To browse Academia. Skip to main content. Log In Sign Up. Wavelet methods in data mining Mitsunori Ogihara. Wavelet methods in data mining. This article presents general overview of their applications in Data Mining. It first presents a high-level data-mining framework in which the overall process is divided into smaller components.

It reviews a p plications of wavelets for each component. It discusses the impact of wavelets on Data Mining research and outlines potential future research directions and applications. Introduction The wavelet transform is a synthesis of ideas that emerged over many years from different fields.

Generally speaking, the wavelet transform is a tool that partitions data, functions, or operators into different frequency com- ponents and then studies each component with a resolution matched to its scale Daubechies, Therefore, it can provide economical and infor- mative mathematical representation of many objects of interest Abramovich et al.

Nowadays many software packages contain fast and efficient pro- grams that perform wavelet transforms. Due to such easy accessibility wavelets have quickly gained popularity among scientists and engineers, both in theo- retical research and in applications. Data Mining is a process of automatically extracting novel, useful, and un- derstandable patterns from a large collection of data. Over the past decade this area has become significant both in academia and in industry.

Wavelet theory could naturally play an important role in Data Mining because wavelets could provide data presentations that enable efficient and accurate mining process and they can also could be incorporated at the kernel for many algorithms. Al- though standard wavelet applications are mainly on data with temporalhpatial localities e. In this chapter we present a general overview of wavelet methods in Data Mining with relevant mathematical foundations and of research in wavelets ap- plications.

An interested reader is encouraged to consult with other chapters for further reading for references, see Li, Li, Zhu, and Ogihara, This chapter is organized as follows: Section 2 presents a high-level Data Mining framework, which reduces Data Mining process into four components. Sec- tion 3 introduces some necessary mathematical background. Sections 4, 5, and 6 review wavelet applications in each of the components.

### What is Wavelet and How We Use It for Data Science

Finally, Sec- tion 7 concludes. A Framework for Data Mining Process Here we view Data Mining as an iterative process consisting of: data man- agement, data preprocessing, core mining process and post-processing. In data management, the mechanism and structures for accessing and storing data are specified.

The subsequent data preprocessing is an important step, which ensures the data quality and improves the efficiency and ease of the mining process. Data preprocessing includes data cleaning to remove noise and outliers, data integration to integrate data from multiple information sources, data reduction to reduce the dimensionality and complexity of the data, and data transformation to convert the data into suitable forms for mining.

Core mining refers to the essential process where various algorithms are applied to perform the Data Mining tasks. The discovered knowledge is refined and evaluated in post-processing stage. The four-component framework above provides us with a simple systematic language for understanding the steps that make up the data mining process.The wavelet transform is similar to the Fourier transform or much more to the windowed Fourier transform with a completely different merit function.

The main difference is this: Fourier transform decomposes the signal into sines and cosines, i. Generally, the wavelet transform can be expressed by the following equation:. This function can be chosen arbitrarily provided that it obeys certain rules. As it is seen, the Wavelet transform is in fact an infinite set of various transforms, depending on the merit function used for its computation. There are also many ways how to sort the types of the wavelet transforms.

Here we show only the division based on the wavelet orthogonality. We can use orthogonal wavelets for discrete wavelet transform development and non-orthogonal wavelets for continuous wavelet transform development. These two transforms have the following properties:. For more details on wavelet transform see any of the thousands of wavelet resources on the Web, or for example [ 1 ].

The discrete wavelet transform DWT is an implementation of the wavelet transform using a discrete set of the wavelet scales and translations obeying some defined rules. In other words, this transform decomposes the signal into mutually orthogonal set of wavelets, which is the main difference from the continuous wavelet transform CWTor its implementation for the discrete time series sometimes called discrete-time continuous wavelet transform DT-CWT.

The wavelet can be constructed from a scaling function which describes its scaling properties. The restriction that the scaling functions must be orthogonal to its discrete translations implies some mathematical conditions on them which are mentioned everywhere, e.

Moreover, the area between the function must be normalized and scaling function must be orthogonal to its integer translations, i. After introducing some more conditions as the restrictions above does not produce a unique solution we can obtain results of all these equations, i.

The wavelet is obtained from the scaling function as N where N is an even integer. The set of wavelets then forms an orthonormal basis which we use to decompose the signal. Note that usually only few of the coefficients a k are nonzero, which simplifies the calculations. In the following figure, some wavelet scaling functions and wavelets are plotted. The most known family of orthonormal wavelets is the family of Daubechies.

Her wavelets are usually denominated by the number of nonzero coefficients a kso we usually talk about Daubechies 4, Daubechies 6, etc.Hello, this is my second post for the signal processing topic. And to be honest for me, this wavelet thing is harder to understand than Fourier Transform. After I felt quite understanding about this topic, I realize something. It will be faster for me to understand this if I learn this topic with the right step by step of the learning process.

