N. Saito. Local Feature Extraction and Its Applications Using a Library of Bases. PhD thesis, Yale University, December 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to compare our results with other researchers. 6.2.1 Cylinder Bell Funnel A warm up The first artificial domain we will be considering is a simple one, but one that has been used and explored by other researchers. The artificial cylinder bell funnel task was originally proposed by Saito [Sai94] and further worked on by Manganaris [Man97] The task is to classify a stream as one of three classes, cylinder (c) bell (b) or funnel (f ) Samples are generated as follows: These datasets are: arrythmia, audiology, bach chorales, echocardiogram, isolet, mobile robots, waveform. c(t) ....

Naoki Saito. Local feature extraction and its application using a library of bases. PhD thesis, Yale University, December 1994.

....1) The Australian Sign Language (ASL) dataset from the UCI KDD archive [2] The dataset consists of various sensors that measure the X axis position of a subject s right hand while signing one of 95 words in Australian Sign Language. 2)The Cylinder Bell Funnel (CBF) synthetic dataset as used in [11,17,19]. This dataset contains three classes, which are generated by the following equations. Figure 8 shows some examples of the Cylinder and Funnel class (members of the Bell class look like mirror images of the Funnel class) For every possible pairing of the ten words in the ASL dataset, we ....

Saito, N. (1994). Local feature extraction and its application using a library of bases. PhD thesis, Yale University.

....the signal space encourage adaptive signal representations. Instead of representing a prescribed signal on a fixed basis, it is often useful to choose a suitable basis that facilitates a desired application, such as compression, identification, classification or noise removal (denoising) [27,32,35]. Of particular interest are the libraries of wavelet packet bases, which consist of translations and dilations of wavelet packets, and libraries of local trigonometric bases, comprising sines and cosines multiplied by smooth window functions [14,35] The basis functions are localized in the ....

N. Saito, Local Feature Extraction and Its Applications Using a Library of Bases, Ph.D. Dissertation, Yale Univ., New Haven, December 1994.

....overcomplete libraries of waveforms have been widely used in recent years. Instead of representing a prescribed signal in a fixed basis, it is useful to choose a suitable basis that facilitates a desired application, such as compression, identification, classification or noise removal (denoising) [1, 2, 3]. Coifman and Meyer were the first to introduce libraries of orthonormal bases which are organized in a binary tree structure, where the best basis can be efficiently searched for, and whose elements are localized in the time frequency plane [4] Of particular interest are the libraries of local ....

N. Saito, Local Feature Extraction and Its Appli- cations Using a Library of Bases, Ph.D. Dissertation, Yale Univ., New Haven, Dec. 1994.

....descending rate of the coe#cients amplitudes, when sorted in a decreasing magnitude order. Whereas for classification, we select a basis which most discriminates between given classes. Such a basis reduces the dimensionality of the problem and emphasizes the dissimilarity between distinct classes [128]. Practical best basis search procedures are necessarily confined to finite size libraries. Such libraries are not only required to be flexible and versatile enough to describe various local features of signals, but also need to be aptly organized in a structure that facilitates 8 a fast ....

....to the children nodes. This flexibility in choosing a basis for each subspace implies adaptive representations, by a recursive comparison between the information costs of parent nodes and their children nodes. Selecting a desirable information cost functional is clearly application dependent [128, 136, 150]. Entropy, for example, may be used to e#ectively measure the energy concentration of the generated nodes [48, 77, 143] Statistical analysis of the best basis coe#cients may provide a characteristic time frequency signature of the signal, potentially useful in simplifying identification and ....

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N. Saito, Local Feature Extraction and Its Applications Using a Library of Bases, Ph.D. Dissertation, Yale Univ., New Haven, Dec. 1994.

....data sets are summarised in table II. The main criterion for selecting them was that the number of examples available were big enough, to ensure that the results were reliable. Figure 1 shows some examples. A. 1 Cylinder, Bell and Funnel (CBF) This is an artificial problem, introduced by Saito [9]. The learning task is to distinguish between these three classes: cylinder (c) bell (b) or funnel (f ) Examples are generated using the following functions: c(t) 6 ) a;b] t) t) b(t) 6 ) a;b] t) t a) b a) t) f(t) 6 ) a;b] t) b t) b a) ....

