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Tutorial 36- Logistic Regression Indepth Intuition- Part 2| Data Science

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{'title': 'Tutorial 36- Logistic Regression Indepth Intuition- Part 2| Data Science', 'heatmap': [{'end': 106.324, 'start': 84.413, 'weight': 0.781}, {'end': 383.177, 'start': 314.096, 'weight': 0.723}, {'end': 1208.175, 'start': 1186.341, 'weight': 0.748}], 'summary': 'This tutorial delves into logistic regression, covering its significance in binary classification, assumptions, cost function, outlier impact, and the application of the sigmoid function in outlier detection, with specific examples and classifications.', 'chapters': [{'end': 106.324, 'segs': [{'end': 42.529, 'src': 'embed', 'start': 16.481, 'weight': 2, 'content': [{'end': 21.185, 'text': "But today, in this particular video, we'll try to understand how does logistic regression actually work?", 'start': 16.481, 'duration': 4.704}, {'end': 23.006, 'text': 'What is this algorithm all about?', 'start': 21.385, 'duration': 1.621}, {'end': 23.987, 'text': 'You know?', 'start': 23.326, 'duration': 0.661}, {'end': 30.686, 'text': "so in this particular video, first of all we'll discuss about the geometric intuition and then, along with the geometric intuition,", 'start': 23.987, 'duration': 6.699}, {'end': 33.567, 'text': "we'll also try to understand the mathematics intuition behind it.", 'start': 30.686, 'duration': 2.881}, {'end': 40.509, 'text': 'You know it is always better that you combine geometric intuition along with maths to understand any machine learning algorithm.', 'start': 33.927, 'duration': 6.582}, {'end': 42.529, 'text': 'That would be very very beneficial for you.', 'start': 40.849, 'duration': 1.68}], 'summary': 'Explanation of logistic regression with geometric and mathematical intuition for better understanding.', 'duration': 26.048, 'max_score': 16.481, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw16481.jpg'}, {'end': 83.492, 'src': 'embed', 'start': 53.792, 'weight': 0, 'content': [{'end': 58.216, 'text': 'We can also modify logistic regression for multiple classification, multi-class classification.', 'start': 53.792, 'duration': 4.424}, {'end': 60.498, 'text': 'But we have to do some things for that.', 'start': 58.637, 'duration': 1.861}, {'end': 64.662, 'text': 'There are some topics that is called as one versus rest, one versus all.', 'start': 60.799, 'duration': 3.863}, {'end': 67.785, 'text': 'So this kind of topics will be learning in the upcoming parts.', 'start': 64.982, 'duration': 2.803}, {'end': 71.028, 'text': 'But just try to understand here we are focusing on binary classification.', 'start': 67.885, 'duration': 3.143}, {'end': 74.77, 'text': 'Okay So to begin with guys, here I have a problem statement.', 'start': 71.408, 'duration': 3.362}, {'end': 75.57, 'text': 'You can see over here.', 'start': 74.79, 'duration': 0.78}, {'end': 78.171, 'text': 'These are my points, the red color points.', 'start': 76.33, 'duration': 1.841}, {'end': 83.492, 'text': 'Suppose I consider these are my negative points and the blue color points are my positive points.', 'start': 78.471, 'duration': 5.021}], 'summary': 'Introduction to logistic regression for binary classification and upcoming topics for multi-class classification.', 'duration': 29.7, 'max_score': 53.792, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw53792.jpg'}, {'end': 113.254, 'src': 'heatmap', 'start': 84.413, 'weight': 0.781, 'content': [{'end': 86.033, 'text': 'Now, what does logistic regression say?', 'start': 84.413, 'duration': 1.62}, {'end': 94.556, 'text': 'is that logistic regression is usually applied to a problem statement where this two classification problem can be linearly separable.', 'start': 86.033, 'duration': 8.523}, {'end': 98.697, 'text': "Now what does linearly separable means? I'm just going to write it down.", 'start': 94.896, 'duration': 3.801}, {'end': 101.138, 'text': 'Linearly separable.', 'start': 99.357, 'duration': 1.781}, {'end': 106.324, 'text': 'this basically indicates that it can be divided with the help of a straight line.', 'start': 101.698, 'duration': 4.626}, {'end': 113.254, 'text': 'okay, and i hope you remember linear regression also, we create a best fit line and we make sure that the points,', 'start': 106.324, 'duration': 6.93}], 'summary': 'Logistic regression is applied to linearly separable classification problems.', 'duration': 28.841, 'max_score': 84.413, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw84413.jpg'}, {'end': 113.254, 'src': 'embed', 'start': 86.033, 'weight': 1, 'content': [{'end': 94.556, 'text': 'is that logistic regression is usually applied to a problem statement where this two classification problem can be linearly separable.', 'start': 86.033, 'duration': 8.523}, {'end': 98.697, 'text': "Now what does linearly separable means? I'm just going to write it down.", 'start': 94.896, 'duration': 3.801}, {'end': 101.138, 'text': 'Linearly separable.', 'start': 99.357, 'duration': 1.781}, {'end': 106.324, 'text': 'this basically indicates that it can be divided with the help of a straight line.', 'start': 101.698, 'duration': 4.626}, {'end': 113.254, 'text': 'okay, and i hope you remember linear regression also, we create a best fit line and we make sure that the points,', 'start': 106.324, 'duration': 6.93}], 'summary': 