So, here the right step by step in my opinion.

**Problem on haar wavelet transform(matrix)**

So first we need to understand why we need wavelet. Wavelets come as a solution to the lack of Fourier Transform. But the summary, Fourier Transform is the dot product between real signal and various frequency of sine wave. And from this Fourier Transformation, we get a frequency spectrum of the real signal. To get both frequency and time resolution we can be dividing the original signal into several parts and apply Fourier Transform to each part. That technique is called Short-Time Fourier Transform.

But this approach raises new problems. So, you cant catch the information about the signal that has a frequency below 1 Hz assuming the total duration of the signal is more than 1 second but keep in mind when you using some module in python i. Summary, we need a bigger time window to catch low frequency and smaller window for higher frequency and That is the Idea of Wavelets. The basic formula of wavelets is. The scale is the same as the size of the window. Here the illustrations using Morlet Wavelet.

The scale is inversely proportional to the frequency of the mother wavelet the window. Remember, the target of the bigger window is a lower frequency. This is similar to the Fourier Transform because we do a dot product between the real signal and some wave an arbitrary mother wavelet.

So instead of the formula above, we can rewrite the formula as. Anyway, the equation of Morlet Wavelet is. Or we can rewrite that equation as. Another new term here is arbitrary mother wavelet?

Wait, what? Yes, wavelet has many kinds of mother wavelet and you can define a new one with several requirements that need to satisfy of course! This is the big difference between Fourier Transform and Wavelet Transform, Fourier Transform just has 1 kind of transformation but Wavelet Transform can have many kinds of transformation the possibilities of the kind of transformation are infinite.

In general, based on how wavelet transforms treat scale and translation, Types of Wavelet Transform is divided into 2 classes:. CWT is a Wavelet Transform where we can set the scale and translation arbitrary.

Some commonly used mother wavelets those belong to CWT are:. CWT often used to generate a scaleogram.This discount cannot be combined with any other discount or promotional offer. Offer expires June 30, Data Mining DM is a process of automatically extracting novel, useful, and understandable patterns from a large collection of data.

Over the past decade, this area has become significant in many fields naming from the retailer -marketing to DNA -bioinformatics. DM techniques involve diverse dynamic and advanced tools, including wavelet to explore data sets as its nature and domain contexts Jiawei, Wavelet theory could naturally play an important role in DM because it could provide data presentations that enable efficient and accurate mining process, which incorporated into the kernel for many algorithms.

It has been successfully applied to analyze large-scale image data using DM techniques. The approach is introducing a novel methodology how to reduce the amount of manual labor that usually comes with visualize and characterize big image data collections.

With numeric and textual data, the techniques of extracting useful information from unstructured data have already been more or less established. However, with image-heavy datasets, processing methods such as object detection and text recognition are complex to be reliable and in most cases do not stand up to a comparison with a human doing the work. Image mining is the process of searching and discovering valuable information and knowledge in large volumes of image data.

However, image processing is one of those things people are still much better at than computers that use to know something new.

Therefore, based on these two facts, we proposed WT based DM for visualization and characterization of the unique feature of image data. Besides DM algorithms, wavelet technique is growing importantly and having a lot of advantages that already exist numerous successful applications in image mining. WT based DM techniques, functions, or operators into different frequency components, the methodologies and image features' component with a resolution matched to its scale discussed in details.

The chapter is organized as first the introduction followed by section 2 about the related works, which focused on the facts and advancement of image DM in different approaches. It also includes image data managements and its attributes, segmentations, mining algorithms, distributed computing and others.

In section 3, the wavelet technology, methodology and approaches are discussed.

Section 4 discussed wavelet-based image annotations and measurements to visualize and characterize the detail and unique features of image data and mining techniques. In section 5, we present the summary of the chapter, which followed by the acknowledgment of the supporters of the chapter works and list of cited references. Image Data : Is a photographic or trace objects that represent the underlying pixel data of an area of an image element, which is created, collected and stored using image constructor devices.

Image Retrieval : Is a process of searching for digital images in large image scale image data, which is computer based for browsing, searching and retrieving images from digital images. Image Characterization : Is the method present for estimating the complexity of an image based on objects or texts real contexts, which provides a means for classifying and evaluating the object features by way of their visual representations.

Image Segmentation : Is the process of clustering or partitioning a digital image features into multiple sets of pixels to simplify or change the representation of an image into something, which understandable to more meaningful and easier to identify objects or other relevant information in digital formats. Visualization : Is any technique for creating images, diagrams, or animations to communicate a message in which both abstract and concrete ideas.

It means that the data must come from something that is abstract or at least not immediately visible from the inside of the human body. This rule out photography and image processing. Feature Extractions : Is a process of transforming a distinctive characteristic of an arbitrary data, such as text or images into numerical features that usable for machine learning.

