level inheritance from parents.
Every
scikit-base
compatible object has a dictionary of tags. Tags may be used to store metadata about the object, or to control behaviour of the object.Tags are key-value pairs specific to an instance
self
, they are static flags that are not changed after construction of the object.The
get_class_tag
method is a class method, and retrieves the value of a tag taking into account only class-level tag values and overrides.It returns the value of the tag with name
tag_name
from the object, taking into account tag overrides, in the following order of descending priority:Tags set in the
_tags
attribute of the class.Tags set in the
_tags
attribute of parent classes,
in order of inheritance.
Does not take into account dynamic tag overrides on instances, set via
set_tags
orclone_tags
, that are defined on instances.To retrieve tag values with potential instance overrides, use the
get_tag
method instead.- Parameters:
- tag_namestr
Name of tag value.
- tag_value_defaultany type
Default/fallback value if tag is not found.
- Returns:
- tag_value
Value of the
tag_name
tag inself
. If not found, returnstag_value_default
.
- classmethod get_class_tags()[source]#
Get class tags from class, with tag level inheritance from parent classes.
Every
scikit-base
compatible object has a dictionary of tags. Tags may be used to store metadata about the object, or to control behaviour of the object.Tags are key-value pairs specific to an instance
self
, they are static flags that are not changed after construction of the object.The
get_class_tags
method is a class method, and retrieves the value of a tag taking into account only class-level tag values and overrides.It returns a dictionary with keys being keys of any attribute of
_tags
set in the class or any of its parent classes.Values are the corresponding tag values, with overrides in the following order of descending priority:
Tags set in the
_tags
attribute of the class.Tags set in the
_tags
attribute of parent classes,
in order of inheritance.
Instances can override these tags depending on hyper-parameters.
To retrieve tags with potential instance overrides, use the
get_tags
method instead.Does not take into account dynamic tag overrides on instances, set via
set_tags
orclone_tags
, that are defined on instances.For including overrides from dynamic tags, use
get_tags
.- Returns:
- collected_tagsdict
Dictionary of tag name : tag value pairs. Collected from
_tags
class attribute via nested inheritance. NOT overridden by dynamic tags set byset_tags
orclone_tags
.
- get_config()[source]#
Get config flags for self.
Configs are key-value pairs of
self
, typically used as transient flags for controlling behaviour.get_config
returns dynamic configs, which override the default configs.Default configs are set in the class attribute
_config
of the class or its parent classes, and are overridden by dynamic configs set viaset_config
.Configs are retained under
clone
orreset
calls.- Returns:
- config_dictdict
Dictionary of config name : config value pairs. Collected from _config class attribute via nested inheritance and then any overrides and new tags from _onfig_dynamic object attribute.
- get_fitted_params(deep=True)[source]#
Get fitted parameters.
- State required:
Requires state to be “fitted”.
- Parameters:
- deepbool, default=True
Whether to return fitted parameters of components.
If True, will return a dict of parameter name : value for this object, including fitted parameters of fittable components (= BaseEstimator-valued parameters).
If False, will return a dict of parameter name : value for this object, but not include fitted parameters of components.
- Returns:
- fitted_paramsdict with str-valued keys
Dictionary of fitted parameters, paramname : paramvalue keys-value pairs include:
always: all fitted parameters of this object, as via
get_param_names
values are fitted parameter value for that key, of this objectif
deep=True
, also contains keys/value pairs of component parameters parameters of components are indexed as[componentname]__[paramname]
all parameters ofcomponentname
appear asparamname
with its valueif
deep=True
, also contains arbitrary levels of component recursion, e.g.,[componentname]__[componentcomponentname]__[paramname]
, etc
- classmethod get_param_defaults()[source]#
Get object’s parameter defaults.
- Returns:
- default_dict: dict[str, Any]
Keys are all parameters of
cls
that have a default defined in__init__
. Values are the defaults, as defined in__init__
.
- classmethod get_param_names(sort=True)[source]#
Get object’s parameter names.
- Parameters:
- sortbool, default=True
Whether to return the parameter names sorted in alphabetical order (True), or in the order they appear in the class
__init__
(False).
- Returns:
- param_names: list[str]
List of parameter names of
cls
. Ifsort=False
, in same order as they appear in the class__init__
. Ifsort=True
, alphabetically ordered.
- get_tag(tag_name, tag_value_default=None, raise_error=True)[source]#
Get tag value from instance, with tag level inheritance and overrides.
Every
scikit-base
compatible object has a dictionary of tags. Tags may be used to store metadata about the object, or to control behaviour of the object.Tags are key-value pairs specific to an instance
self
, they are static flags that are not changed after construction of the object.The
get_tag
method retrieves the value of a single tag with nametag_name
from the instance, taking into account tag overrides, in the following order of descending priority:Tags set via
set_tags
orclone_tags
on the instance,
at construction of the instance.
