Matrix Methods in Machine Learning

Transcription

1 Matrix Methods in Machine Learning 1/34 Matrix Methods in Machine Learning V. Vijaya Saradhi Dept. of CSE, IIT Guwahati 11-April-2015 Matrix Methods in Machine Learning 1/34

2 Classification Examples Matrix Methods in Machine Learning 2/34 Machine - Classification Employee Churn Prediction: Problem Description and Importance 1 For any organization employee churn is a common challenge 2 IT services industry in particular employee churn is very high approximately 12-15%. 3 Cost of an employee leaving organization is 1.5 annual salary of an employee. 4 Assuming a 5% churn, an organization with 1,40,000 employees having annual salary of $12,000 estimated loss is: ( = $ 126 Million). Matrix Methods in Machine Learning 2/34

3 Classification Examples Matrix Methods in Machine Learning 2/34 Machine - Classification Employee Churn Prediction: Organization Challenges 1 Difficult to find suitable replacement (Experience, special skill sets). 2 Involve time, effort, money for new recruitment. 3 Loss of employee adversely affects ongoing projects. 4 Involve time, effort to train people to bring to the required productivity. 5 Loss of employee costs money to organization. Matrix Methods in Machine Learning 2/34

4 Classification Examples Matrix Methods in Machine Learning 2/34 Machine - Classification Employee Churn Prediction: Why employees resign? Positive Reasons 1 Better pay packages 2 Better work 3 Better perks 4 Better career growth 5 Location 6 Leadership Matrix Methods in Machine Learning 2/34

5 Classification Examples Matrix Methods in Machine Learning 2/34 Machine - Classification Employee Churn Prediction: Why employees resign? Negative Reasons 1 Conflict with supervisor or colleague 2 Lack of appreciation 3 Uninteresting work 4 Low pay 5 Bad working conditions Matrix Methods in Machine Learning 2/34

6 Classification Examples Matrix Methods in Machine Learning 2/34 Machine - Classification Employee Churn Prediction: Impact 1 Retention better than new hire (offer promotion, increments, on site work) 2 Identifying root cause improves controlling churn rate 3 Proactively value employee Matrix Methods in Machine Learning 2/34

7 Classification Problem Matrix Methods in Machine Learning 3/34 Problem Formulation The Learning Problem: Given N training data points randomly drawn from probability distribution P(X, Y ), learn a function f chosen from a set of functions F which map inputs to outputs such that the expected error is minimized. As we have points sampled from distribution, instead of minimizing the expected error, one minimizes the empirical risk which is given as: R emp (f) = 1 N N l(f(x i ),y i ) i=1 Matrix Methods in Machine Learning 3/34

8 Clustering Examples Matrix Methods in Machine Learning 4/34 Machine - Clustering Document Clustering: Matrix Methods in Machine Learning 4/34

9 Clustering Examples Matrix Methods in Machine Learning 4/34 Machine - Clustering Document Clustering: Matrix Methods in Machine Learning 4/34

10 Clustering Problem Matrix Methods in Machine Learning 5/34 Problem Formulation A clustering function is a function f that takes a distance function d on D and returns a partition Γ of D. The sets in Γ will be called its clusters. Source: An Impossibility Theorem of Clustering, Jon Kleinberg, NIPS Matrix Methods in Machine Learning 5/34

11 Examples Matrix Methods in Machine Learning 6/34 Machine - : Representation 1 Indexing of text documents for efficient retrieval plays a significant role 2 Vector space model (VSM) 3 Let N be the number of documents; T be the number of distinct terms. 4 A document d i is represented as a vector of T elements. j th element of this document is 1 if T th j d i ; 0 otherwise. 5 Document retrieval methods hinge on the effectiveness of the VSM. Matrix Methods in Machine Learning 6/34

12 Examples Matrix Methods in Machine Learning 6/34 Machine - : Limitations 1 Words used for searching are often not the same as the index one. 2 The above stems from synonymy: eg. tip suggestion; pointer and polysemy: tip pointed end; small present of money given to some one. 3 Incompleteness of the indexing terms. 4 Lack of automated methods in dealing with polysemy words. 5 Size of the index. Matrix Methods in Machine Learning 6/34