The process starts with an initial set of measured data and builds derived values features intended to be informative, non-redundant, which facilitating the subsequent learning and generalization steps, in some cases leading to better human interpretations that related to dimensionality reduction. It is the technique of dealing the image characterizations and segmentations of the big image into smaller windows that the features are easily extracted.

Wavelet Transforms : Are a mathematical means for performing signal or wave-like oscillation with an amplitude analysis when the signal frequency varies over time. You are using a new version of the IGI Global website. If you experience a problem, submit a ticket to helpdesk igi-global.

Special Offers. Browse Titles. Learn More. IGI Global offers a rich volume of content related to treatment, mitigation, and emergency and disaster preparedness surrounding epidemics and pandemics such as COVIDWavelets have recently migrated from Maths to Engineering, with Information Engineers starting to explore the potential of this field in signal processing, data compression and noise reduction.

In doing this they are opening up a new way to make sense of signals, which is the bread and butter of Information Engineering. Because there are very few rules about what defines a wavelet, there are hundreds of different types. These little waves are shaking things up because now Wavelet Transforms are available to Engineers as well as the Fourier Transform.

What are these transforms then and why are they so important? It ends by describing how wavelets can be used for transforms and why they are sometimes preferred because they give better resolution. This blog post does not have much maths in it, but it does deal with concepts that might be slightly beyond someone with no mathematical background.

In Engineering, a signal is usually something you want to send or record. For instance it could be a clip of a voice recording, like the graph below altered from this website It could also be an image, a video, a word file, a graph or a multitude of other things. Basically think of a signal as a squiggly line on a graph, like above. The picture of the voice is a signal in the time domain.

This means that along the x-axis of this graph left to right is time, while on the y-axis up and down is the amplitude of the voice — how loud it is. While plotting a signal in the time domain is often a nice way to visualise it, Engineers find it useful to deal with a signal in the frequency domain. In the frequency domain, the frequency of the signal is on the x-axis, while the amplitude or loudness of the signal is still on the y-axis.

Below, the bottom graph is a signal similar to the voice signal in the time domain. The line on the top graph is the same signal represented in the frequency domain. On the frequency graph, the three spikes would represent the low, medium and high tones of the voice.

### What is Wavelet and How We Use It for Data Science

The process of getting from the time domain to the frequency domain, and from the frequency domain back to the time domain, is called the Fourier Transform. For instance the formula for a square wave a binary signal, 1,0,1,0,1,0 is:. For instance sin x and sin 3x look like this in the time domain:. They are spikes because each sin term is oscillating at different speeds, meaning they are different frequencies.

Every sin wave has a frequency. In the frequency domain 2 different frequencies represent 2 points on the x-axis, so they are spikes of a certain height.Recently there has been significant development in the use of wavelet methods in various Data Mining processes. This article presents general overview of their applications in Data Mining. It first presents a high-level data-mining framework in which the overall process is divided into smaller components.

It reviews applications of wavelets for each component. It discusses the impact of wavelets on Data Mining research and outlines potential future research directions and applications. Unable to display preview. Download preview PDF. Skip to main content. Advertisement Hide.

Wavelet Methods in Data Mining. This is a preview of subscription content, log in to check access. Abramovich, T. Bailey, and T. Wavelet analysis and its statistical applications. JRSSD48 : 1—30, CrossRef Google Scholar. Abry and V. Wavelet analysis of long-range-dependent traffic. On effective classification of strings with wavelets. Google Scholar. Wavelets in statistics: a review. Ardizzoni, I. Bartolini, and M. Windsurf: Region-based image retrieval using wavelets.

Brambilla, A. Ventura, I. Gagliardi, and R. Multiresolution wavelet transform and supervised learning for content-based image retrieval.Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions.

Personal Sign In. For IEEE to continue sending you helpful information on our products and services, please consent to our updated Privacy Policy. Email Address. Sign In. Access provided by: anon Sign Out. Power quality data mining using soft computing and wavelet transform Abstract: This paper presents a new approach to power quality data mining using a modified wavelet transform for feature extraction of power disturbance signal data and a fuzzy multilayer perceptron network to generate the rules and classify the patterns.

## Wavelet Methods in Data Mining

The choice of modified wavelet transform known as multiresolution s-transform is essential for processing very short duration nonstationary time series data from transient disturbances occurring on an electric supply network as they can not be handled by conventional Fourier and other transform methods for extraction of relevant features pertinent for data mining applications.

The trained fuzzy neural network infers the output class membership value of an input pattern and a certainty measure is also presented to facilitate rule generation. Using the electric supply network disturbance data obtained from numerical algorithms and MATLAB software, the paper presents transient disturbance pattern classification scores.

A knowledge discovery approach is also highlighted in the paper to convert raw power disturbance signal data to knowledge in the form of an answer module to the queries by the end-users. The pattern classification approach used in this paper can also be applied to speech, cardiovascular system and other medical and engineering databases. Article :. DOI: Need Help?

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