Welcome to py-iCFOF’s documentation!

Cette documentation présente le fonctionnement des classes Python pour l’approximation des scores CFOF à l’aide d’un ou plusieurs arbres d’indexation iSAX.

CFOF using iSAX trees

class pyCFOFiSAX._cfofisax.CFOFiSAX

The class for iCFOF approximation using iSAX index trees. Contains the iSAX tree forest.

init_forest_isax(size_word: int, threshold: int, data_ts: numpy.ndarray, base_cardinality: int = 2, number_tree: int = 1, indices_partition: Optional[list] = None, max_card_alphabet: int = 128, boolean_card_max: bool = True)

Initializes the forest of iSAX trees. Requires the parameters of the class ForestISAX.

Paramètres

• size_word (int) – The size of the SAX words

• threshold (int) – The threshold, maximal size of nodes

• data_ts (numpy.ndarray) – The sequences to be inserted, to compute the stats of dataset

• base_cardinality (int) – The smallest cardinality to encode iSAX

• number_tree (int) – The number of iSAX trees in the forest

• indices_partition (list) – A list of indices list where, for each tree, specifies the indices of the sequences to be inserted

• max_card_alphabet (int) – if boolean_card_max == True, the maximum cardinality of iSAX encoding in each tree

• boolean_card_max (bool) – if == True, defines maximum cardinality for iSAX sequences encoding in each of the trees

score_icfof(query: numpy.array, ntss: numpy.ndarray, rho=[0.001, 0.005, 0.01, 0.05, 0.1], each_tree_score: bool = False, fast_method: bool = True)

Compute the iCFOF approximations. Call one of the two functions according to the parameter fast_method :

• if True (default) : vranglist_by_idtree_faster()

• if False : vranglist_by_idtree()

Then sort the vrang list to get CFOF scores approximations based on rho parameter values.

Paramètres

• query (numpy.array) – The sequence to be evaluated

• ntss (numpy.ndarray) – Reference sequences

• rho (list) – Rho values for the computation of approximations

• each_tree_score (bool) – if True, returns the scores obtained in each of the trees

• fast_method (bool) – if True, uses the numpy functions for computation, otherwise goes through the tree via a FIFO list of nodes

Renvoie

iCFOF score approximations

Type renvoyé

numpy.ndarray

Forest iSAX

class pyCFOFiSAX._forest_iSAX.ForestISAX(size_word: int, threshold: int, data_ts: numpy.ndarray, base_cardinality: int = 2, number_tree: int = 1, indices_partition: Optional[list] = None, max_card_alphabet: int = 128, boolean_card_max: bool = True)

ForestISAX class containing one or more trees and pretreatment functions on the data contained in these trees

Paramètres

• size_word (int) – The size of the SAX words

• threshold (int) – The maximum threshold of nodes

• data_ts (numpy.ndarray) – The sequences to be inserted to extract the stats

• base_cardinality (int) – The smallest cardinality for encoding iSAX

• number_tree (int) – The number of TreeISAX trees in the forest

• indices_partition (list) – a list of index list where, for each tree, specifies the indices of

sequences to be inserted :param int max_card_alphabet: if boolean_card_max == True, the maximum cardinality of encoding iSAX in each of the trees :param boolean boolean_card_max: if == True, Defines a maximum cardinality for encoding iSAX Sequences in each of the trees

Variables

length_partition (list) – The length of the SAX words in each tree (== [size_word] if ``number_tree

== 1``)

_count_nodes(id_tree: int)

The _count_nodes function returns the number of nodes and leaf nodes for a given tree. Uses count_nodes_by_tree().

Paramètres

id_tree (int) – The tree ID to be analyzed

Renvoie

the number of internal nodes, the number of leaf nodes

Type renvoyé

int, int

_init_trees(data_ts: numpy.ndarray, max_card_alphabet: int, boolean_card_max: bool)

Function that initializes the tree (s) when creating a ForestISAX object

Paramètres

• data_ts (numpy.ndarray) – The sequences to be inserted to extract the stats

• max_card_alphabet (int) – if boolean_card_max == True, The maximum cardinality of encoding iSAX

dans chacun des arbres :param boolean boolean_card_max: if boolean_card_max == True, defines maximum cardinality for encoding iSAX sequences in each tree

index_data(new_sequences: numpy.ndarray)

The Index_Data function allows you to insert a large number of sequences

Paramètres

new_sequences (numpy.ndarray) – The sequences to be inserted

Renvoie

The number of sequences (sub sequences) insert into the tree (in the trees)

Type renvoyé

numpy.array

list_nodes(id_tree: int, bool_print: bool = False)

Returns lists of nodes and barycenters of the tree id_tree.Displays statistics on standard output if bool_print == True Uses get_list_nodes_and_barycentre().