Tags set in the
_tags
attribute of the class.Tags set in the
_tags
attribute of parent classes,
in order of inheritance.
- Parameters:
- tag_namestr
Name of tag to be retrieved
- tag_value_defaultany type, optional; default=None
Default/fallback value if tag is not found
- raise_errorbool
whether a
ValueError
is raised when the tag is not found
- Returns:
- tag_valueAny
Value of the
tag_name
tag inself
. If not found, raises an error ifraise_error
is True, otherwise it returnstag_value_default
.
- Raises:
- ValueError, if
raise_error
isTrue
. The
ValueError
is then raised iftag_name
is not inself.get_tags().keys()
.
- ValueError, if
- get_tags()[source]#
Get tags from instance, with tag level inheritance and overrides.
Every
scikit-base
compatible object has a dictionary of tags. Tags may be used to store metadata about the object, or to control behaviour of the object.Tags are key-value pairs specific to an instance
self
, they are static flags that are not changed after construction of the object.The
get_tags
method returns a dictionary of tags, with keys being keys of any attribute of_tags
set in the class or any of its parent classes, or tags set viaset_tags
orclone_tags
.Values are the corresponding tag values, with overrides in the following order of descending priority:
Tags set via
set_tags
orclone_tags
on the instance,
at construction of the instance.
Tags set in the
_tags
attribute of the class.Tags set in the
_tags
attribute of parent classes,
in order of inheritance.
- Returns:
- collected_tagsdict
Dictionary of tag name : tag value pairs. Collected from
_tags
class attribute via nested inheritance and then any overrides and new tags from_tags_dynamic
object attribute.
- is_composite()[source]#
Check if the object is composed of other BaseObjects.
A composite object is an object which contains objects, as parameters. Called on an instance, since this may differ by instance.
- Returns:
- composite: bool
Whether an object has any parameters whose values are
BaseObject
descendant instances.
- property is_fitted[source]#
Whether
fit
has been called.Inspects object’s
_is_fitted` attribute that should initialize to ``False
during object construction, and be set to True in calls to an object’s fit method.- Returns:
- bool
Whether the estimator has been fit.
- classmethod load_from_path(serial)[source]#
Load object from file location.
- Parameters:
- serialresult of ZipFile(path).open(“object)
- Returns:
- deserialized self resulting in output at
path
, ofcls.save(path)
- deserialized self resulting in output at
- classmethod load_from_serial(serial)[source]#
Load object from serialized memory container.
- Parameters:
- serial1st element of output of
cls.save(None)
- serial1st element of output of
- Returns:
- deserialized self resulting in output
serial
, ofcls.save(None)
- deserialized self resulting in output
- reset()[source]#
Reset the object to a clean post-init state.
Results in setting
self
to the state it had directly after the constructor call, with the same hyper-parameters. Config values set byset_config
are also retained.A
reset
call deletes any object attributes, except:hyper-parameters = arguments of
__init__
written toself
, e.g.,self.paramname
whereparamname
is an argument of__init__
object attributes containing double-underscores, i.e., the string “__”. For instance, an attribute named “__myattr” is retained.
config attributes, configs are retained without change. That is, results of
get_config
before and afterreset
are equal.
Class and object methods, and class attributes are also unaffected.
Equivalent to
clone
, with the exception thatreset
mutatesself
instead of returning a new object.After a
self.reset()
call,self
is equal in value and state, to the object obtained after a constructor call``type(self)(**self.get_params(deep=False))``.- Returns:
- self
Instance of class reset to a clean post-init state but retaining the current hyper-parameter values.
- save(path=None, serialization_format='pickle')[source]#
Save serialized self to bytes-like object or to (.zip) file.
Behaviour: if
path
is None, returns an in-memory serialized self ifpath
is a file location, stores self at that location as a zip filesaved files are zip files with following contents: _metadata - contains class of self, i.e., type(self) _obj - serialized self. This class uses the default serialization (pickle).
- Parameters:
- pathNone or file location (str or Path)
if None, self is saved to an in-memory object if file location, self is saved to that file location. If:
path=”estimator” then a zip file
estimator.zip
will be made at cwd. path=”/home/stored/estimator” then a zip fileestimator.zip
will be stored in/home/stored/
.- serialization_format: str, default = “pickle”
Module to use for serialization. The available options are “pickle” and “cloudpickle”. Note that non-default formats might require installation of other soft dependencies.
- Returns:
- if
path
is None - in-memory serialized self - if
path
is file location - ZipFile with reference to the file
- if
- set_config(**config_dict)[source]#
Set config flags to given values.