13 Examples Matrix Methods in Machine Learning 6/34 Machine - : Example Access Document Retrieval Information Theory Database Indexing Computer Doc1 Y Y Y - - Y Y - Doc Y Y - - Y Doc3 - - Y Y Y Query: IDF in computer-based information look-up Matrix Methods in Machine Learning 6/34

14 Visualization Examples Matrix Methods in Machine Learning 7/34 Machine - Visualization Visualization 1 Large matrices occur in many places. 2 Internet traffic represented as origin-destination matrix. 3 Term-Document matrix. 4 Visualization provide meaningful insights into the problem domain. We will emphasize this in detail. Matrix Methods in Machine Learning 7/34

15 Clustering Matrix Methods in Machine Learning 8/34 Machine - Clustering NMF Formulation 1 Given a data matrix A m n find a rank-k approximation that is constrained to have non-negative factors. 2 That is A = UV T where U m k and with non negative entries and V k n with non negative entries. 3 The objective is: Find U and V such that the following quantity is minimized: J = 1 2 A UV T Matrix Methods in Machine Learning 8/34

16 Clustering Matrix Methods in Machine Learning 8/34 Machine - Clustering NMF Formulation J = 1tr ( (A UV T )(A UV T ) T) 2 = 1tr ( AA T 2AV U T + UV T V U T) 2 ( = 1 2 tr(aa T ) 2tr(AV U T ) + tr(uv T V U T ) ) Minimize J with respect to U,V under the constraint that U 0 and V 0. Matrix Methods in Machine Learning 8/34

17 Clustering Matrix Methods in Machine Learning 8/34 Machine - Clustering NMF Formulation 1 Lagrangin of the above formulation is: 2 Setting L U L V L = J + tr(αu T ) + tr(βv T ) = 0 = AV + UV T V + α = 0 = A T U + V U T U + β Matrix Methods in Machine Learning 8/34

18 Clustering Matrix Methods in Machine Learning 8/34 Machine - Clustering NMF Formulation 1 (AV ) ij u ij + (UV T V ) ij u ij + α ij u ij = 0 (A T U)v ij + (V U T U) ij v ij + β ij v ij = 0 2 u ij = u ij (AV ) ij (UV T V ) ij 3 v ij = v ij (A T U) ij (V U T U) ij Matrix Methods in Machine Learning 8/34

19 Clustering Matrix Methods in Machine Learning 8/34 Machine - Clustering NMF Algorithm: through alternating least squares (ALT) method (Alternating optimization method). 1 Guess an initial U (1). 2 For k = 1, 2,, until convergence Fix U k and find V using update rule above. Fix V k and find U using update rule above. Normalize U and V. Matrix Methods in Machine Learning 8/34

20 Clustering Matrix Methods in Machine Learning 8/34 Machine - Clustering NMF Example 1 Doc1: The Google matrix P is a model of the Internet. 2 Doc2: P ij is nonzero if there is a link from Web page j to i. 3 Doc3: The Google matrix is used to rank all Web pages. 4 Doc4: The ranking is done by solving a matrix eigenvalue problem. 5 Doc5: England dropped out of the top ten in the FIFA rankings. Matrix Methods in Machine Learning 8/34

21 Clustering Matrix Methods in Machine Learning 8/34 Machine - Clustering Term-Document Matrix Doc1 Doc2 Doc3 Doc4 Doc5 Term eigenvalue England FIFA Google Internet link matrix page rank Web Matrix Methods in Machine Learning 8/34

22 Clustering Matrix Methods in Machine Learning 8/34 Machine - Clustering NMF: U and V matrices are 0 U = v C A A Matrix Methods in Machine Learning 8/34