Paramètres

• id_tree (int) – The tree ID to be analyzed

• bool_print (boolean) – Displays the nodes stats on the standard output

Renvoie

The list of nodes, the list of internal nodes, the list of barycenters

Type renvoyé

list, list, list

number_nodes_visited(query: numpy.array, ntss: numpy.ndarray)

Count the number of average visited nodes in each tree for calculating the approximation.

Paramètres

• query (numpy.array) – The sequence to be evaluated

• ntss (numpy.ndarray) – Reference sequences

Renvoie

Returns the number of nodes visited in each tree for the approximation iCFOF

Type renvoyé

numpy.array

preprocessing_forest_for_icfof(ntss: numpy.ndarray, bool_print: bool = False, count_num_node: bool = False)

Allows us to call, for the id_tree to the pre-treatment for the calculation iCFOF

Paramètres

• ntss – Reference sequences

• bool_print (boolean) – if True, displays the times of each pre-treatment step

• count_num_node (boolean) – if True, count the number of nodes

Renvoie

if count_num_node, returns the number of nodes contained in each tree

Type renvoyé

numpy.array

Tree iSAX

class pyCFOFiSAX._tree_iSAX.TreeISAX(size_word, threshold, data_ts, base_cardinality=2, max_card_alphabet=128, boolean_card_max=True)

La classe TreeISAX contenant

• ISAX distribution of sequences to index

• and towards the first root node

Avertissement

In this version, the data_ts are mandatory to define in advance the future breakpoints

Paramètres

• size_word (int) – The number of Sax discretization for each sequence

• threshold (int) – The maximum capacity of the nodes of the tree

• data_ts (numpy.ndarray) – Sequence array to be inserted

• base_cardinality (int) – The smallest cardinality for encoding iSAX

• max_card_alphabet (int) – if self.boolean_card_max == True, Max cardinality for encoding iSAX

Variables

• size_word (int) – Number of letters contained in the SAX words indexed in the tree

• threshold (int) – Threshold before the separation of a sheet into two leaf nodes

_minmax_nodes()

Returns the breakpoints of the nodes of the tree. Uses _do_bkpt().

Renvoie

The min and max breakpoints of the nodes of the tree

Type renvoyé

numpy.ndarray

_minmax_obj_vs_node(ntss_tmp, bool_print: bool = False)

Compute distance min and max between the sequences ntss_tmp and the nodes of the tree.

Paramètres

• ntss_tmp (numpy.ndarray) – Reference sequences

• bool_print (boolean) – if True, Displays the times of each preprocessing step

Renvoie

Minimum distances between sequences and nodes, Maximum distances between sequences and nodes

Type renvoyé

numpy.ndarray, numpy.ndarray

_minmax_obj_vs_nodeleaf()

Computes the min and max distances between the ntss_tmp sequences and the leaf nodes of the tree.

Avertissement

Attention must be executed after _minmax_obj_vs_node() and distrib_nn_for_cdf().

count_nodes_by_tree()

The COUNT_NODES_BY_TREE function returns the number of nodes and leaf nodes of the shaft. Uses get_number_internal_and_terminal().

Renvoie

the number of internal nodes, the number of leaves nodes

Type renvoyé

int, int

distrib_nn_for_cdf(ntss_tmp, bool_print: bool = False)

Calculates the two indicators, average and standard deviation of the distances, necessary for the use of the CDF of the normal distribution. The computation of these indicators are described in Scoring Message Stream Anomalies in Railway Communication Systems, L.Foulon et al., 2019, ICDMWorkshop.

