Claims:WE CLAIM:
1.A processor implemented method, comprising:
receiving (202), from one or more sensors, time series training data X_train and time series test data X_test;
generating (204), an augmented unsupervised feature training set F_(aug_train)by mapping X_train into dimension vectors;
iteratively training (206) a Deep Residual Neural Network (DRNN), using the augmented unsupervised feature training set F_(aug_train)and the time series training data (X_train) along with corresponding time series training labels L_train;
dynamically computing (208), a patience value ? based on the entropy of X_train, and a clipper value for regularizing the training process of the DRNN, wherein the regularization comprises:
performing, during the iteratively training of the DRNN, a comparison of a validation error of (i) a current iteration and (ii) a previous iteration with a predefined threshold, based on the patience value; and
stopping the iterative training of the DRNN based on the comparison, wherein the comparison is indicative of a dynamic early stopping criteria;
iteratively performing an updated training (210), based on the early stopping criteria, on the deep residual neural network to obtain a dynamically regularized trained deep residual neural network M.

2. The method as claimed in claim 1, wherein the augmented unsupervised feature training set F_(aug_train) is generated based on derivation of a first subset of features, called macro-features and a second subset of features, called micro-features.

3. The method as claimed in claim 2, wherein the first subset of features is derived by performing one or more signal processing operations over complete time series training data (X_train) and the second subset of features are derived from performing the one or more signal processing operations over segmented time series training data (X_(seg_train)).

4. The method as claimed in claim 1, further comprising:
classifying, using the regularized trained deep residual neural network M, the time series testing data X_test into one or more predefined classes

5. A system (100), comprising:
a memory(102);
one or more communication interfaces(104); and
one or more hardware processors (106) coupled to said memory through said one or more communication interfaces, wherein said one or more hardware processors are configured to:
receive, from one or more sensors, time series training data X_train and time series test data X_test;
generate, an augmented unsupervised feature training set F_(aug_train) by mapping X_train into dimension vectors;
iteratively train a Deep Residual Neural Network (DRNN), using the augmented unsupervised feature training set F_(aug_train) and the time series training data (X_train) along with corresponding time series training labels L_train;
dynamically compute, a patience value ? based on the entropy of X_train, and a clipper value for regularizing the training process of the DRNN, wherein the regularization using the one or more hardware processors is configured to:
perform, during the iteratively training of the DRNN, a comparison of a validation error of (i) a current iteration and (ii) a previous iteration with a predefined threshold, based on the patience value; and
stop the iterative training of the DRNN based on the comparison, wherein the comparison is indicative of a dynamic early stopping criteria;
iteratively perform an updated training (210), based on the early stopping criteria, on the deep residual neural network to obtain a dynamically regularized trained deep residual neural network M.

6. The system as claimed in claim 5, wherein the augmented unsupervised feature training set F_(aug_train) is generated based on derivation of a first subset of features, called macro-features and a second subset of features, called micro-features.

7. The system as claimed in claim 6, wherein the first subset of features is derived by performing one or more signal processing operations over complete time series training data (X_train)and the second subset of features are derived from performing the one or more signal processing operations over segmented time series training data (X_(seg_train)).

8. The system as claimed in claim 5, using one or more hardware processors is further configured to:
classify, using the regularized trained deep residual neural network M, the time series testing data X_test into one or more predefined classes.
, Description:TECHNICAL FIELD
The disclosure herein generally relates to field of residual learning, more particularly, to methods and systems for dynamically regularized feature augmented residual learning.