23 SVD Theory Matrix Methods in Machine Learning 9/34 Theorem: Any matrix A m n with m n can be factorized as: ( ) Σ A = U V T 0 where U R m m ; columns of U s are eigenvectors of AA T. V R n n are orthonormal and columns of V are eigenvectors of A T A and Σ R n n is diagonal matrix. 1 First r columns of U: column space of A. 2 First r columns of V: row space of A. Matrix Methods in Machine Learning 9/34

24 SVD Theory Matrix Methods in Machine Learning 9/34 SVD based classification: 1 Obtain A c and A nc matrices for churn data and rest. 2 Obtain U c Σ c V T c using A c. 3 Obtain U nc Σ nc V T nc using A nc. 4 Given a test data point z, understand how well basis of U c and U nc represent z. That is: min α z (U c ) k α Matrix Methods in Machine Learning 9/34

25 SVD Theory Matrix Methods in Machine Learning 9/34 SVD based classification: 1 α = (U c ) T k z 2 Measure of effectiveness in representing z by U c is: ( I (U c ) k (U c ) T k ) z 2. 3 Compute the above measure for (U nc ) k. 4 Classify z to one that has least value. Matrix Methods in Machine Learning 9/34

26 - Applications Matrix Methods in Machine Learning 10/34 Statistics in Cricket Measures individual players performance. Example: 1 Batting average. 2 Number of centuries scored. 3 Strike rate. 4 Run rate. 5 Number of overs bowled, wickets taken, etc. Matrix Methods in Machine Learning 10/34

27 - Applications Matrix Methods in Machine Learning 10/34 Statistics in Cricket Team performance. Example: 1 How many matches played between any two teams. 2 How many matches own by a particular team. Matrix Methods in Machine Learning 10/34

28 - Applications Matrix Methods in Machine Learning 10/34 Statistics in Cricket Target score computation in case of interruptions. 1 ICC Champions Trophy Pakistan scored 165 runs in 39.4 overs (all out). 3 Indian batting interrupted at 19.1 overs with a score of 102/1. 4 Target to achieve: 102 runs in 22 overs. 5 Result: India Won based on Duck Worth Lewis. Matrix Methods in Machine Learning 10/34

29 - Applications Matrix Methods in Machine Learning 10/34 Statistics in Cricket Wagon Wheel display Matrix Methods in Machine Learning 10/34

30 in Practise Matrix Methods in Machine Learning 11/34 Statistics in Cricket Graphics Packages - Batting, bowling score cards, match summaries etc. Matrix Methods in Machine Learning 11/34

31 in Practise Matrix Methods in Machine Learning 11/34 Statistics in Cricket Edge detection: Snikometer Matrix Methods in Machine Learning 11/34

32 in Practise Matrix Methods in Machine Learning 11/34 Statistics in Cricket Hawk Eye: Matrix Methods in Machine Learning 11/34

33 /Machine Learning in Cricket Matrix Methods in Machine Learning 12/34 Finding interesting moments in the game from video data Roddick and Rice Type of shot played by a batsman from cricket videos Lazarescu Predicting game s outcome Clark Cricket video segmenting into individual balls being bowled Sankar A-Eye (Automated Eye) to perform the role of third umpire to arrive at a decision about run outs Mahmood Prediction of players performance cricket team selection Iyer and Sharada Matrix Methods in Machine Learning 12/34

34 /Machine Learning in Cricket Matrix Methods in Machine Learning 12/34 Finding interesting moments in the game from video data Roddick and Rice Type of shot played by a batsman from cricket videos Lazarescu Predicting game s outcome Clark Cricket video segmenting into individual balls being bowled Sankar A-Eye (Automated Eye) to perform the role of third umpire to arrive at a decision about run outs Mahmood Prediction of players performance cricket team selection Iyer and Sharada Matrix Methods in Machine Learning 12/34

35 /Machine Learning in Cricket Matrix Methods in Machine Learning 12/34 Finding interesting moments in the game from video data Roddick and Rice Type of shot played by a batsman from cricket videos Lazarescu Predicting game s outcome Clark Cricket video segmenting into individual balls being bowled Sankar A-Eye (Automated Eye) to perform the role of third umpire to arrive at a decision about run outs Mahmood Prediction of players performance cricket team selection Iyer and Sharada Matrix Methods in Machine Learning 12/34