Naoki Saito, Local Feature Extraction and Its Applications Using a Library of Bases, PhD thesis, Department of Mathematics, Yale University, 1994.

....is based on a further variant of AdaBoost.OC, named AdaBoost.ECC [11] but dealing with con dence based predictions. 4 Experimental Validation The characteristics of the data sets are summarized in table 1. The data sets waveform, waveform with noise [5, 6] CBF (cylinder, bell and funnel) [19] and control charts [1, 3] were already used in our work on boosting distance literals [18] Auslan is the Australian sign language, the language of the Australian deaf community. Instances of the signs were collected using an instrumented glove [12] Each example is composed by 8 series The ....

Naoki Saito. Local Feature Extraction and Its Applications Using a Library of Bases. PhD thesis, Department of Mathematics, Yale University, 1994.

....dicult problem. For settings 4 5 and all the iterations considered the results are better than for the setting 1. For setting 5 and all iterations considered, except the rst one, these di erences are signi cant. 4. 4 Cylinder, Bell and Funnel (CBF) This is an arti cial problem, introduced in [Sai94]. The learning task is to distinguish between three classes: cylinder (c) bell (b) or funnel (f ) Examples are generated using the following functions: c(t) 6 ) a;b] t) t) b(t) 6 ) a;b] t) t a) b a) t) f(t) 6 ) a;b] t) b t) b a) t) ....

Naoki Saito. Local Feature Extraction and Its Applications Using a Library of Bases. PhD thesis, Department of Mathematics, Yale University, 1994.

....characteristics of the datasets are summarized in table 1. Datasets for classification of time series are not easy to find [16] For this reason we have used four artificial datasets and only one real world dataset. Cylinder, Bell and Funnel (CBF) This is an artificial problem, introduced in [26]. The learning task is to distinguish between three classes: cylinder (c) bell (b) or funnel (f ) Examples are generated using the following functions: not true percentage( Example, x, 1 4, 22, 86, 50 ) 193, 18 not true percentage( Example, x, 3, 78, 110, 30 ) 182, 0 . class( Example, ....

Naoki Saito. Local Feature Extraction and Its Applications Using a Library of Bases. PhD thesis, Department of Mathematics, Yale University, 1994.

....way than the previous one, but 19 points are added at the end of each example, with mean 0 and variance 6 1. Again, we used the rst 300 examples of each class of the corresponding dataset from the UCI ML Repository. Cylinder, Bell and Funnel (CBF) This is an arti cial problem, introduced by Saito [Saito, 1994]. The learning task is to distinguish between these three classes: cylinder (c) bell (b) or funnel (f ) Examples are generated using the following functions: c(t) 6 ) a;b] t) t) b(t) 6 ) a;b] t) t a) b a) t) f(t) 6 ) a;b] t) b t) b a) ....

....10 20 30 40 50 0 5 10 15 20 25 0 10 20 30 40 50 0 5 10 15 20 25 0 10 20 30 40 50 Figure 1: Graphs of the results for the di erent datasets. For each graph, the maximum and combined errors are plotted. The best previously published result, to our knowledge, for this dataset is an error of 15:90 [Saito, 1994], using 100 training examples and 1000 test examples, although the results reported after averaging 10 times gives a result of 16:16 [Saito and Coifman, 1995] The error of an optimal Bayes classi er on this dataset is approximately of 14 [Breiman et al. 1993] Since our results when using the ....

Saito, N. (1994). Local Feature Extraction and Its Applications Using a Library of Bases. PhD thesis, Department of Mathematics, Yale University. http: //math.ucdavis.edu/~saito/publications/saito_phd.html.

....Each time series is defined by 60 time points. In what follows, we will use indifferently the terms scenario and object to denote an element of U . Without loss of generality we assume start time of scenario being always 0. Cylinder Bell Funnel (CBF) This problem was first introduced in [12] and then used in [11, 8, 2] for validation. The goal is to separate three classes of object: cylinder(c) bell(b) and funnel(f) Each object is described by one temporal attribute given by: a(o; t) 8 : 6 j) Delta [a;b] t) ffl(t) if c(o) c; 6 j) Delta [a;b] t) Delta (t ....