BACKGROUND
Sensors play major role in realizing development of intelligent systems, and Internet of Things (IoT) applications. Thus, proper characterization of time series sensor signals is necessary to understand the underlying event(s) and to provide accurate inference. Further, many sensor-based applications demand near-perfect inference. For example, an automated automobile health check using engine noise requires significantly high accuracy. Thus, an effective automated learning system for classification of time series sensor signals is required which would invariably reduce human effort, bias, provide better accuracy and empower rapid deployment of important applications for industrial, social or personal purposes.
Conventional methods utilize shape-let based transformation that captures short and discriminatory sub-sequences of the signals. Some conventional methods convert time series signals into discrete series using symbolic aggregate approximation (SAX) and analyze the signal on the SAX representation. Also, conventional methods for time series classification employ structure-based similarity measure learning and dynamic time warping which fail to provide consistent results. Such conventional methods are highly dependent on hand-crafted feature engineering and expert-driven analysis in the form of tailored hyper parameter tuning and customized feature space development.
SUMMARY
Embodiments of the present disclosure present technological improvements as solutions to one or more of the above-mentioned technical problems recognized by the inventors in conventional systems. For example, in one aspect, there is provided a processor implemented method, comprising: receiving, from one or more sensors, time series training data X_train and time series test data X_test; generating, an augmented unsupervised feature training set F_(aug_train) by mapping X_train into dimension vectors. In an embodiment, the augmented unsupervised feature training set F_(aug_train) is generated based on derivation of a first subset of features and a second subset of features. In an embodiment, the first subset of features is derived by performing one or more signal processing operations over complete time series training data (X_train) and the second subset of features are derived from performing the one or more signal processing operations over segmented time series training data (X_(seg_train)). In an embodiment, the method further comprising: iteratively training a deep residual neural network (DRNN), using the augmented feature training set F_(aug_train) and the time series training data (X_train) along with corresponding time series training labels L_train; dynamically computing, , a patience value ? based on the entropy of X_train, and a clipper value for regularizing training process of the DRNN, wherein the regularization comprises: performing, during the iteratively training of the DRNN, a comparison of a validation error of (i) a current iteration and (ii) a previous iteration with a predefined threshold, based on the patience value; and stopping the iterative training of the DRNN based on the comparison, wherein the comparison is indicative of a dynamic early stopping criteria; iteratively performing an updated training, based on the dynamic early stopping criteria, on the DRNN to obtain a dynamically regularized trained deep residual neural network M.
In an embodiment, the method further comprising classifying, using the regularized trained deep residual neural network M, the time series testing data X_test into one or more predefined classes.
In another aspect, there is provided a system comprising: a memory storing instructions; one or more communication interfaces; and one or more hardware processors coupled to the memory through the one or more communication interfaces, wherein the one or more hardware processors are configured by the instructions to receive, from one or more sensors, time series training data X_train and time series test data X_test; generate, an augmented unsupervised feature training set F_(aug_train) by mapping X_train into dimension vectors. In an embodiment, the augmented unsupervised feature training set F_(aug_train) is generated based on derivation of a first subset of features and a second subset of features. In an embodiment, the first subset of features is derived by performing one or more signal processing operations over complete time series training data (X_train)and the second subset of features are derived from performing the one or more signal processing operations over segmented time series training data (X_(seg_train)). In an embodiment, the one or more hardware processors are further configured by the instructions to iteratively train a deep residual neural network (DRNN), using the augmented feature training set F_(aug_train) and the time series training data (X_train) along with corresponding time series training labels L_train; dynamically compute, , a patience value ? based on the entropy of X_train, and a clipper value for regularizing for training process of the DRNN, wherein the regularization using the one or more hardware processors is configured to perform, during the iteratively training of the DRNN, a comparison of a validation error of (i) a current iteration and (ii) a previous iteration with a predefined threshold, based on the patience value; and stop the iterative training of the DRNN based on the comparison, wherein the comparison is indicative of a dynamic early stopping criteria; iteratively perform an updated training, based on the dynamic early stopping criteria, on the DRNN to obtain a dynamically regularized trained deep residual neural network M.
In an embodiment, the one or more hardware processors are further configured by the instructions to classify, using the regularized trained deep residual neural network M, the time series testing data X_test into one or more predefined classes
In yet another aspect, there are provided one or more non-transitory machine readable information storage mediums comprising one or more instructions which when executed by one or more hardware processors cause receiving, from one or more sensors, time series training data X_train and time series test data X_test; generating, an augmented feature training set F_(aug_train) by mapping X_train into dimension vectors. In an embodiment, the augmented feature training set F_(aug_train) is generated based on derivation of a first subset of features and a second subset of features. In an embodiment, the first subset of features is derived by performing one or more signal processing operations over complete time series training data (X_train)and the second subset of features are derived from performing the one or more signal processing operations over segmented time series training data (X_(seg_train)). In an embodiment, the instructions may further cause iteratively training a deep residual neural network (DRNN), using the augmented unsupervised feature training set F_(aug_train) and the time series training data (X_train) along with corresponding time series training labels L_train; dynamically computing, , a patience value ? based on the entropy of X_train, and a clipper value for regularizing X_train, a clipper value and entropy of X_train for training process of the DRNN, wherein the regularization comprises: performing, during the iteratively training of the DRNN, a comparison of a validation error of (i) a current iteration and (ii) a previous iteration with a predefined threshold, based on the patience value; and stopping the iterative training of the DRNN based on the comparison, wherein the comparison is indicative of a dynamic early stopping criteria; iteratively performing an updated training, based on the dynamic early stopping criteria, on the DRNN to obtain a dynamically regularized trained deep residual neural network M.
In an embodiment, the instructions may further cause classifying, using the regularized trained deep residual neural network M, the time series testing data X_test into one or more predefined classes.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are incorporated in and constitute a part of this disclosure, illustrate exemplary embodiments and, together with the description, serve to explain the disclosed principles:
FIG. 1 illustrates a system diagram for dynamically regularized feature augmented residual learning, according to some embodiments of the present disclosure; and
FIG. 2 illustrate an exemplary flow diagram of a processor implemented method for dynamically regularized feature augmented residual learning, in accordance with some embodiments of the present disclosure;
FIG. 3 illustrates an architecture of a deep residual network used for dynamically regularized feature augmented residual learning, in accordance with some embodiments of the present disclosure; and
FIGS. 4A and 4B illustrate graphs depicting a comparative analysis of conventional methods with the method of present disclosure, in accordance with some embodiments of the present disclosure.
It should be appreciated by those skilled in the art that any block diagrams herein represent conceptual views of illustrative systems and devices embodying the principles of the present subject matter. Similarly, it will be appreciated that any flow charts, flow diagrams, and the like represent various processes which may be substantially represented in computer readable medium and so executed by a computer or processor, whether or not such computer or processor is explicitly shown.