Paramètres

• ntss_tmp (numpy.ndarray) – Reference sequences

• bool_print (boolean) – and True, Displays the nodes stats on the standard output

Renvoie

Type renvoyé

list(numpy.ndarray, numpy.array)

get_level_max()

Function to return the max level considering root level = 0

Renvoie

The max depth level

Type renvoyé

int

get_list_nodes_and_barycentre()

Returns Lists of Nodes and centroids

Renvoie

List of nodes, List of Leaf Nodes, List of Leaf centroids

Type renvoyé

list, list, list

get_list_nodes_leaf()

Returns List of Leaves Nodes

Renvoie

List of leaves nodes

Type renvoyé

list

get_nodes_of_level(level: int)

Function to return the nodes of a level, considering root level = 0

Paramètres

level (int) – The level of the tree to evaluate

Renvoie

The nodes of the ith level of the three

Type renvoyé

list

get_number_internal_and_terminal()

Function to return the number of leaf nodes and internal nodes

Renvoie

the number of internal nodes, the number of leaves nodes

Type renvoyé

int, int

get_size()

Function to return the memory size of the tree, nodes and sequences contained in the tree

Renvoie

Total memory size, nodes” memory size, memory size of the sequences

Type renvoyé

int, int, int

get_size_and_width_and_number_types_nodes()

Feature grouping:

• get_size()

• get_width_of_all_level()

• get_number_internal_and_terminal()

Renvoie

Total memory size, memory size of nodes, memory size of the sequences, the number of nodes on each level, the number of internal nodes, the number of sheet nodes, and the number of sequence inserted in the tree

Type renvoyé

int, int, int, list, int, int, int

get_width_of_all_level()

Function to return the width of all levels in a list, considering root level = 0

Renvoie

The number of node on each level of the tree

Type renvoyé

list

get_width_of_level(level: int)

Return the width of a level, considering root level = 0

Renvoie

the number of node on the level of the tree

Type renvoyé

int

insert(new_sequence)

This insert function convert new sequence in PAA values then call the function insert_paa

Paramètres

new_sequence (numpy.array) – The new sequence to be inserted

insert_paa(new_paa)

The insert function that directly calls the function of its root node

Paramètres

new_paa (numpy.array) – The new sequence to be inserted

number_nodes_visited(sub_query: numpy.array, ntss_tmp: numpy.ndarray)

Account the number of average visited nodes in the tree for calculating the approximation.

Paramètres

• sub_query (numpy.array) – The sequence to be evaluated

• ntss_tmp (numpy.ndarray) – Reference sequences

Renvoie

Returns the number of nodes visited in the tree for the approximation iCFOF

Type renvoyé

numpy.array

preprocessing_for_icfof(ntss_tmp, bool_print: bool = False, count_num_node: bool = False)

Allows us to appeal, for the id_tree tree, to the two methods of preprocessing:

• _minmax_obj_vs_node(),

• distrib_nn_for_cdf().

Paramètres

• ntss_tmp – Reference sequences

• bool_print (boolean) – if True, Displays the times of each preprocessing step

• count_num_node (boolean) – if True, count the number of nodes

Renvoie

if count_num_node True, Returns the number of nodes in the tree

Rtypes

int

vrang_list(sub_query: numpy.array, ntss_tmp: numpy.ndarray)

Get the vrang list for the sub_query sequence in the tree. Necessary for the calculation of the approximation. The same method faster but without the tree course: vrang_list_faster().

Paramètres

• sub_query – The sequence to be evaluated

• ntss_tmp – Reference sequences (IE. Reference history)

Renvoie

The vrang list of``sub_query``

Type renvoyé

list(float)

vrang_list_faster(sub_query: numpy.array, ntss_tmp: numpy.ndarray)

Get the vrang list for the sub_query sequence in the tree. Necessary for the calculation of the approximation. This method is the fast version of the method vrang_list().

Note

This method does not travel the tree, but directly prunes the leaves nodes. Preserved (uncut) leaves will be used by the approximation function.

Paramètres

• sub_query – The sequence to be evaluated

• ntss_tmp – Reference sequences (IE. Reference history) in PAA format

Renvoie

The vrang list of``sub_query``

Type renvoyé

list(float)

Fonctions Numba pour Tree iSAX

Pour l’obtention du vrang

pyCFOFiSAX._tree_iSAX.vrang_seq_ref(distance, max_array, min_array, cdf_mean, cdf_std, num_ts_by_node, index_cdf_bin, cdf_bins)

Calculates the vrang from the distance between the sequence to be evaluated and the reference sequence.