N. Saito. Local feature extraction and its application using a library of bases. PhD thesis, Department of Mathematics, Yale University, 1994.

....scale estimation and classification problems. 7. 2 Multiscale Statistical Signal Analysis and Modeling On the analysis front the good localization properties of wavelets have played a key role in the development of various applications such as compression [253, 328] and signal reconstruction [253, 94, 211, 275, 347] (also referred to as denoising) The tree like structure of the wavelet analysis framework has also led to efficient multiresolution stochastic modeling techniques with a remarkable impact on large scale physics based estimation and classification problems [19, 249] 7.2.1 Fractal Analysis ....

....an unconditional basis for a great many smoothness spaces [253] they showed that the reconstruction error was within a scalar multiple of the minimum worst case error over these signal spaces. Other developments ensued as other interpretations of signal enhancement or denoising were adopted. In [275, 347, 211] the notion of coding was independently used to lead to algorithms with more or less the same type of nonlinear thresholding. The information theoretic criterion Minimum Description Length (MDL) developed in the late seventies [338, 365] proved to be very useful in not only providing the ....

N. Saito, Local feature extraction and its applications using a library of bases, PhD thesis, Yale University, Dec. 1994.

....we compare DTW to Euclidean distance, the most commonly used distance measure for time series [2, 7, 8, 10, 15] 2.1.1 Classification There has been much work on classification of time series. The most commonly studied benchmark dataset is Cylinder Bell Funnel, a synthetic dataset introduced in [28] and used by [21, 13, 9] and others. The dataset consists of a 3 class problem, with the classes generated by the following equations: c(t) 6 h) X [a,b] t) e(t) b(t) 6 h) X [a,b] t) t a) b a) e(t) f(t) 6 h) X [a,b] t) b a) b t) e(t) X [a,b] 1, if a t b, ....

Saito, N. (1994). Local feature extraction and its application using a library of bases. PhD thesis, Yale University.

....characteristics of the datasets are summarized in table 1. Datasets for classification of time series are not easy to find [9] For this reason we have used four artificial datasets and only one real world dataset: Cylinder, Bell and Funnel (CBF) This is an artificial problem, introduced in [12]. The learning task is to distinguish between three classes: cylinder (c) bell (b) or funnel (f ) Examples are generated using the following functions: c(t) 6 #) # [a,b] t) #(t) b(t) 6 #) # [a,b] t) t a) b a) #(t) f(t) 6 #) # [a,b] t) b t) b a) ....

Naoki Saito. Local Feature Extraction and Its Applications Using a Library of Bases. PhD thesis, Department of Mathematics, Yale University, 1994.

....The characteristics of the datasets are summarized in table 1. Datasets for classi cation of time series are not easy to nd [16] For this reason we have used four arti cial datasets and only one real world dataset. Cylinder, Bell and Funnel (CBF) This is an arti cial problem, introduced in [26]. The learning task is to distinguish between three classes: cylinder (c) bell (b) or funnel (f ) Examples are generated using the following functions: class( Example, cylinder ) 213, 426 not true percentage( Example, x, 1 4, 22, 86, 50 ) 193, 18 not true percentage( Example, x, 3, ....

Naoki Saito. Local Feature Extraction and Its Applications Using a Library of Bases. PhD thesis, Department of Mathematics, Yale University, 1994.

....overcomplete libraries of waveforms have been widely used in recent years. Instead of representing a prescribed signal in a fixed basis, it is useful to choose a suitable basis that facilitates a desired application, such as compression, identification, classification or noise removal (denoising) [1, 2, 3]. Coifman and Meyer were the first to introduce libraries of orthonormal bases which are organized in a binary tree structure, where the best basis can be efficiently searched for, and whose elements are localized in the time frequency plane [4] Of particular interest are the libraries of local ....

N. Saito, Local Feature Extraction and Its Applications Using a Library of Bases, Ph.D. Dissertation, Yale Univ., New Haven, Dec. 1994.