DETAILED DESCRIPTION OF EMBODIMENTS
Exemplary embodiments are described with reference to the accompanying drawings. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. Wherever convenient, the same reference numbers are used throughout the drawings to refer to the same or like parts. While examples and features of disclosed principles are described herein, modifications, adaptations, and other implementations are possible without departing from the spirit and scope of the disclosed embodiments. It is intended that the following detailed description be considered as exemplary only, with the true scope and spirit being indicated by the following claims.
The embodiments herein provide methods and systems for dynamically regularized feature augmented residual learning. Typical interpretation of results obtained from conventional time series classification methods have been modified to solve a problem of inconsistent results in time series classification for heterogeneous datasets. The method in the present disclosure proposes a sensor feature space augmented deep residual neural network, which ensures effective and robust learning task for sensor signal analytics. In the present disclosure, a deep residual neural network is integrated with feature space of sensor signal processing based representation learning. The present disclosure proposes a feature space augmented deep residual neural network that facilitates representation space that ensembles rich sensor signal processing features and residual mapping of the deep residual neural network. The rich sensor signal processing features comprise information theoretic and statistical function based high dimensional features that inherently capture the intrinsic properties of the sensor signals. The proposed method exploits the classification capability of the deep residual neural network that learns through residual mapping while exploring the unsupervised sensor signal processing features to boost the representation space by introducing lower level representation and dynamic regularization.
Referring now to the drawings, and more particularly to FIGS. 1 through FIG. 4B, where similar reference characters denote corresponding features consistently throughout the figures, there are shown preferred embodiments and these embodiments are described in the context of the following exemplary system and/or method.
FIG. 1 illustrates a functional block diagram of a system for dynamically regularized feature augmented residual learning, according to some embodiments of the present disclosure. The system 100 includes or is otherwise in communication with one or more hardware processors such as a processor 106, an I/O interface 104, at least one memory such as a memory 102, and a learning module 108. In an embodiment, the learning module 108 can be implemented as a standalone unit in the system 100. In another embodiment, the learning module 108 can be implemented as a module in the memory 102. The processor 106, the I/O interface 104, and the memory 102, may be coupled by a system bus.
The I/O interface 104 may include a variety of software and hardware interfaces, for example, a web interface, a graphical user interface, and the like. The interfaces 104 may include a variety of software and hardware interfaces, for example, interfaces for peripheral device(s), such as a keyboard, a mouse, an external memory, a camera device, and a printer. The interfaces 104 can facilitate multiple communications within a wide variety of networks and protocol types, including wired networks, for example, local area network (LAN), cable, etc., and wireless networks, such as Wireless LAN (WLAN), cellular, or satellite. For the purpose, the interfaces 104 may include one or more ports for connecting a number of computing systems with one another or to another server computer. The I/O interface 104 may include one or more ports for connecting a number of devices to one another or to another server.
The hardware processor 106 may be implemented as one or more microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, state machines, logic circuitries, and/or any devices that manipulate signals based on operational instructions. Among other capabilities, the hardware processor 106 is configured to fetch and execute computer-readable instructions stored in the memory 102.
The memory 102 may include any computer-readable medium known in the art including, for example, volatile memory, such as static random access memory (SRAM) and dynamic random access memory (DRAM), and/or non-volatile memory, such as read only memory (ROM), erasable programmable ROM, flash memories, hard disks, optical disks, and magnetic tapes. In an embodiment, the memory 102 includes the learning module 108 and a repository 110 for storing data processed, received, and generated by the learning module 108. The learning module 108 may include routines, programs, objects, components, data structures, and so on, which perform particular tasks or implement particular abstract data types.
The data repository 110, amongst other things, includes a system database and other data. The other data may include data generated as a result of the execution of the learning module 108. The system database stores the training data, test data and number of classes the test data belongs to, which are generated as a result of the execution of the learning module 108. The data stored in system database can be learnt to further provide modified training data.
In an embodiment, the learning module 108 can be configured to perform dynamically regularized feature augmented residual learning which can be carried out by using methodology, described in conjunction with FIG. 2 through and use case examples.