36 /Machine Learning in Cricket Matrix Methods in Machine Learning 12/34 Finding interesting moments in the game from video data Roddick and Rice Type of shot played by a batsman from cricket videos Lazarescu Predicting game s outcome Clark Cricket video segmenting into individual balls being bowled Sankar A-Eye (Automated Eye) to perform the role of third umpire to arrive at a decision about run outs Mahmood Prediction of players performance cricket team selection Iyer and Sharada Matrix Methods in Machine Learning 12/34

37 /Machine Learning in Cricket Matrix Methods in Machine Learning 12/34 Finding interesting moments in the game from video data Roddick and Rice Type of shot played by a batsman from cricket videos Lazarescu Predicting game s outcome Clark Cricket video segmenting into individual balls being bowled Sankar A-Eye (Automated Eye) to perform the role of third umpire to arrive at a decision about run outs Mahmood Prediction of players performance cricket team selection Iyer and Sharada Matrix Methods in Machine Learning 12/34

38 /Machine Learning in Cricket Matrix Methods in Machine Learning 12/34 Finding interesting moments in the game from video data Roddick and Rice Type of shot played by a batsman from cricket videos Lazarescu Predicting game s outcome Clark Cricket video segmenting into individual balls being bowled Sankar A-Eye (Automated Eye) to perform the role of third umpire to arrive at a decision about run outs Mahmood Prediction of players performance cricket team selection Iyer and Sharada Matrix Methods in Machine Learning 12/34

39 Players Weakness Identification Matrix Methods in Machine Learning 13/34 Weakness Definition We acknowledge to the fact that there is no universally accepted definition for weakness. Matrix Methods in Machine Learning 13/34

40 Players Weakness Identification Matrix Methods in Machine Learning 13/34 Weakness Definition Our Interpretation of Weakness: Batsman or Bowler exhibiting imperfection in type of shot played or ball bowled. Matrix Methods in Machine Learning 13/34

41 Example and Motivation Matrix Methods in Machine Learning 14/34 Example 0.5 Sharma to Powell, FOUR, kp, leading edge, but safe. Ishant s natural curve into the right hander, opens up the left-handed Powell as it lands on leg and swerves away. The edge kept low and flew away between third slip and gully ( Matrix Methods in Machine Learning 14/34

42 Example and Motivation Matrix Methods in Machine Learning 14/34 Example Contains minute details of games proceedings. Easy to analyze compared to audio commentary. ( Matrix Methods in Machine Learning 14/34

43 Problem Definition Matrix Methods in Machine Learning 15/34 Problem Statement Given text commentary of test cricket matches in which India was featured, we are interested in finding individual player s weakness. Matrix Methods in Machine Learning 15/34

44 Matrix Methods in Machine Learning 16/34 1 A total of 1, 25, 026 text commentary lines were analyzed. 2 Each ball of cricket commentary is expressed in less than 50 words. 3 Talks about type of ball bowled and manner in which batsman played the ball. 4 Every commentary line contains focused technical words pertaining to cricket. 5 Many of the technical words fall in the category of stop words. off on room across behind back out place good great into away up down long below turn point from further under full open high Matrix Methods in Machine Learning 16/34

45 Matrix Methods in Machine Learning 16/34 1 A total of 1, 25, 026 text commentary lines were analyzed. 2 Each ball of cricket commentary is expressed in less than 50 words. 3 Talks about type of ball bowled and manner in which batsman played the ball. 4 Every commentary line contains focused technical words pertaining to cricket. 5 Many of the technical words fall in the category of stop words. off on room across behind back out place good great into away up down long below turn point from further under full open high Matrix Methods in Machine Learning 16/34

46 Matrix Methods in Machine Learning 16/34 1 A total of 1, 25, 026 text commentary lines were analyzed. 2 Each ball of cricket commentary is expressed in less than 50 words. 3 Talks about type of ball bowled and manner in which batsman played the ball. 4 Every commentary line contains focused technical words pertaining to cricket. 5 Many of the technical words fall in the category of stop words. off on room across behind back out place good great into away up down long below turn point from further under full open high Matrix Methods in Machine Learning 16/34