Paramètres

• distance (float) – The distance between the two sequences

• max_array (np_array) – Max distances between the nodes of the tree and the reference sequence

• min_array (np_array) – MIN distances between the nodes of the tree and the reference sequence

• cdf_mean (np_array) – The average distances between the nodes of the tree and the reference sequence

• cdf_std (np_array) – Dispersion of distances in each leaf node

• num_ts_by_node (np_array) – The number of sequence in each node sheet

• index_cdf_bin (np_array) – index of the cdf_bins CDF

• cdf_bins (np_array) – Normal distribution cdf values centered at the origin and standard deviation

Renvoie

le vrang

Type renvoyé

int

pyCFOFiSAX._tree_iSAX.vrang_list_for_all_seq_ref(len_seq_list, distance, max_array, min_array, cdf_mean, cdf_std, num_ts_by_node, index_cdf_bin, cdf_bins)

Uses the function vrang_seq_ref() For each reference sequence.

Paramètres

• len_seq_list (float) – The number of reference sequence

• distance (np_array) – The distance between the two sequences

• max_array (np_ndarray) – Max distances between the nodes of the tree and the reference sequence

• min_array (np_ndarray) – MIN distances between the nodes of the tree and the reference sequence

• cdf_mean (np_ndarray) – The average distances between the nodes of the tree and the reference sequence

• cdf_std (np_array) – Dispersion of distances in each leaf node

• num_ts_by_node (np_array) – The number of sequence in each node sheet

• index_cdf_bin (np_array) – The index of the CDF cdf_bins

• cdf_bins (np_array) – Normal distribution cdf values centered at the origin and standard deviation

Renvoie

la liste des vrang

Type renvoyé

np_array

Pour compter les nœuds visités

pyCFOFiSAX._tree_iSAX.nodes_visited_for_seq_ref(distance, max_array, min_array, list_parent_node)

pyCFOFiSAX._tree_iSAX.nodes_visited_for_all_seq_ref(len_seq_list, distance, max_array, min_array, list_parent_node)

Node iSAX

Nœud Racine

class pyCFOFiSAX._node.RootNode(tree, parent, sax, cardinality)

The RootNode class creates the only node of the ancestor tree common to all other nodes

Paramètres

• tree (tree_iSAX) – the tree in which the node is contained

• parent (Node) – The parent parent node

• sax (numpy.array) – SAX values of the node

• cardinality (numpy.array) – Cardinality of SAX values

_do_bkpt()

The _do_bkpt function calculates the min and max terminals of the node on each dimension of the node.

Renvoie

an array containing the min terminals and one containing the max terminals

Type renvoyé

numpy.array, numpy.array

get_nb_sequences() → int

Returns the number of sequences contained in the node and its descendants

Renvoie

The number of sequences of the subtree

Type renvoyé

int

get_sequences()

Returns the sequences contained in the node (leaf only) or its descendants

Renvoie

Sequences

Type renvoyé

numpy.ndarray

id_global = 0

Attribute to define an ID for each node

insert_paa(new_paa)

The insert_paa(new_paa) function to insert a new converted sequence into PAA

Paramètres

new_paa – The converted sequence in PAA to insert

nb_sequences

The incremental computing part for CFOF

Nœud Interne

class pyCFOFiSAX._node.InternalNode(tree, parent, sax, cardinality, sequences)

The InternalNode class creates the internal nodes having at least one direct descendant, and a single direct ascendant

Paramètres

• tree (tree_iSAX) – the tree in which the node is contained

• parent (Node) – The parent parent node

• sax (list) – SAX values of the node

• cardinality (numpy.array) – Cardinality of Sax Values

• sequences (numpy.ndarray) – The sequences to be inserted in this node

split(next_cardinality, mean, stdev)

Calcule the next cardinality and split in two

Paramètres

• next_cardinality (numpy.array) – The list of next cardinalities

• mean (numpy.array) – The list of averages of distribution of sequence values on each dimension

• stdev (numpy.array) – The list of different types of distribution of sequence values on each dimension

Nœud Feuille

class pyCFOFiSAX._node.TerminalNode(tree, parent, sax, cardinality)

The TerminalNode class creates the leaves nodes having no descendant, and a single direct ascendant

Paramètres

• tree (tree_iSAX) – the tree in which the node is contained

• parent (Node) – The parent parent node

• sax (list) – SAX values of the node

• cardinality (numpy.array) – Cardinality of Sax Values

get_sequences()

Returns the sequences contained in the node

Renvoie

The sequences contained in the node

Type renvoyé

list

insert_paa(ts_paa)

Function that inserts a new sequence in PAA format

Paramètres

ts_paa – The new Paa sequence

iSAX

class pyCFOFiSAX._isax.IndexableSymbolicAggregateApproximation(n_segments, alphabet_size_min=2, mean=0.0, std=1.0)

Indexable Symbolic Aggregate approXimation (iSAX) transformation.