FIG. 2, with reference to FIG. 1, is an exemplary flow diagram of a processor implemented method for dynamically regularized feature augmented residual learning using the learning module 108 of FIG. 1, in accordance with some embodiments of the present disclosure. Referring to FIG. 2, at step 202, the one or more hardware processors 106 are configured to receive, from one or more sensors, time series training data X_train and time series test data X_test. In an embodiment, the one or more sensors are used to capture time series data pertaining to intelligent systems such as smart healthcare, smart energy management and other Internet of Things (IoT) applications. In an embodiment, the one or more sensors may include but not limited to electrocardiogram, smart energy meter, and the like.
Further, at step 204 of FIG. 2, the one or more hardware processors are configured to generate, an augmented unsupervised feature training set F_(aug_train) by mapping X_train into dimension vectors. The generated augmented unsupervised feature training set F_(aug_train) is used for representation space construction which plays an important role in the learning process by improving the training process. The generation process of augmented unsupervised feature training set F_(aug_train) utilizes ? number of transformations to map the time series training data X_train into ? dimension vectors. The generated augmented unsupervised feature training set F_(aug_train) characterizes the time series training data X_train received from one or more sensors and is represented as: F_(aug_train) ={F_(1 ),F_2,F_3,……F_n }. In an embodiment, the augmented unsupervised feature training set F_(aug_train) is generated based on derivation of a first subset of features and a second subset of features. In an embodiment, the first subset of features are derived based on extraction of macro granular characteristics of the time series training data X_train and interchangeably referred as macro features, herein. Similarly, the second subset of features are derived based on extraction of micro granular characteristics of the time series training data X_train, thus, interchangeably referred as micro features, herein. In an embodiment, the first subset of features is derived by performing one or more signal processing operations over complete time series training data (X_train)and the second subset of features are derived from performing the one or more signal processing operations over segmented time series training data (X_(seg_train )). In an embodiment, the one or more signal processing for determining macro features and micro features may include but are not limited to Fast Fourier Transform (FFT), multiresolution analysis by wavelet transform, spectral analysis through spectral estimation, spectral centroid, entropy functions like Shannon and Renyi entropies and statistical functions such as mean, median, variance and kurtosis, etc. In an example, macro features derived over complete time series training data is represented as mean (X_train). Here, X_train denotes complete time series training data. Further, in an example, for deriving micro features, first the time series training data X_train is segmented with segment length l (say 30). The segmented time series training data is shown in equation (1) below as:
X_(seg_train) = (?(?X_train?^1,… ?X_train?^l )-(segment # 1), ?(?X_train?^(l+1),?X_train?^(l+2),...,?X_train?^2l )-(segment # 2),… ) (1)
Further, micro features are derived by calculating kurtosis of each of the segments and performing median operation over it as: median (kurtosis(X_(seg_train) )). In an embodiment, the micro features help in describing micro-changes and non-stationarity of the time series data. For example, if the time series data is segmented by N (say, N= 30) number of segments, then each of the segment is analysed to extract micro features (e.g., FFT coefficients are computed). Further, when characteristics of time series data change over time depicting non-stationarity, then each of the segments capture the characteristics and the change of property of the time series data. Thus micro-feature enables to find micro-changes over time and non-stationarity.
Referring back to FIG. 2, at step 206, the one or more hardware processors are configured to iteratively train a deep residual neural network (DRNN), using the augmented unsupervised feature training set F_(aug_train) and the time series training data (X_train) along with corresponding time series training labels L_train. FIG. 3 illustrates architecture of the deep residual neural network, in accordance with some embodiments of the present disclosure. The deep residual neural network comprises of six stacked residual blocks followed by addition of augmented unsupervised feature training set F_(aug_train) at a fully connected layer and a softmax layer. Each of the residual blocks of the deep residual neural network consists of 3 convolution networks with Batch Normalization and Rectified Linear Unit (ReLU) activation function. Convolutional networks of all the residual blocks have filter(s) of size 128, stride length 1 and smoothly decreasing kernel size [8,7,6,5,4,3] from convolution network of first residual block to convolution network of sixth residual block respectively. The convolution network parameters of each of the six residual blocks as shown in FIG. 3 are provided in Table 1.
Table 1
Optimizer Filter Kernel Size Stride length
Conv (1) 128 8 1
Conv (2) 128 7 1
Conv (3) 128 6 1
Conv (4) 128 5 1
Conv (5) 128 4 1
Conv (6) 128 3 1