47 Matrix Methods in Machine Learning 16/34 1 A total of 1, 25, 026 text commentary lines were analyzed. 2 Each ball of cricket commentary is expressed in less than 50 words. 3 Talks about type of ball bowled and manner in which batsman played the ball. 4 Every commentary line contains focused technical words pertaining to cricket. 5 Many of the technical words fall in the category of stop words. off on room across behind back out place good great into away up down long below turn point from further under full open high Matrix Methods in Machine Learning 16/34

48 Matrix Methods in Machine Learning 16/34 1 A total of 1, 25, 026 text commentary lines were analyzed. 2 Each ball of cricket commentary is expressed in less than 50 words. 3 Talks about type of ball bowled and manner in which batsman played the ball. 4 Every commentary line contains focused technical words pertaining to cricket. 5 Many of the technical words fall in the category of stop words. off on room across behind back out place good great into away up down long below turn point from further under full open high Matrix Methods in Machine Learning 16/34

49 - Continued Matrix Methods in Machine Learning 17/34 1 The term frequency is significantly less in every document (line of text commentary). 2 Inverse term frequency dominates. 3 Technical words lose their significance in the TFIDF representation. 4 Domain specific features capture sufficient information from short sentences. Word Off On Stump Outside Leg Length Frequency Word Ball Short Defend Line Full Frequency Matrix Methods in Machine Learning 17/34

50 - Continued Matrix Methods in Machine Learning 17/34 1 The term frequency is significantly less in every document (line of text commentary). 2 Inverse term frequency dominates. 3 Technical words lose their significance in the TFIDF representation. 4 Domain specific features capture sufficient information from short sentences. Word Off On Stump Outside Leg Length Frequency Word Ball Short Defend Line Full Frequency Matrix Methods in Machine Learning 17/34

51 - Continued Matrix Methods in Machine Learning 17/34 1 The term frequency is significantly less in every document (line of text commentary). 2 Inverse term frequency dominates. 3 Technical words lose their significance in the TFIDF representation. 4 Domain specific features capture sufficient information from short sentences. Word Off On Stump Outside Leg Length Frequency Word Ball Short Defend Line Full Frequency Matrix Methods in Machine Learning 17/34

52 - Continued Matrix Methods in Machine Learning 17/34 1 The term frequency is significantly less in every document (line of text commentary). 2 Inverse term frequency dominates. 3 Technical words lose their significance in the TFIDF representation. 4 Domain specific features capture sufficient information from short sentences. Word Off On Stump Outside Leg Length Frequency Word Ball Short Defend Line Full Frequency Matrix Methods in Machine Learning 17/34

53 - Continued Matrix Methods in Machine Learning 18/34 1 Technical words alone cannot distinguish type of ball bowled or the way batsman played. Example: Flintoff to Mishra, no run, Swings in from outside off, well left in the end as it scoots past off stump. Swing signifies the type of ball Flintoff to Dhoni, 1 run, Short ball over middle stump, Dhoni swings into a pull and takes it down to fine leg. Swing signifies the way batsman played the ball Matrix Methods in Machine Learning 18/34

54 - Continued Matrix Methods in Machine Learning 18/34 1 Technical words alone cannot distinguish type of ball bowled or the way batsman played. Example: Flintoff to Mishra, no run, Swings in from outside off, well left in the end as it scoots past off stump. Swing signifies the type of ball Flintoff to Dhoni, 1 run, Short ball over middle stump, Dhoni swings into a pull and takes it down to fine leg. Swing signifies the way batsman played the ball Matrix Methods in Machine Learning 18/34

55 - Continued Matrix Methods in Machine Learning 18/34 1 Technical words alone cannot distinguish type of ball bowled or the way batsman played. Example: Flintoff to Mishra, no run, Swings in from outside off, well left in the end as it scoots past off stump. Swing signifies the type of ball Flintoff to Dhoni, 1 run, Short ball over middle stump, Dhoni swings into a pull and takes it down to fine leg. Swing signifies the way batsman played the ball Matrix Methods in Machine Learning 18/34

