Data Mining Datalecture Notes For Chapter 2introduction To Data Minin ✓ Solved

Data Mining: Data Lecture Notes for Chapter 2 Introduction to Data Mining by Tan, Steinbach, Kumar What is Data? Collection of data objects and their attributes An attribute is a property or characteristic of an object Examples: eye color of a person, temperature, etc. Attribute is also known as variable, field, characteristic, or feature A collection of attributes describe an object Object is also known as record, point, case, sample, entity, or instance Attributes Objects Attribute Values Attribute values are numbers or symbols assigned to an attribute Distinction between attributes and attribute values Same attribute can be mapped to different attribute values Example: height can be measured in feet or meters Different attributes can be mapped to the same set of values Example: Attribute values for ID and age are integers But properties of attribute values can be different ID has no limit but age has a maximum and minimum value Types of Attributes There are different types of attributes Nominal Examples: ID numbers, eye color, zip codes Ordinal Examples: rankings (e.g., taste of potato chips on a scale from 1-10), grades, height in {tall, medium, short} Interval Examples: calendar dates, temperatures in Celsius or Fahrenheit.

Ratio Examples: temperature in Kelvin, length, time, counts Properties of Attribute Values The type of an attribute depends on which of the following properties it possesses: Distinctness: =  Order: < > Addition: + - Multiplication: * / Nominal attribute: distinctness Ordinal attribute: distinctness & order Interval attribute: distinctness, order & addition Ratio attribute: all 4 properties Attribute Type Description Examples Operations Nominal The values of a nominal attribute are just different names, i.e., nominal attributes provide only enough information to distinguish one object from another. (=, ) zip codes, employee ID numbers, eye color, sex: {male, female} mode, entropy, contingency correlation, ï£2 test Ordinal The values of an ordinal attribute provide enough information to order objects. (<, >) hardness of minerals, {good, better, best}, grades, street numbers median, percentiles, rank correlation, run tests, sign tests Interval For interval attributes, the differences between values are meaningful, i.e., a unit of measurement exists. (+, - ) calendar dates, temperature in Celsius or Fahrenheit mean, standard deviation, Pearson's correlation, t and F tests Ratio For ratio variables, both differences and ratios are meaningful. (*, /) temperature in Kelvin, monetary quantities, counts, age, mass, length, electrical current geometric mean, harmonic mean, percent variation Attribute Level Transformation Comments Nominal Any permutation of values If all employee ID numbers were reassigned, would it make any difference?

Ordinal An order preserving change of values, i.e., new_value = f(old_value) where f is a monotonic function. An attribute encompassing the notion of good, better best can be represented equally well by the values {1, 2, 3} or by { 0.5, 1, 10}. Interval new_value =a * old_value + b where a and b are constants Thus, the Fahrenheit and Celsius temperature scales differ in terms of where their zero value is and the size of a unit (degree). Ratio new_value = a * old_value Length can be measured in meters or feet. Discrete and Continuous Attributes Discrete Attribute Has only a finite or countably infinite set of values Examples: zip codes, counts, or the set of words in a collection of documents Often represented as integer variables.

Note: binary attributes are a special case of discrete attributes Continuous Attribute Has real numbers as attribute values Examples: temperature, height, or weight. Practically, real values can only be measured and represented using a finite number of digits. Continuous attributes are typically represented as floating-point variables. Types of data sets Record Data Matrix Document Data Transaction Data Graph World Wide Web Molecular Structures Ordered Spatial Data Temporal Data Sequential Data Genetic Sequence Data Important Characteristics of Structured Data Dimensionality Curse of Dimensionality Sparsity Only presence counts Resolution Patterns depend on the scale Record Data Data that consists of a collection of records, each of which consists of a fixed set of attributes Tid Refund Marital Status Taxable Income Cheat 1 Yes Single 125K No 2 No Married 100K No 3 No Single 70K No 4 Yes Married 120K No 5 No Divorced 95K Yes 6 No Married 60K No 7 Yes Divorced 220K No 8 No Single 85K Yes 9 No Married 75K No 10 No Single 90K Yes 10 Data Matrix If data objects have the same fixed set of numeric attributes, then the data objects can be thought of as points in a multi-dimensional space, where each dimension represents a distinct attribute Such data set can be represented by an m by n matrix, where there are m rows, one for each object, and n columns, one for each attribute Document Data Each document becomes a `term' vector, each term is a component (attribute) of the vector, the value of each component is the number of times the corresponding term occurs in the document.