Further, at step 208 of FIG. 2, the one or more hardware processors are configured to dynamically compute, a patience value ? based on entropy of X_train, and a clipper value for regularizing training process of Deep Residual Neural Network (DRNN). In an embodiment, regularization in the training phase is incorporated to reduce the overfitting error by restricting the training iterations over training datasets such that trained network growth is restricted. Referring to Table 1 provided below in the experimental results, results obtained using a method which is a subset of the method of the present disclosure are provided. This subset of the method of the present disclosure performs training without regularization. It can be seen from Table 1 that the subset of the method of the present disclosure performs poorly by providing less accuracy or more error when tested over hidden or unseen datasets for large pool of different datasets (here, 44 datasets). Such observation ascertains that the dynamic regularization of the proposed method reduces the overfitting error.
In an embodiment, training is performed on 80% of training datasets and remaining 20 % training datasets are used for validation. At some points in iterative training steps, validation error increases, thus the deep residual neural network overfits to the training dataset and generalization capability that measures the performance of trained model over unseen datasets decreases. Thus, regularization is performed to compute a patience value ?, to dynamically determine the early stopping criteria by exploring the statistical characteristics of the trained datasets X_train for forcibly stopping the training process of the deep residual neural network. Initially, value of one or more training parameters is set for training of the deep residual neural network. The one or more training parameters include maximum training time in terms of number of epochs denoted by t_max (Alternatively referred as maximum number of iterations or epochs), and a clipper value denoted by C_ES. In an embodiment, t_max and C_ES could be an integer value (e.g., t_max?Z_+ and C_ES?Z_+). A recommended value selected for C_ES is C_ES=[?t_max/50?,?t_max/10? ]. Further, validation error at a training iteration (epoch) t is determined which is denoted by e_Valid^t. Further, the patience value is computed based on equation 2 shown below as:
t_patience= min(C_ES,??_norm/?_entr ?) (2)