56 - Continued Matrix Methods in Machine Learning 18/34 1 Technical words alone cannot distinguish type of ball bowled or the way batsman played. Example: Flintoff to Mishra, no run, Swings in from outside off, well left in the end as it scoots past off stump. Swing signifies the type of ball Flintoff to Dhoni, 1 run, Short ball over middle stump, Dhoni swings into a pull and takes it down to fine leg. Swing signifies the way batsman played the ball Matrix Methods in Machine Learning 18/34

57 - Continued Matrix Methods in Machine Learning 18/34 1 Technical words alone cannot distinguish type of ball bowled or the way batsman played. Example: Flintoff to Mishra, no run, Swings in from outside off, well left in the end as it scoots past off stump. Swing signifies the type of ball Flintoff to Dhoni, 1 run, Short ball over middle stump, Dhoni swings into a pull and takes it down to fine leg. Swing signifies the way batsman played the ball Matrix Methods in Machine Learning 18/34

58 - Continued Matrix Methods in Machine Learning 19/34 1 The meaning of technical words change when combined with other technical words. 2 Short refers to the type of ball. 3 When combined with leg or midwicket or cover refers to field position. Short on the body, he gets up and nicely plays it to square leg but declines the single. Full outside off, Dhoni reaches out and pushes it to short cover. Matrix Methods in Machine Learning 19/34

59 - Continued Matrix Methods in Machine Learning 19/34 1 The meaning of technical words change when combined with other technical words. 2 Short refers to the type of ball. 3 When combined with leg or midwicket or cover refers to field position. Short on the body, he gets up and nicely plays it to square leg but declines the single. Full outside off, Dhoni reaches out and pushes it to short cover. Matrix Methods in Machine Learning 19/34

60 - Continued Matrix Methods in Machine Learning 19/34 1 The meaning of technical words change when combined with other technical words. 2 Short refers to the type of ball. 3 When combined with leg or midwicket or cover refers to field position. Short on the body, he gets up and nicely plays it to square leg but declines the single. Full outside off, Dhoni reaches out and pushes it to short cover. Matrix Methods in Machine Learning 19/34

61 - Continued Matrix Methods in Machine Learning 19/34 1 The meaning of technical words change when combined with other technical words. 2 Short refers to the type of ball. 3 When combined with leg or midwicket or cover refers to field position. Short on the body, he gets up and nicely plays it to square leg but declines the single. Full outside off, Dhoni reaches out and pushes it to short cover. Matrix Methods in Machine Learning 19/34

62 - Continued Matrix Methods in Machine Learning 19/34 1 The meaning of technical words change when combined with other technical words. 2 Short refers to the type of ball. 3 When combined with leg or midwicket or cover refers to field position. Short on the body, he gets up and nicely plays it to square leg but declines the single. Full outside off, Dhoni reaches out and pushes it to short cover. Matrix Methods in Machine Learning 19/34

63 Matrix Methods in Machine Learning 20/34 Line: Indicates the direction of the ball with respect to batsman s wickets. Matrix Methods in Machine Learning 20/34

64 Matrix Methods in Machine Learning 20/34 Line: Indicates the direction of the ball with respect to batsman s wickets. Line Off Middle Leg outside off bowl straight down leg wide off straight ball wide leg pitch off straight line outside leg off stump on middle leg stump from off into middle Negative pitch middle fine leg middle stump square leg Negative short leg straight bat long leg straight drive Matrix Methods in Machine Learning 20/34

65 Matrix Methods in Machine Learning 20/34 Length: Area where the ball is pitched. Matrix Methods in Machine Learning 20/34

66 Matrix Methods in Machine Learning 20/34 Length: Area where the ball is pitched. Length Short Full Good length short full length bounce fuller good length bouncer overpitch length delivery bumper full toss Negative shortpitch half volley short length back length toss up full length Negative blockhole back length short midwicket fuller length short cover shorten length short leg Matrix Methods in Machine Learning 20/34