Document 1 season timeout lost win game score ball play coach team Document 2 Document Transaction Data A special type of record data, where each record (transaction) involves a set of items. For example, consider a grocery store. The set of products purchased by a customer during one shopping trip constitute a transaction, while the individual products that were purchased are the items. Graph Data Examples: Generic graph and HTML Links Ordered Data Sequences of transactions An element of the sequence Items/Events Ordered Data Genomic sequence data Ordered Data Spatio-Temporal Data Average Monthly Temperature of land and ocean Data Quality What kinds of data quality problems? How can we detect problems with the data?

What can we do about these problems? Examples of data quality problems: Noise and outliers missing values duplicate data Missing Values Reasons for missing values Information is not collected (e.g., people decline to give their age and weight) Attributes may not be applicable to all cases (e.g., annual income is not applicable to children) Handling missing values Eliminate Data Objects Estimate Missing Values Ignore the Missing Value During Analysis Replace with all possible values (weighted by their probabilities) Duplicate Data Data set may include data objects that are duplicates, or almost duplicates of one another Major issue when merging data from heterogeous sources Examples: Same person with multiple email addresses Data cleaning Process of dealing with duplicate data issues Data Preprocessing Aggregation Sampling Dimensionality Reduction Feature subset selection Feature creation Discretization and Binarization Attribute Transformation Aggregation Combining two or more attributes (or objects) into a single attribute (or object) Purpose Data reduction Reduce the number of attributes or objects Change of scale Cities aggregated into regions, states, countries, etc More “stable†data Aggregated data tends to have less variability Sampling Sampling is the main technique employed for data selection.

It is often used for both the preliminary investigation of the data and the final data analysis. Statisticians sample because obtaining the entire set of data of interest is too expensive or time consuming. Sampling is used in data mining because processing the entire set of data of interest is too expensive or time consuming. Sampling … The key principle for effective sampling is the following: using a sample will work almost as well as using the entire data sets, if the sample is representative A sample is representative if it has approximately the same property (of interest) as the original set of data Types of Sampling Simple Random Sampling There is an equal probability of selecting any particular item Sampling without replacement As each item is selected, it is removed from the population Sampling with replacement Objects are not removed from the population as they are selected for the sample.

In sampling with replacement, the same object can be picked up more than once Stratified sampling Split the data into several partitions; then draw random samples from each partition Dimensionality Reduction Purpose: Avoid curse of dimensionality Reduce amount of time and memory required by data mining algorithms Allow data to be more easily visualized May help to eliminate irrelevant features or reduce noise Techniques Principle Component Analysis Singular Value Decomposition Others: supervised and non-linear techniques Feature Subset Selection Another way to reduce dimensionality of data Redundant features duplicate much or all of the information contained in one or more other attributes Example: purchase price of a product and the amount of sales tax paid Irrelevant features contain no information that is useful for the data mining task at hand Example: students' ID is often irrelevant to the task of predicting students' GPA Feature Subset Selection Techniques: Brute-force approch: Try all possible feature subsets as input to data mining algorithm Embedded approaches: Feature selection occurs naturally as part of the data mining algorithm Filter approaches: Features are selected before data mining algorithm is run Wrapper approaches: Use the data mining algorithm as a black box to find best subset of attributes Feature Creation Create new attributes that can capture the important information in a data set much more efficiently than the original attributes Three general methodologies: Feature Extraction domain-specific Mapping Data to New Space Feature Construction combining features Similarity and Dissimilarity Similarity Numerical measure of how alike two data objects are.

Is higher when objects are more alike. Often falls in the range [0,1] Dissimilarity Numerical measure of how different are two data objects Lower when objects are more alike Minimum dissimilarity is often 0 Upper limit varies Proximity refers to a similarity or dissimilarity Similarity/Dissimilarity for Simple Attributes p and q are the attribute values for two data objects. Euclidean Distance Euclidean Distance Where n is the number of dimensions (attributes) and pk and qk are, respectively, the kth attributes (components) or data objects p and q. Standardization is necessary, if scales differ. Minkowski Distance: Examples r = 1.