Here, ?_entr denotes the entropy of X_train and ?_norm denotes normalization factor on ?_entr. The normalization factor on ?_entr is computed as ?_norm = (t_max )^E, wherein typically the value of E=0.5. In an embodiment, the regularization technique comprises performing, during the iteratively training of the DRNN, a comparison of a validation error of (i) a current iteration and (ii) a previous iteration with a predefined threshold, based on the patience value; and stopping the iterative training of the DRNN based on the comparison, wherein the comparison is indicative of a dynamic early stopping criteria. In other words, the computed patience value is defined as an observational window ?_w?Z+ over which the validation error is checked. Further, if validation error is not improved, training process is stopped. In an embodiment, the dynamic early stopping criteria is represented by a condition shown in shown below as:
IF: (e_valid^(t-1)-e_valid^t )=0 for t_patience number of training iterations (epochs) ? stop training.
Here, early stopping is a function of patience value which is dependent on entropy of X_train. Since entropy of X_train is expected to be different for different training datasets, early stopping is dynamically varied with the characteristics of the training dataset.
Referring back to FIG. 2, at step 210, the one or more hardware processors are configured to iteratively perform an updated training, based on the dynamic early stopping criteria, on the DRNN to obtain a dynamically regularized trained deep residual neural network M. In an embodiment, one or more parameters utilized for performing the updated training to obtain the dynamically regularized deep residual neural network are shown in Table 2.

