1. Algorithms Emerging IT Fall 2015 Team 1 Avenbaum, Hamilton, Mirilla, Pisano

2. AGENDA Algorithm Basics (intro) –PB&J Algorithms in computing Popular Algorithms for data mining Conclusion

3. A book on algebra written by Al-Khwarizmi –The term ‘algebra’ was translated from the title as al-jabr and Al-Khwarizmi became algoritme and later algorithm The concept of algorithms has existed for centuries Animate This offers 2500 BC as one of the earliest citations of a documented algorithm History of Algorithm

4. Algorithm distilled Algorithm: 1.Input 2.Finite number of steps 3.Outputs Also important, a well stated goal or objective

5. From Wikipedia …self-contained, step-by-step operations to be performed For math and computing the goal of algorithms is calculation, data processing and automated reasoning What algorithms do you use daily?

6. Related Side Bar: How to… Give some thought to all the little steps involved when: –Making a PB&J or other favorite sandwich –Coffee or Tea in the morning –Morning ritual or preparations

7. More Formal – any textbook Effective method that can be expressed within a finite amount of space and time …in a well-defined formal language For calculating a function Initial state and initial input A finite set of Instructions to be executed with well defined successive states May produce output Terminates in an ending state

8. CLRS – Introduction to Algorithms Cormen, T, Leiserson, C, Rivest, R & Stein, C (2009). Introduction to Algorithms Third Edition. The MIT Press a tool for solving a well-specified computational problem. statement of the problem specifies in general terms the desired input/output relationship describes a specific computational procedure CORRECTNESS: --for every input instance, it halts with the correct output.

9. Real-World Algorithm Fourier Transform –This transforms signals from their time domain into their frequency domain and vice versa. –The internet, your WiFi, smartphone, phone, computer, router, satellites, almost everything that has a computer inside uses these algorithms in one way or another to function.

10. Sorting Algorithms Bubble Sort –Simple sorting algorithm Quick Sort –Classic Divide and conquer Insertion Sort - closest to how most people sort things Selection Sort –also close to how people sort things Merge Sort –better divide and conquer Heap Sort - Priority queue to reduce search time O(n log n) – general worst case

11. Advanced Examples “Top 10 Data Mining Algorithms” -2007 Wu, Kumer, et al Systems that construct a classifier input: a collection of cases –Each belong to one of small number of classes –Described by values for fixed number of attributes output: a classifier that accurately predict a class to which a new case belongs

12. Advanced Examples 1.C4.5 Algorithm – grow a decision tree using divide-and-conquer 2.k-Means Algorithm – iterative method to partition a given dataset into a user specified number of clusters, k. 3.SVM –support vector machine for machine learning.

13. Advanced Examples 4. The Apriori Algorithm -characterized as a level-wise complete search algorithm using anti- monotonicity of itemsets, “if an itemset is not frequent, any of its superset is never frequent”. 5. Expectation-Maximization (EM) Algorithm. -Finite mixture distributions provide a flexible and mathematical-based approach to the modling and clustering of data observed on randdom phenomena

14. Advanced Examples 6. PageRank –statically rank web pages based on number of links leading to it and other simple characteristics (still classification algorithm) 7. AdaBoost – Ensemble Learning employs multiple learners to solve a problem 8. kNN Algorithm. k-nearest neighbor classifier algorithm -the simplest of machine learning algorithms, classifications based on nearest neighbor

15. Advanced Examples 9. Naïve Bayes –easy to construct and apply to large data sets 10. CART– Classification and Regression Trees --Binary recursive partitioning procedure --capable of processing continuous and nominal attributes both as targets and predictors

16. Conclusion (Validation) Algorithm should be FINITE –If it never ends it is useless for solving a problem Well defined instructions –Unambiguously specified or precisely defined. Effective –Should solve the problem it was designed to solve –Verifiable convergence (provable on paper)

17. The End