First presented by J. Shieh & E. Keogh in iSAX: Indexing and Mining Terabyte Sized Time Series. Class that inherits the class PiecewiseAggregateApproximation proposed by Romain Tavenard in ``tslearn`` Available here <https://tslearn.readthedocs.io/en/stable/>`_.

Paramètres

• n_segments (int) – The number of letters in the word sax

• alphabet_size_min (int) – The minimum size of the Sax alphabet at initialization (2 default)

• mean (float) – The average of the distribution of encoder sequences (0.0 default)

• std (float) – The standard deviation of the distribution of encoder sequences (0.0 default)

_card_to_bkpt(max_cardinality)

Returns the breakpoints associated with the cardinations <= max_cardinality. The function calculates and stores the BKPT if they have never been calculated.

Paramètres

max_cardinality (int) – Maximum cardinality

Renvoie

Breakpoints associated with cardinality <= max_cardinality

Type renvoyé

dict

_card_to_bkpt_only(max_cardinality)

Returns the breakpoints associated with cardinality == max_cardinality. The function calculates and stores the BKPs if they have never been calculated.

Paramètres

max_cardinality (int) – cardinality

Renvoie

Breakpoints associated with cardinality == max_cardinality

Type renvoyé

list

_row_sax_word_array(ntss_tmp, bigger_cardinality, size_word)

Convert all sequences according to the different cardinality of the tree. For each cardinality, uses transform_sax().

Paramètres

• ntss_tmp – The sequences to be analyzed

• bigger_cardinality (int) – The greatest cardinality iSAX of the tree

• size_word (int) – The size of the SAX sequences of the tree

Renvoie

SAX words from all ntss_tmp sequences according to all the cardinalities of the tree, a dict returning the cardinality index iSAX

Type renvoyé

numpy.ndarray, dict

_transform(X, card)

Transforms X data in parameter first into PAA and then in cardinate cardinality card.

Paramètres

• X (numpy.ndarray) – Data to transform

• card (int) – Cardinality to use for processing

Renvoie

Transformed data in SAX

Type renvoyé

numpy.ndarray

_transform_paa_to_isax(X_paa, card)

Transforms X_paa data into iSAX parameters according to cardinality card.

Paramètres

• X_paa (numpy.ndarray) – PAA data to transform into iSAX

• card (list) – Cardinalities to use for processing

Renvoie

Transformed data in SAX

Type renvoyé

numpy.ndarray

_transform_sax(X, card)

Transforms X data in parameter first into PAA and then in cardinate cardinality card.

Paramètres

• X (numpy.ndarray) – Data to transform

• card (int) – Cardinality to use for processing

Renvoie

Transformed data in SAX

Type renvoyé

numpy.ndarray

fit(X)

Prepares the data for encoding iSAX according to``PiecewiseAggregateApproximation``

Renvoie

Received data for encoding, defined by tslearn

Type renvoyé

numpy.ndarray of PiecewiseAggregateApproximation

fit_transform(X, card, **fit_params)

Prepares the X data provided in parameter for encoding``tslearn``. Then transforms the X data provided as a parameter first in PAA and then in cardinate cardinality card.

Paramètres

• X (numpy.ndarray) – Data to transform

• card (int) – Cardinality to use for processing

Renvoie

data transformed into SAX

Type renvoyé

numpy.ndarray

transform(X, card)

Prepares the X data provided in parameter for encoding tslearn. Then transforms X data in parameter first into PAA and then in cardinatlity of cardinality card.

Paramètres

• X (numpy.ndarray) – Data to transform

• card (int) – Cardinality to use for processing

Renvoie

Transformed data in SAX

Type renvoyé

numpy.ndarray

transform_paa(X)

Prepares the X data provided in parameter for encoding``tslearn``. Then transforms X data into parameter in PAA.

Paramètres

X (numpy.ndarray) – Data to transform

Renvoie

Transformed data in PAA

Type renvoyé

numpy.ndarray

transform_paa_to_isax(X_paa, card)

Prepares X_paa data provided as a parameter for encoding``tslearn``. Then transforms X_paa data into iSAX parameter according to cardinalities card.

Paramètres

• X_paa (numpy.ndarray) – PAA data to transform into iSAX

• card (list) – Cardinalities to use for processing

Renvoie

Transformed data in SAX

Type renvoyé

numpy.ndarray

transform_sax(X, card)

Prepares the X data provided in parameter for encoding``tslearn``. Then transforms X data in parameter first into PAA and then in cardinate cardinality``card``.