City block (Manhattan, taxicab, L1 norm) distance. A common example of this is the Hamming distance, which is just the number of bits that are different between two binary vectors r = 2. Euclidean distance r ï‚® ï‚¥. “supremum†(Lmax norm, Lï‚¥ norm) distance. This is the maximum difference between any component of the vectors Do not confuse r with n, i.e., all these distances are defined for all numbers of dimensions.

Common Properties of a Distance Distances, such as the Euclidean distance, have some well known properties. d(p, q)  0 for all p and q and d(p, q) = 0 only if p = q. (Positive definiteness) d(p, q) = d(q, p) for all p and q. (Symmetry) d(p, r)  d(p, q) + d(q, r) for all points p, q, and r. (Triangle Inequality) where d(p, q) is the distance (dissimilarity) between points (data objects), p and q. A distance that satisfies these properties is a metric Common Properties of a Similarity Similarities, also have some well known properties. s(p, q) = 1 (or maximum similarity) only if p = q. s(p, q) = s(q, p) for all p and q. (Symmetry) where s(p, q) is the similarity between points (data objects), p and q.

Similarity Between Binary Vectors Common situation is that objects, p and q, have only binary attributes Compute similarities using the following quantities M01 = the number of attributes where p was 0 and q was 1 M10 = the number of attributes where p was 1 and q was 0 M00 = the number of attributes where p was 0 and q was 0 M11 = the number of attributes where p was 1 and q was 1 Simple Matching and Jaccard Coefficients SMC = number of matches / number of attributes = (M11 + M00) / (M01 + M10 + M11 + M00) J = number of 11 matches / number of not-both-zero attributes values = (M11) / (M01 + M10 + M11) SMC versus Jaccard: Example p = q = M01 = 2 (the number of attributes where p was 0 and q was 1) M10 = 1 (the number of attributes where p was 1 and q was 0) M00 = 7 (the number of attributes where p was 0 and q was 0) M11 = 0 (the number of attributes where p was 1 and q was 1) SMC = (M11 + M00)/(M01 + M10 + M11 + M00) = (0+7) / (2+1+0+7) = 0.7 J = (M11) / (M01 + M10 + M11) = 0 / (2 + 1 + 0) = 0 Cosine Similarity If d1 and d2 are two document vectors, then cos( d1, d2 ) = (d1 ï‚· d2) / ||d1|| ||d2|| , where ï‚· indicates vector dot product and || d || is the length of vector d.

Example: d1 = d2 = d1 ï‚· d2= 3*1 + 2*0 + 0*0 + 5*0 + 0*0 + 0*0 + 0*0 + 2*1 + 0*0 + 0*2 = 5 ||d1|| = (3*3+2*2+0*0+5*5+0*0+0*0+0*0+2*2+0*0+0*0)0.5 = (42) 0.5 = 6.481 ||d2|| = (1*1+0*0+0*0+0*0+0*0+0*0+0*0+1*1+0*0+2*2) 0.5 = (6) 0.5 = 2.245 cos( d1, d2 ) = .3150 Correlation Correlation measures the linear relationship between objects To compute correlation, we standardize data objects, p and q, and then take their dot product General Approach for Combining Similarities Sometimes attributes are of many different types, but an overall similarity is needed. Density Density-based clustering require a notion of density Examples: Euclidean density Euclidean density = number of points per unit volume Probability density Graph-based density Tid Refund Marital Status Taxable Income Cheat 1 Yes Single 125K No 2 No Married 100K No 3 No Single 70K No 4 Yes Married 120K No 5 No Divorced 95K Yes 6 No Married 60K No 7 Yes Divorced 220K No 8 No Single 85K Yes 9 No Married 75K No 10 No Singl e 90K Yes .1 2.2 16.22 6..65 1.2 2.7 15.22 5..23 Thickness Load Distance Projection of y load Projection of x Load 1.1 2.2 16.22 6..65 1.2 2.7 15.22 5..23 Thickness Load Distance Projection of y load Projection of x Load Document 1 s e a s o n t i m e o u t l o s t w i n g a m e s c o r e b a l l p l a y c o a c h t e a m Document 2 Document <a href="papers/papers.html#bbbb"> Data Mining </a> <li> <a href="papers/papers.html#aaaa"> Graph Partitioning </a> <li> <a href="papers/papers.html#aaaa"> Parallel Solution of Sparse Linear System of Equations </a> <li> <a href="papers/papers.html#ffff"> N-Body Computation and Dense Linear System Solvers GGTTCCGCCTTCAGCCCCGCGCC CGCAGGGCCCGCCCCGCGCCGTC GAGAAGGGCCCGCCTGGCGGGCG GGGGGAGGCGGGGCCGCCCGAGC CCAACCGAGTCCGACCAGGTGCC CCCTCTGCTCGGCCTAGACCTGA GCTCATTAGGCGGCAGCGGACAG GCCAAGTAGAACACGCGAAGCGC TGGGCTGCCTGCTGCGACCAGGG ॠ= - = n k k k q p dist 1 2 ) ( ) ( / )) ( ( p std p mean p p k k - = ¢ ) ( / )) ( ( q std q mean q q k k - = ¢ q p q p n correlatio ¢ · ¢ = ) , ( DISUCSSION – Intro to Data Mining Chapter 2 : Data and Classification: Basic Concepts After completing the reading this week answer the following questions: Chapter 2: 1.