Optimizer Adam
?t ?_max (Maximum number of epochs) 1500
C_ES (Early stop clipper) 50
Learning rate 10-4
? (Number of features in augmented unsupervised feature training set) 392
Table 2
In an embodiment, pseudo code for obtaining the dynamically regularized trained deep residual neural network M based on the dynamic early stopping criteria is provided below as:
Input parameters: t_max= 1500, C_ES=[?t_max/50?,?t_max/10? ], and e_Valid^t
Compute ?_entr = Entropy (X_train)
Compute ?_norm (normalization factor on ?_entr) = (t_max )^?, where E=0.5; recommended E=0.5
Compute t_patience= min(C_ES,??_norm/?_entr ?)
IF (e_valid^(t-1)-e_valid^t )=0 for t_patience number of training iterations (epochs) ? stop training
RETURN: + ?M_reg?^ES ¦|_(X_train ): Dynamically regularized trained deep residual neural network at t, when training is forced to stopped.
END

In an embodiment, the one or more hardware processors 106 are further configured to classify (e.g.), using the dynamically regularized trained deep residual neural network M, the time series testing data X_test into one or more predefined classes. In an embodiment, for classification of the time series testing data X_test, first an augmented unsupervised feature testing set F_test is generated. Further, an inference or classification decision is derived using the dynamically regularized trained deep residual neural network M, the time series testing data X_test, and the augmented unsupervised feature testing set F_test. In an embodiment, the inference or classification decision may be, but not limited to, a binary decision (e.g., 0 for positive and 1 for negative). Here, the binary decision refers to classification of the time series testing data X_test into one of two predefined classes based on the binary decision. For example, for a cardiac normal and abnormal detection from electrocardiogram dataset, if the predefined classes include class 1 (cardiac normal) and class 2 (cardiac abnormal), then, the time series testing data pertaining to cardiac normal and abnormal detection would be classified into class 1 and/or class 2. Further, one or more performance parameters pertaining to classification are evaluated based on testing time series labels L_test. The one or more performance parameters may include but not limited to classification accuracy, misclassification rate, and precision and are evaluated using a confusion matrix.
Experimental results:
In an embodiment, a comparative analysis of conventional methods with the method of present disclosure in terms of accuracy on known test datasets is provided with reference to Table 3, and FIGS. 4A and 4B. As depicted in Table 3, that the method of present disclosure solves 8 Time series classification (TSC) problems with 100% accuracy. Further, it can be seen from Table 3 that 64 % (for 29 out of total 44 TSC cases) of new benchmark results are created by the method of present disclosure. Also, in 24 cases listed in Table 3, the method of present disclosure outperforms the known benchmark results. Thus, it is evident from Table 3 that the method of present disclosure demonstrate a stellar achievement in solving the TSC problems.

Dataset Length No. of classes No. of Training Examples Benchmark Conventional method 1 Conventional method 2 Conventional method 3 Conventional method 4 A subset of method of present disclosure without regularization Method of present disclosure
Dataset 1 176 37 390 80.98 82.60 80.98 74.94 60.33 93.44 100
Dataset 2 166 3 467 84.57 82.80 73.55 65.95 64.55 75.19 75.32
Dataset 3 300 12 390 81.40 82.10 81.40 76.35 76.45 92.89 96.72
Dataset 4 84 2 20 91.65 89.50 90.16 84.59 83.20 94.01 94.73
Dataset 5 152 2 1000 99.98 99.70 99.94 99.90 98.40 97.06 97.86
Dataset 6 577 4 60 90.18 93.30 89.90 85.50 66.56 100 100
Dataset 7 500 2 3601 96.54 92.80 95.45 91.95 57.69 91.30 91.70
Dataset 8 500 2 3636 92.86 90.00 92.86 91.10 64.72 89.15 89.96
Dataset 9 1024 3 1000 97.96 97.50 97.96 97.75 91.42 98.10 100
Dataset 10 512 2 322 75.92 78.60 74.68 74.58 70.30 79.29 80.80
Dataset 11 70 2 20 91.84 98.50 89.90 89.74 80.08 89.02 93.82
Dataset 12 65 2 27 95.98 96.20 95.98 88.77 84.60 92.79 95.07
Dataset 13 345 4 16 95.78 93.10 92.47 93.93 95.81 96.80 97.60
Dataset 14 24 2 67 97.03 96.00 97.03 86.60 92.25 94.50 97.55
Dataset 15 275 4 100 99.99 100 99.99 99.99 99.97 100 100
Dataset 16 637 15 60 83.7 75.40 78.47 81.00 82.29 71.67 71.67
Dataset 17 319 7 70 79.95 83.60 79.95 66.56 69.83 89.47 89.47
Dataset 18 300 12 390 81.49 80.50 81.49