Paramètres

• X (numpy.ndarray) – Data to transform

• card (int) – Cardinality to use for processing

Renvoie

Transformed data in SAX

Type renvoyé

numpy.ndarray

Pour commencer

Installation

Lancer pip install -r requirements.txt ou python3 -m pip install -r requirements.txt.

Utilisation

>>> from pyCFOFiSAX import CFOFiSAX
>>> cfof_isax = CFOFiSAX()

Un jeu de données artificiel Clust2 contenant 10000 séquences en dimension 200 est disponible dans le projet avec les résultats CFOF (attention : ce ne sont pas les scores CFOFiSAX) pour \(\varrho = [0.01, 0.05, 0.1]\) :

>>> import numpy as np
>>> # chargement du jeu, avec usecols=list(range(0, 200)) pour ne pas charger les scores
>>> ndarray_dataset = np.genfromtxt("pyCFOFiSAX/tests/data_test/data/clust2_200d_20200319_125226_withrealcfof.csv",
>>>                                 delimiter=',',
>>>                                 skip_header=1,
>>>                                 usecols=list(range(0, 200)))
>>> ndarray_dataset.shape
(10000, 200)

Initialisation de la forêt avec 20 arbres iSAX :

>>> cfof_isax.init_forest_isax(size_word=200,
>>>                            threshold=30,
>>>                            data_ts=ndarray_dataset,
>>>                            base_cardinality=2, number_tree=20)

Insertion des données :

>>> cfof_isax.forest_isax.index_data(ndarray_dataset)

Puis pré-traitement :

>>> # va afficher les temps de pré-traitement pour chaque arbre et afficher le nombre de nœuds dans chaque arbre
>>> cfof_isax.forest_isax.preprocessing_forest_for_icfof(ndarray_dataset,
>>>                                                      bool_print=True, count_num_node=True)

Ensuite, le calcul de l’approximation iCFOF, pour la ième séquence est effectué avec la fonction :

>>> tmp_ite = np.random.randint(0,10000)
>>> tmp_ite
8526
>>> score = cfof_isax.score_icfof(
>>>         ndarray_dataset[tmp_ite], ndarray_dataset,
>>>         rho=[0.1], each_tree_score=True,
>>>         fast_method=True)
>>> # les approximations pour chaque valeur de rho sont dans score[0]
>>> score[0]
array([0.21357929])
>>> # si each_tree_score=True,
>>> # il est possible de regarder les scores obtenus dans chaque arbre avec score[1]

Pour connaître le nombre de nœuds visités dans chaque arbre lors du calcul :

>>> cfof_isax.forest_isax.number_nodes_visited(ndarray_dataset[tmp_ite],
>>>                                            ndarray_dataset)
array([1086.    , 1044.    , 1061.    , 1087.    , 1013.    , 1115.    ,
       1067.    , 1101.    , 1069.    , 1065.    , 1104.    , 1104.    ,
       1115.    , 1059.    , 1009.    , 1001.    , 1097.    , 1018.    ,
       1081.    , 1084.    ,  838.215 ,  804.8092,  826.3052,  853.1703,
        769.1603,  870.4031,  829.9387,  853.9431,  833.5567,  830.6371,
        849.1152,  861.5018,  864.5723,  820.4267,  762.5597,  763.3633,
        863.6749,  785.884 ,  850.051 ,  832.9658])

Réferences

• Scoring Message Stream Anomalies in Railway Communication Systems, L.Foulon et al., 2019, ICDMWorkshop

• Approximation du score CFOF de détection d’anomalie dans un arbre d’indexation iSAX: Application au contexte SI de la SNCF, L.Foulon et al., 2019, Actes de la conférence EGC’2019

• CFOF: A Concentration Free Measure for Anomaly Detection, F. Angiulli, 2020, TKDD

• Concentration Free Outlier Detection, F. Angiulli, 2017, ECML-PKDD

• iSAX 2.0: Indexing and Mining One Billion Time Series, A. Camerrea et al., 2010, ICDM

• iSAX: Disk-Aware Mining and Indexing of Massive Time Series Datasets, J. Shieh et al., 2009, DMKD

• Unsupervised real-time anomaly detection for streaming data, Ahmad, S. et al., 2017, Neurocomputing

• Tslearn, A Machine Learning Toolkit for Time Series Data, R.Tavenard et al., 2020 , JMLR

Autres

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