....have had to use one artificial domain and one natural domain where we collected the data ourselves. We discuss these domains first to give a practical example of typical temporal classification problems. 2. 1 CYLINDER BELL FUNNEL The artificial cylinder bell funnel task was originally proposed by Saito [Saito, 1994], and further worked on by Manganaris [Manganaris, 1997] The task is to classify a stream as one of three classes, cylinder (c) 1 It is also possible to conceive of a more complex learning task, where each stream has a sequence of class labels. However, for the rest of this paper, we will only ....

....in the small Auslan task where there is no significant difference 8 between it and the TClass approach. At 2.4 per cent error it outperforms the best known published results for the CBF task, including complex approaches involving local discriminant bases using wavelets (3. 75 per cent) [Saito, 1994] and trend episode analysis (2.98 per cent) Manganaris, 1997] but is beaten by TClass s 1.9 per cent error rate. TClass has a better error rate overall compared to the naive segmentation technique, regardless of the underlying learner. Learner performance is consistent with previous results ....

Saito, N. (1994). Local feature extraction and its application using a library of bases. PhD thesis, Yale University.

....After this step, we have a complete orthonormal basis LDB. Proposition 1 The basis obtained by Step 3 of Algorithm 1 maximizes the additive discriminant measure D on the time frequency energy distributions among all the bases in the dictionary obtainable by the divide andconquer algorithm. See [3] for the proof. 3. LOCAL REGRESSION BASES For regression problems, we need a different measure to access the goodness of the subspaces. Here, we use regression (or prediction) error as a criterion: the smaller the error using a chosen regression method on the data belonging to a subspace, the ....

....classifier and Classification Tree (CT) with and without pruning) using the training signals represented in the original coordinate (i.e. standard Euclidean) system, and computed resubstitution (or apparent) error rates. We used the pruning algorithm based on the MDL principle described in [3]. Then we fed the test signals into these classifiers and computed the error rates. Next we computed the LDB (using the 6 tap coiflet filter [7] and asymmetric relative entropy) as a discriminant measure using the training signals. Then we selected five individually most discriminant basis ....

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N. Saito, Local Feature Extraction and Its Applications Using a Library of Bases, Ph.D. thesis, Dept. of Mathematics, Yale University, New Haven, CT 06520 USA, 1994.

.... are given a new set of sonic waveforms recorded in a geological environment similar to that of the training waveforms (which were used for constructing the algorithms) Then, we apply recently developed methods, the so called local discriminant basis (LDB) and local regression basis (LRB) methods (Saito, 1994; Coifman and Saito, 1994; Saito and Coifman, 1994, 1995, 1996) to this inference problem. Bothmethods have automatic feature extraction capability. Given a training data set (i.e. waveforms and their associated lithologic information at specific depth levels) the LDB and LRB methods ....

.... waveforms recorded in a geological environment similar to that of the training waveforms (which were used for constructing the algorithms) Then, we apply recently developed methods, the so called local discriminant basis (LDB) and local regression basis (LRB) methods (Saito, 1994; Coifman and Saito, 1994; Saito and Coifman, 1994, 1995, 1996) to this inference problem. Bothmethods have automatic feature extraction capability. Given a training data set (i.e. waveforms and their associated lithologic information at specific depth levels) the LDB and LRB methods automatically extract useful ....

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Saito, N., 1994, Local feature extraction and its applications using a library of bases: Ph.D. thesis, Yale Univ.

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N. Saito. Local Feature Extraction and Its Applications Using a Library of Bases. PhD thesis, Yale University, December 1994.

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N. Saito, Local feature extraction and its applications using a library of bases, Ph.D. thesis, Yale University, Department of Mathematics, 10 Hillhouse Avenue, BIBLIOGRAPHY 91 P.O. Box

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N. Saito, Local Feature Extraction and Its Applications Using a Library of Bases, dissertation, Yale University (1994). 121

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Naoki Saito. Local Feature Extraction and Its Applications Using a Library of Bases . PhD thesis, Yale University, Department of Mathematics, 10 Hillhouse Avenue, P.O. Box 208283 New Haven, CT 06520-8283, 1994. Available online at http://www.math.yale.edu/pub/papers/.

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N. Saito, Local feature extraction and its applications using a library of bases. PhD thesis, Yale University, Dec. 1994.

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Saito, N. "Local feature extraction and its application using a library of bases." Phd thesis, Yale University (1994).

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