67 Matrix Methods in Machine Learning 20/34 Line and Length Coverage: Majority of the balls are short placed outside off stump. Matrix Methods in Machine Learning 20/34

68 Matrix Methods in Machine Learning 20/34 Type: Refers to swing, spin or a normal delivery. Quality: Ball is good or bad as described by commentator. Spin Swing Good ball Poor Ball spin swing away good bowling poor bowling turn swing in good ball poor ball googly swing back great ball poor line doosra late swing superb ball bad line topspin inswing well bowled bad delivery legspin outswing tight line bad ball offspin reverse swing good delivery superb delivery jaffa Matrix Methods in Machine Learning 20/34

69 Matrix Methods in Machine Learning 20/34 Speed and Movement: whether ball is moving into the batsman or moving away. Speed Moment Fast Slow Away Into fast slow move away move in pace slower swing away swing in quick turn away turn in quicker seam away seam in angle away angle in Matrix Methods in Machine Learning 20/34

70 - Coverage Matrix Methods in Machine Learning 21/34 Matrix Methods in Machine Learning 21/34

71 - Batting Matrix Methods in Machine Learning 22/34 Attack: A well executed shot or display aggressive play. Attack boundary deep cut sweep pull hook flick third man long on long off down ground Negative down track leave whip defend punch deep crease whack block four leave alone six down under deep edge nice timing shoulder arm great timing push back drive miss Matrix Methods in Machine Learning 22/34

72 - Batting Matrix Methods in Machine Learning 22/34 Defense: Intension of not scoring any run or the delivery is a difficulty one to play a shot. Defense leave shoulder arm defend push back defense play back block tap back leave alone down under Matrix Methods in Machine Learning 22/34

73 - Batting Matrix Methods in Machine Learning 22/34 Shot Type: Various orthodox shots offered. Shot Type drive pull driven hook cut Matrix Methods in Machine Learning 22/34

74 - Batting Matrix Methods in Machine Learning 22/34 Shot Area: Region where the ball is hit. Matrix Methods in Machine Learning 22/34

75 - Batting Matrix Methods in Machine Learning 22/34 Shot Area: Region where the ball is hit. Shot Area R1 R2 R3 R4 R5 R6 third man square mid off mid on square leg fine leg late cut cover long off long on sweep long leg cut point off drive on drive hook leg glance gully square cut straight drive pull Negative square drive flick square cut cover drive midwicket point Negative leg gully square leg Matrix Methods in Machine Learning 22/34

76 - Batting Matrix Methods in Machine Learning 22/34 Shot Area: Region where the ball is hit. Matrix Methods in Machine Learning 22/34

77 - Batting Matrix Methods in Machine Learning 22/34 Weakness: Exhibiting imperfection on a delivery. Weakness miss struck pad beat wrong line edge lbw plumb poor shot hit stump bad shot knock stump out mistimed miss stump out bowled uproot stump out pad expose stump out stump crash stump out lbw crash glove Outcome: Result from batting perspective for a particular delivery. Matrix Methods in Machine Learning 22/34

78 Batting - Weakness, Defense, Attack, Outcome Matrix Methods in Machine Learning 23/34 Matrix Methods in Machine Learning 23/34

79 Batting Overview Matrix Methods in Machine Learning 24/34 Matrix Methods in Machine Learning 24/34

80 Contingency Tables - Example Matrix Methods in Machine Learning 25/34 Every element in the contingency table indicate the frequency of i th row and j th column elements. Length Line Spin Speed Moving short good full midwicket off leg Total Weakness Attack Defend Zero One Two Three Four Five Six Total spin swing Matrix Methods in Machine Learning 25/34 fast slow in-swing out-swing

81 Row Profile, Column Profile, Average Profile Matrix Methods in Machine Learning 26/34 Row Profile: Each element in a row divided with corresponding sum of elements. Length Line Spin Speed Moving short good full midwicket off leg spin Total Every row profile is a point in 12 dimensional feature space. swing fast slow in-swing out-swing Matrix Methods in Machine Learning 26/34