74.92 73.80 86.76 89.71
Dataset 19 300 12 390 82.69 81.30 82.69 77.57 77.18 90.14 90.83
Dataset 20 80 2 600 82.12 82.00 80.45 81.46 76.11 80.33 80.33
Dataset 21 80 6 400 69.32 74.00 69.32 67.30 60.46 48.65 54.76
Dataset 22 140 5 500 94.61 93.10 94.61 94.04 92.56 99.00 99.19
Dataset 23 136 2 23 98.62 95.50 98.62 98.33 76.03 97.67 97.67
Dataset 24 96 7 8926 89.54 72.80 88.28 79.95 77.14 84.42 84.42
Dataset 25 99 10 381 78.50 77.20 78.50 71.45 74.11 72.44 73.17
Dataset 26 235 2 613 97.43 95.80 96.31 97.02 95.53 96.76 97.43
Dataset 27 60 6 300 99.92 100 99.92 96.78 99.11 100 100
Dataset 28 128 4 1000 100 100 99.97 99.11 100 100 100
Dataset 29 315 8 896 76.56 78.70 76.56 75.32 72.57 99.95 100
Dataset 30 315 8 896 77.60 66.80 76.56 66.12 62.32 99.09 99.09
Dataset 31 315 8 896 96.83 75.50 75.95 69.51 65.65 89.58 89.58
Dataset 32 426 2 300 90.99 85.80 89.78 90.99 84.88 99.61 99.79
Dataset 33 128 3 30 99.80 99.40 99.80 99.80 99.32 99.78 99.83
Dataset 34 251 3 36 87.68 81.70 87.68 87.52 71.98 87.34 86.35
Dataset 35 470 5 30 81.87 76.70 76.40 61.50 49.70 91.67 91.67
Dataset 36 512 2 20 94.85 80.00 92.10 94.85 77.85 76.00 80.00
Dataset 37 1092 5 155 51.69 50.60 51.69 45.90 39.00 78.27 78.27
Dataset 38 720 3 375 93.25 89.30 90.00 83.65 79.65 94.00 95.60
Dataset 39 720 3 375 81.26 79.70 78.78 75.02 64.01 85.20 85.60
Dataset 40 512 2 20 98.4 90.00 94.10 98.40 83.45 80.00 85.00
Dataset 41 80 2 600 84.84 91.80 87.08 86.73 81.19 90.03 91.96
Dataset 42 720 2 250 80.23 82.40 76.96 80.23 70.07 80.80 80.80
Dataset 43 256 11 220 63.89 53.10 63.89 51.02 34.94 70.32 71.11
Dataset 44 463 7 175 97.42 98.90 96.22 96.87 76.32 100 100
Table 3
Further, FIG. 4A provides a comparative analysis of Mean and Median Accuracies of the method of present disclosure, conventional methods with the known benchmark. In a similar way, FIG. 4B provides a comparative analysis of performance in terms of Mean Absolute Difference of the method of present disclosure and conventional methods with the known benchmark. It can be seen from FIGS. 4A and 4B, that the method of present disclosure demonstrates statistically significant better result than known benchmark results.
In an embodiment, a Wilcoxon Rank-sum Test, which is a non-parametric statistical hypothesis test to compare two samples, is performed. Table 3 provides p-values of the Wilcoxon Rank-sum Test results. In the Wilcoxon Rank-sum Test results, 0 represents rejection of null hypotheses and 1 represents acceptance of null hypotheses. Here null hypotheses for two independent samples at 5 % significance level demonstrate that the method of present disclosure is closely paired with the known benchmark(s), and most of the conventional methods (e.g., conventional method 1, conventional method 2, and conventional method 3) except conventional method 4. Thus, the method of present disclosure is proved to be near-perfect method for TSC, consistently and considerably outperforming all the conventional methods.
Method of present disclosure Conventional method 1 Conventional method 2 Conventional method 3 Conventional method 4 Benchmark
Method of present disclosure ---- 0.014 0.04 .004 5.91 0.163
Conventional method 1 0.0318 ---- 0.997 0.348 0.001 0.321
Conventional method 2 0.396 1 ---- 0.263 0.0013 0.309
Conventional method 3 .0040 0.348 0.2529 --- 0.035 0.07
Conventional method 4 5.905 0.001 0.001 0.035 --- 1.257
Benchmark 0.163 0.321 0.309 0.70 1.257 ---
Table 4
The proposed method can be incorporated for Time Series Classification and other domains such as image or video analytics. Further, the proposed method provides consistent performance on heterogeneous time series datasets with no manual intervention and have capability of representing morphological characteristics of time series data.
The illustrated steps of method 200 is set out to explain the exemplary embodiments shown, and it should be anticipated that ongoing technological development may change the manner in which particular functions are performed. These examples are presented herein for purposes of illustration, and not limitation.
The written description describes the subject matter herein to enable any person skilled in the art to make and use the embodiments. The scope of the subject matter embodiments is defined by the claims and may include other modifications that occur to those skilled in the art. Such other modifications are intended to be within the scope of the claims if they have similar elements that do not differ from the literal language of the claims or if they include equivalent elements with insubstantial differences from the literal language of the claims.
It is to be understood that the scope of the protection is extended to such a program and in addition to a computer-readable means having a message therein; such computer-readable storage means contain program-code means for implementation of one or more steps of the method, when the program runs on a server or mobile device or any suitable programmable device. The hardware device can be any kind of device which can be programmed including e.g. any kind of computer like a server or a personal computer, or the like, or any combination thereof. The device may also include means which could be e.g. hardware means like e.g. an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or a combination of hardware and software means, e.g. an ASIC and an FPGA, or at least one microprocessor and at least one memory with software modules located therein. Thus, the means can include both hardware means and software means. The method embodiments described herein could be implemented in hardware and software. The device may also include software means. Alternatively, the embodiments may be implemented on different hardware devices, e.g. using a plurality of CPUs.
The embodiments herein can comprise hardware and software elements. The embodiments that are implemented in software include but are not limited to, firmware, resident software, microcode, etc. The functions performed by various modules described herein may be implemented in other modules or combinations of other modules. For the purposes of this description, a computer-usable or computer readable medium can be any apparatus that can comprise, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.
The illustrated steps are set out to explain the exemplary embodiments shown, and it should be anticipated that ongoing technological development will change the manner in which particular functions are performed. These examples are presented herein for purposes of illustration, and not limitation. Further, the boundaries of the functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternative boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed. Alternatives (including equivalents, extensions, variations, deviations, etc., of those described herein) will be apparent to persons skilled in the relevant art(s) based on the teachings contained herein. Such alternatives fall within the scope and spirit of the disclosed embodiments. Also, the words “comprising,” “having,” “containing,” and “including,” and other similar forms are intended to be equivalent in meaning and be open ended in that an item or items following any one of these words is not meant to be an exhaustive listing of such item or items, or meant to be limited to only the listed item or items. It must also be noted that as used herein and in the appended claims, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise.
Furthermore, one or more computer-readable storage media may be utilized in implementing embodiments consistent with the present disclosure. A computer-readable storage medium refers to any type of physical memory on which information or data readable by a processor may be stored. Thus, a computer-readable storage medium may store instructions for execution by one or more processors, including instructions for causing the processor(s) to perform steps or stages consistent with the embodiments described herein. The term “computer-readable medium” should be understood to include tangible items and exclude carrier waves and transient signals, i.e., be non-transitory. Examples include random access memory (RAM), read-only memory (ROM), volatile memory, nonvolatile memory, hard drives, CD ROMs, DVDs, flash drives, disks, and any other known physical storage media.
It is intended that the disclosure and examples be considered as exemplary only, with a true scope and spirit of disclosed embodiments being indicated by the following claims.