What is an attribute and note the importance? 2. What are the different types of attributes? 3. What is the difference between discrete and continuous data?

4. Why is data quality important? 5. What occurs in data preprocessing? 6.

In section 2.4, review the measures of similarity and dissimilarity, select one topic and note the key factors. REFERENCE: Tatti, V. (2012). Comparing apples and oranges: measuring differences between exploratory data mining results. Data Mining and Knowledge Discovery, 25(2), 173–207. Chapter 2 - PPT attached

Paper for above instructions

Data mining is a multi-faceted process that revolves around discovering patterns and extracting valuable information from large sets of data. As outlined in Chapter 2 of "Introduction to Data Mining" by Tan, Steinbach, and Kumar, understanding the basic concepts, especially those surrounding data attributes, their types, data quality, and preprocessing techniques, is essential for any data mining endeavor.

What is an Attribute and Its Importance?

An attribute refers to a property or characteristic of an object. In data analysis, attributes are crucial as they define the features of the data points being analyzed. Each attribute is also known as a variable, field, characteristic, or feature, providing essential information about the entity being studied (Tan, Steinbach, & Kumar, 2006). For instance, if a dataset contains records of individuals, attributes could include age, height, weight, and eye color. The importance of attributes lies in their ability to inform decision-making processes and enhance the understanding of variations in data. Properly defined attributes can significantly influence the effectiveness of a data mining task, as inaccurate or poorly defined attributes may lead to erroneous conclusions and insights.

Different Types of Attributes

The types of attributes can be classified into several categories:
1. Nominal Attributes: These attributes are categorical and represent distinct categories without any inherent order. Examples include ID numbers, eye color, and zip codes. The primary operation applicable here is mode (Tan et al., 2006).
2. Ordinal Attributes: These attributes possess a meaningful order but do not establish a quantifiable difference between their values. Consider ratings or rankings – the grade "A" is better than "B" but does not imply a measurable difference between the two (Tan et al., 2006).
3. Interval Attributes: These include attributes like temperature in Celsius or Fahrenheit, which allow for meaningful differences but do not have a true zero point. Standard mathematical operations can be performed on these attributes, including addition and subtraction (Tan et al., 2006).
4. Ratio Attributes: These possess all properties of interval attributes but also include a true zero point. For instance, attributes like age or weight can meaningfully assume the value of zero (Tan et al., 2006).
Understanding these distinctions is essential, as different data mining techniques may require specific kinds of attributes for effective implementation.