- Parameters:
- config_dictdict
Dictionary of config name : config value pairs. Valid configs, values, and their meaning is listed below:
- displaystr, “diagram” (default), or “text”
how jupyter kernels display instances of self
“diagram” = html box diagram representation
“text” = string printout
- print_changed_onlybool, default=True
whether printing of self lists only self-parameters that differ from defaults (False), or all parameter names and values (False). Does not nest, i.e., only affects self and not component estimators.
- warningsstr, “on” (default), or “off”
whether to raise warnings, affects warnings from sktime only
“on” = will raise warnings from sktime
“off” = will not raise warnings from sktime
- backend:parallelstr, optional, default=”None”
backend to use for parallelization when broadcasting/vectorizing, one of
“None”: executes loop sequentally, simple list comprehension
“loky”, “multiprocessing” and “threading”: uses
joblib.Parallel
“joblib”: custom and 3rd party
joblib
backends, e.g.,spark
“dask”: uses
dask
, requiresdask
package in environment
- backend:parallel:paramsdict, optional, default={} (no parameters passed)
additional parameters passed to the parallelization backend as config. Valid keys depend on the value of
backend:parallel
:“None”: no additional parameters,
backend_params
is ignored“loky”, “multiprocessing” and “threading”: default
joblib
backends any valid keys forjoblib.Parallel
can be passed here, e.g.,n_jobs
, with the exception ofbackend
which is directly controlled bybackend
. Ifn_jobs
is not passed, it will default to-1
, other parameters will default tojoblib
defaults.“joblib”: custom and 3rd party
joblib
backends, e.g.,spark
. Any valid keys forjoblib.Parallel
can be passed here, e.g.,n_jobs
,backend
must be passed as a key ofbackend_params
in this case. Ifn_jobs
is not passed, it will default to-1
, other parameters will default tojoblib
defaults.“dask”: any valid keys for
dask.compute
can be passed, e.g.,scheduler
- Returns:
- selfreference to self.
Notes
Changes object state, copies configs in config_dict to self._config_dynamic.
- set_random_state(random_state=None, deep=True, self_policy='copy')[source]#
Set random_state pseudo-random seed parameters for self.
Finds
random_state
named parameters viaself.get_params
, and sets them to integers derived fromrandom_state
viaset_params
. These integers are sampled from chain hashing viasample_dependent_seed
, and guarantee pseudo-random independence of seeded random generators.Applies to
random_state
parameters inself
, depending onself_policy
, and remaining component objects if and only ifdeep=True
.Note: calls
set_params
even ifself
does not have arandom_state
, or none of the components have arandom_state
parameter. Therefore,set_random_state
will reset anyscikit-base
object, even those without arandom_state
parameter.- Parameters:
- random_stateint, RandomState instance or None, default=None
Pseudo-random number generator to control the generation of the random integers. Pass int for reproducible output across multiple function calls.
- deepbool, default=True
Whether to set the random state in skbase object valued parameters, i.e., component estimators.
If False, will set only
self
’srandom_state
parameter, if exists.If True, will set
random_state
parameters in component objects as well.
- self_policystr, one of {“copy”, “keep”, “new”}, default=”copy”
“copy” :
self.random_state
is set to inputrandom_state
“keep” :
self.random_state
is kept as is“new” :
self.random_state
is set to a new random state,
derived from input
random_state
, and in general different from it
- Returns:
- selfreference to self
- set_tags(**tag_dict)[source]#
Set instance level tag overrides to given values.
Every
scikit-base
compatible object has a dictionary of tags. Tags may be used to store metadata about the object, or to control behaviour of the object.Tags are key-value pairs specific to an instance
self
, they are static flags that are not changed after construction of the object.set_tags
sets dynamic tag overrides to the values as specified intag_dict
, with keys being the tag name, and dict values being the value to set the tag to.The
set_tags
method should be called only in the__init__
method of an object, during construction, or directly after construction via__init__
.Current tag values can be inspected by
get_tags
orget_tag
.- Parameters:
- **tag_dictdict
Dictionary of tag name: tag value pairs.
- Returns:
- Self
Reference to self.
- to_classification(change_points: list[int]) Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] [source]#
Convert change point locations to a classification vector.
Change point detection results can be treated as classification with true change point locations marked with 1’s at position of the change point and remaining non-change point locations being 0’s.
For example change points [2, 8] for a time series of length 10 would result in: [0, 0, 1, 0, 0, 0, 0, 0, 1, 0].
- to_clusters(change_points: list[int]) Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes] [source]#
Convert change point locations to a clustering vector.
Change point detection results can be treated as clustering with each segment separated by change points assigned a distinct dummy label.
For example change points [2, 8] for a time series of length 10 would result in: [0, 0, 1, 1, 1, 1, 1, 1, 2, 2].