82 Row Profile, Column Profile, Average Profile Matrix Methods in Machine Learning 26/34 Column Profile: Each element in a column divided with corresponding sum of elements. Weakness Attack Defend Zero One Two Total Every column profile is a point in 10 dimensional feature space. Three Four Five Six Matrix Methods in Machine Learning 26/34

83 Row Profile, Column Profile, Average Profile Matrix Methods in Machine Learning 26/34 Average Row Profile: Each element in a total column sum is divided with corresponding sum of elements. Length Line Spin Speed Moving short good full midwicket off leg spin Total swing fast slow in-swing out-swing Matrix Methods in Machine Learning 26/34

84 Problem Formulation Matrix Methods in Machine Learning 27/34 Closeness of profiles to subspace In order to project the 12 dimensional row profiles onto a subspace, the objective is to minimize the sum of the distance between row profiles and subspace. Matrix Methods in Machine Learning 27/34

85 Problem Formulation Matrix Methods in Machine Learning 27/34 Closeness of profiles to subspace Minimize: i r i(d i (S)) 2. Where d i (s) is the distance between i th row profile and the subspace S. and r i is the row sum Matrix Methods in Machine Learning 27/34

86 Three Stage Computation - PCA Like Approach Matrix Methods in Machine Learning 28/34 Stage Symbol Definition Description 1 N indicator P P matrix Records frequencies n i j=1 N ij Grand total of table N r r i = N i. n Row masses c c j = N.j Column masses n P 1 n N Matrix D c (columns columns) diagonal matrix Masses of c on diagonal D r (rows rows) diagonal matrix Masses of r on diagonal A D 1 2 r (P rc T )D 1 2 c Standardized residuals 2 A UΣV T SVD of A 3 F D 1 2 r UΣ Principal component of rows G D 1 2 c VΣ Principal component of columns Table reproduced from Using Analysis to Combine Classifiers, Christopher J. Merz, Machine Learning Journal, Vol. 36, pp: 33-58, Matrix Methods in Machine Learning 28/34

87 Zaheer Khan: Length vs Batting Matrix Methods in Machine Learning 29/34 Figure: Zaheer Khan s weaknesses/strengths. Matrix Methods in Machine Learning 29/34

88 Zaheer Khan: Line vs Batting Matrix Methods in Machine Learning 30/34 Figure: Zaheer Khan s weaknesses/strengths. Matrix Methods in Machine Learning 30/34

89 Zaheer Khan Strength/Weakness Matrix Methods in Machine Learning 31/34 Good length and fast deliveries are always defended by batsmen (quadrant II). Full length deliveries are beaten (quadrant I). Slow balls are driven to boundary (quadrant IV). Spin balls are opportunity for batsmen to tick the score card by at least 2 runs (quadrant IV). Shot balls are driven to boundary (6 runs) (quadrant IV). Matrix Methods in Machine Learning 31/34

90 Mahendra Singh Dhoni s Response Matrix Methods in Machine Learning 32/34 Figure: Mahendra Singh Dhoni s weaknesses. Dhoni gets beaten on spin, swing delivers pitched on the leg stump. Matrix Methods in Machine Learning 32/34

91 Summary Matrix Methods in Machine Learning 33/34 Examples of learning problems such as classification, clustering, dimensionality reduction are discussed. Alternating optimization is introduced. Application of SVD is demonstrated. We do not intend to hurt any ones sentiments by building the above rules. Our intention is limited to strengthening the game through this research. Matrix Methods in Machine Learning 33/34

92 Thank you IEEE ADMAT 2015 Matrix Methods in Machine Learning 34/34 I thank Dr. Gaurav Trivedi, Dr. Indrani Kar, Chairman IEEE SB, Vice Chairman IEEE SB, Entire team of IEEE ADMAT 2015 and Dept. of EEE, IITG for providing this opportunity. Matrix Methods in Machine Learning 34/34