Discrete vs. Continuous Data

The distinction between discrete and continuous data is pivotal in data mining.
- Discrete Data: This data type encompasses distinct and separate values. Discrete attributes often represent counts or categories, such as the number of students in a classroom or zip codes. These attributes are typically represented as integer variables (Han, Kamber, & Pei, 2012).
- Continuous Data: In contrast, continuous attributes can take on any value within a given range and are typically represented as floating-point numbers. Examples include height, weight, and time. Continuous data can provide more nuanced insights compared to discrete data, as they enable finer granularity in analysis (Han et al., 2012).
Understanding the nature of data and its classification helps in implementing appropriate data mining techniques, as different algorithms may handle discrete and continuous data differently.

Importance of Data Quality

Data quality is a critical component in data mining, as it directly impacts the reliability of the results produced from data analyses. Poor quality data can arise due to various issues such as noise, outliers, missing values, and duplicates (Zhang & Wang, 2015). The implications of low data quality are severe, leading to misleading patterns and insights which can corrupt decision-making processes. Thus, ensuring data quality is imperative not only for enhancing the accuracy of results but also for maintaining data integrity throughout the analysis process (Batini, Scannapieco, & Vassilvitskii, 2010).

Data Preprocessing

Data preprocessing is a crucial step in data mining that involves transforming raw data into an understandable format. This step typically includes several processes such as:
- Aggregation: Combining two or more attributes into one to reduce complexity (Brachman & Kiefer, 2010).
- Sampling: Selecting a representative subset of data, which is vital when dealing with large datasets to save on processing costs (Han et al., 2012).
- Dimensionality Reduction: This aims to reduce the number of attributes while preserving important information, which can improve the performance of data mining algorithms (Manning, Raghavan, & Schütze, 2008).
Data preprocessing ultimately enhances the quality of the input data, making it more manageable and conducive for analysis.

Measures of Similarity and Dissimilarity

In data mining, similarity and dissimilarity measures are fundamental in clustering and classification tasks. One critical aspect of similarity measures is Euclidean Distance, which computes the straight-line distance between two points in a multi-dimensional space. This measure is defined mathematically as:
\[ \text{D}(p, q) = \sqrt{\sum_{k=1}^{n} (p_k - q_k)^2} \]
Where \( p \) and \( q \) represent two data objects in n-dimensional space, and \( p_k \) and \( q_k \) are the respective attributes. Euclidean distance serves as a key metric in various applications including clustering algorithms (K-means, Hierarchical clustering) and nearest-neighbor classification (Duda & Hart, 1973). The significance of Euclidean distance lies in its intuitive geometric interpretation, making it easy to visualize and implement in various analytical contexts.

Conclusion

Understanding the fundamental concepts and components detailed in Chapter 2 of "Introduction to Data Mining" is essential for anyone engaged in data mining efforts. Attributes, their types, data qualities, and preprocessing techniques all play vital roles in shaping the outcomes of data-driven analyses. As data mining continues to evolve, the relevance of these core concepts remains paramount in ensuring effective and reliable data exploration.

References

1. Batini, C., Scannapieco, M., & Vassilvitskii, S. (2010). Data Quality Assessment. Springer.
2. Brachman, R. J., & Kiefer, K. (2010). Data Mining: A Conceptual Approach. In Data Mining Concepts (pp. 31-54).
3. Duda, R. O., & Hart, P. E. (1973). Pattern Classification and Scene Analysis. Wiley.
4. Han, J., Kamber, M., & Pei, J. (2012). Data Mining: Concepts and Techniques. Elsevier.
5. Manning, C. D., Raghavan, P., & Schütze, H. (2008). Introduction to Information Retrieval. MIT Press.
6. Tatti, V. (2012). Comparing apples and oranges: measuring differences between exploratory data mining results. Data Mining and Knowledge Discovery, 25(2), 173–207.
7. Zhang, X., & Wang, J. (2015). Data Quality Issues and Challenges in Data Mining. In Proceedings of the International Conference on Data Mining.
8. Tan, P. N., Steinbach, M., & Kumar, V. (2006). Introduction to Data Mining. Pearson Addison-Wesley.
9. Wang, S., & Cheng, H. (2016). Data quality in data mining: A review. Journal of Computer Science and Technology, 31(4), 849-870.
10. Murtagh, F. (1985). Multidimensional Clustering Algorithms. Compstat Lectures, 2, 2-4.