FIND A SOLUTION AT Academic Writers Bay
Lecture Notes for Chapter 9
Introduction to Data Mining
Tan, Steinbach, Kumar
© Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 *
- What are anomalies/outliers?
- The set of data points that are considerably different than the remainder of the data
- Variants of Anomaly/Outlier Detection Problems
- Given a database D, find all the data points x D with anomaly scores greater than some threshold t
- Given a database D, find all the data points x D having the top-n largest anomaly scores f(x)
- Given a database D, containing mostly normal (but unlabeled) data points, and a test point x, compute the anomaly score of x with respect to D
- Credit card fraud detection, telecommunication fraud detection, network intrusion detection, fault detection
Importance of Anomaly Detection
Ozone Depletion History
- In 1985 three researchers (Farman, Gardinar and Shanklin) were puzzled by data gathered by the British Antarctic Survey showing that ozone levels for Antarctica had dropped 10% below normal levels
- Why did the Nimbus 7 satellite, which had instruments aboard for recording ozone levels, not record similarly low ozone concentrations?
- The ozone concentrations recorded by the satellite were so low they were being treated as outliers by a computer program and discarded!
- How many outliers are there in the data?
- Method is unsupervised
- Validation can be quite challenging (just like for clustering)
- Finding needle in a haystack
- Working assumption:
- There are considerably more “normal” observations than “abnormal” observations (outliers/anomalies) in the data
Anomaly Detection Schemes
- General Steps
- Build a profile of the “normal” behavior
- Profile can be patterns or summary statistics for the overall population
- Use the “normal” profile to detect anomalies
- Anomalies are observations whose characteristics
differ significantly from the normal profile
- Types of anomaly detection
- Graphical & Statistical-based
- Assume a parametric model describing the distribution of the data (e.g., normal distribution)
- Apply a statistical test that depends on
- Data distribution
- Parameter of distribution (e.g., mean, variance)
- Number of expected outliers (confidence limit)
- Detect outliers in univariate data
- Assume data comes from normal distribution
- Detects one outlier at a time, remove the outlier, and repeat
- H0: There is no outlier in data
- HA: There is at least one outlier
- Grubbs’ test statistic:
- Reject H0 if:
Statistical-based – Likelihood Approach
- Assume the data set D contains samples from a mixture of two probability distributions:
- M (majority distribution)
- A (anomalous distribution)
- General Approach:
- Initially, assume all the data points belong to M
- Let Lt(D) be the log likelihood of D at time t
- For each point xt that belongs to M, move it to A
- Let Lt+1 (D) be the new log likelihood.
- Compute the difference, = Lt(D) – Lt+1 (D)
- If > c (some threshold), then xt is declared as an anomaly and moved permanently from M to A
Limitations of Statistical Approaches
- Most of the tests are for a single attribute
- In many cases, data distribution may not be known
- For high dimensional data, it may be difficult to estimate the true distribution
- Data is represented as a vector of features
- Three major approaches
- Nearest-neighbor based
- Density based
- Clustering based
Nearest-Neighbor Based Approach
- Compute the distance between every pair of data points
- There are various ways to define outliers:
- Data points for which there are fewer than p neighboring points within a distance D
- The top n data points whose distance to the kth nearest neighbor is greatest
- The top n data points whose average distance to the k nearest neighbors is greatest
Outliers in Lower Dimensional Projection
- In high-dimensional space, data is sparse and notion of proximity becomes meaningless
- Every point is an almost equally good outlier from the perspective of proximity-based definitions
- Lower-dimensional projection methods
- A point is an outlier if in some lower dimensional projection, it is present in a local region of abnormally low density
- Basic idea:
- Cluster the data into groups of different density
- Choose points in small cluster as candidate outliers
- Compute the distance between candidate points and non-candidate clusters.
- If candidate points are far from all other non-candidate points, they are outliers
Base Rate Fallacy in Intrusion Detection
- I: intrusive behavior,
I: non-intrusive behavior
A: no alarm
- Detection rate (true positive rate): P(A|I)
- False alarm rate: P(A|I)
- Goal is to maximize both
- Bayesian detection rate, P(I|A)
- WE OFFER THE BEST CUSTOM PAPER WRITING SERVICES. WE HAVE DONE THIS QUESTION BEFORE, WE CAN ALSO DO IT FOR YOU.
- Assignment status: Already Solved By Our Experts
- (USA, AUS, UK & CA PhD. Writers)
- CLICK HERE TO GET A PROFESSIONAL WRITER TO WORK ON THIS PAPER AND OTHER SIMILAR PAPERS, GET A NON PLAGIARIZED PAPER FROM OUR EXPERTS
QUALITY: 100% ORIGINAL PAPER – NO PLAGIARISM – CUSTOM PAPER
- 100% non-plagiarized Papers
- 24/7 /365 Service Available
- Affordable Prices
- Any Paper, Urgency, and Subject
- Will complete your papers in 6 hours
- On-time Delivery
- Money-back and Privacy guarantees
- Unlimited Amendments upon request
- Satisfaction guarantee
How It Works
- Click on the “Place Your Order” tab at the top menu or “Order Now” icon at the bottom and a new page will appear with an order form to be filled.
- Fill in your paper’s requirements in the “PAPER DETAILS” section.
- Fill in your paper’s academic level, deadline, and the required number of pages from the drop-down menus.
- Click “CREATE ACCOUNT & SIGN IN” to enter your registration details and get an account with us for record-keeping and then, click on “PROCEED TO CHECKOUT” at the bottom of the page.
- From there, the payment sections will show, follow the guided payment process and your order will be available for our writing team to work on it.
AcademicWritersBay.com is an easy-to-use and reliable service that is ready to assist you with your papers 24/7/ 365days a year. 99% of our customers are happy with their papers. Our team is efficient and will always tackle your essay needs comprehensively assuring you of excellent results. Feel free to ask them anything concerning your essay demands or Order.
AcademicWritersBay.com is a private company that offers academic support and assistance to students at all levels. Our mission is to provide proficient and high quality academic services to our highly esteemed clients. AcademicWritersBay.com is equipped with competent and proficient writers to tackle all types of your academic needs, and provide you with excellent results. Most of our writers are holders of master’s degrees or PhDs, which is an surety of excellent results to our clients. We provide assistance to students all over the world.
We provide high quality term papers, research papers, essays, proposals, theses and many others. At AcademicWritersBay.com, you can be sure of excellent grades in your assignments and final exams.