'Logistic regression is used for linearly separable classification problems.', 'duration': 27.221, 'max_score': 86.033, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw86033.jpg'}], 'start': 0.269, 'title': 'Understanding logistic regression', 'summary': 'Delves into the significance of logistic regression in binary classification, highlighting its relevance in addressing linearly separable problems and introducing upcoming discussions on multi-class classification.', 'chapters': [{'end': 106.324, 'start': 0.269, 'title': 'Understanding logistic regression', 'summary': 'Discusses the need for logistic regression in binary classification, emphasizing its application to linearly separable problems and the mention of upcoming topics on multi-class classification.', 'duration': 106.055, 'highlights': ['Logistic regression is used for binary classification and can be modified for multi-class classification through topics such as one versus rest and one versus all.', 'The algorithm is applied to problems that are linearly separable, meaning they can be divided with a straight line.', 'The video aims to provide both geometric and mathematical intuition to understand how logistic regression works.']}], 'duration': 106.055, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw269.jpg', 'highlights': ['Logistic regression is used for binary classification and can be modified for multi-class classification through topics such as one versus rest and one versus all.', 'The algorithm is applied to problems that are linearly separable, meaning they can be divided with a straight line.', 'The video aims to provide both geometric and mathematical intuition to understand how logistic regression works.']}, {'end': 643.349, 'segs': [{'end': 165.265, 'src': 'embed', 'start': 125.125, 'weight': 0, 'content': [{'end': 130.127, 'text': 'If I just consider something like a two dimensional graph at that particular point of time, I can call this as a plane.', 'start': 125.125, 'duration': 5.002}, {'end': 138.513, 'text': 'OK, so we need to actually find out this particular best fit line, such that it will be able to linearly separate these two particular points,', 'start': 130.488, 'duration': 8.025}, {'end': 139.634, 'text': 'the classification points.', 'start': 138.513, 'duration': 1.121}, {'end': 141.435, 'text': 'Now, this is pretty much simple, guys.', 'start': 140.134, 'duration': 1.301}, {'end': 147.899, 'text': 'And you obviously know that whenever we are creating this particular straight line, the equation is pretty much simple.', 'start': 141.895, 'duration': 6.004}, {'end': 155.562, 'text': 'the equation, I can write it as y is equal to mx plus c, right? And there are some other notations also, which I have already discussed yesterday.', 'start': 148.379, 'duration': 7.183}, {'end': 165.265, 'text': 'I can also write y is equal to beta 0 plus beta 1 into x, y is equal to wt x plus b, right?', 'start': 156.002, 'duration': 9.263}], 'summary': 'Finding the best fit line for linear separation using y=mx+c or y=β0+β1x equations.', 'duration': 40.14, 'max_score': 125.125, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw125125.jpg'}, {'end': 212.304, 'src': 'embed', 'start': 186.925, 'weight': 1, 'content': [{'end': 191.548, 'text': 'What is the important thing that you need to understand? Because this does not work like linear regression.', 'start': 186.925, 'duration': 4.623}, {'end': 196.131, 'text': 'okay, the best fit line is not calculated with the help of linear regression.', 'start': 192.068, 'duration': 4.063}, {'end': 197.753, 'text': 'there is some other way.', 'start': 196.131, 'duration': 1.622}, {'end': 203.517, 'text': 'we need to find out this exact coefficient, which will be able to understand which is the best fit line,', 'start': 197.753, 'duration': 5.764}, {'end': 206.299, 'text': 'and we need to modify this particular coefficient.', 'start': 203.517, 'duration': 2.782}, {'end': 208.201, 'text': 'okay, coefficient or slopes.', 'start': 206.299, 'duration': 1.902}, {'end': 209.742, 'text': 'in this particular case, it is w.', 'start': 208.201, 'duration': 1.541}, {'end': 212.304, 'text': 'in this particular case, it is m right.', 'start': 209.742, 'duration': 2.562}], 'summary': 'Understanding the coefficient w or m is crucial for finding the best fit line in this non-linear regression scenario.', 'duration': 25.379, 'max_score': 186.925, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw186925.jpg'}, {'end': 244.107, 'src': 'embed', 'start': 222.672, 'weight': 3, 'content': [{'end': 231.698, 'text': 'some of the assumptions that we usually do is that for the positive points, that is for this, blue points, i am going to take it as plus one.', 'start': 222.672, 'duration': 9.026}, {'end': 235.481, 'text': 'okay, i hope you are easily able to understand this thing, because it is important.', 'start': 231.698, 'duration': 3.783}, {'end': 240.424, 'text': 'guys, this is the major assumptions that is actually made in logistic regression.', 'start': 235.481, 'duration': 4.943}, {'end': 244.107, 'text': 'all the positive points is actually denoted as plus one.', 'start': 240.424, 'duration': 3.683}], 'summary': 'In logistic regression, positive points are denoted as plus one.', 'duration': 21.435, 'max_score': 222.672, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw222672.jpg'}, {'end': 383.177, 'src': 'heatmap', 'start': 314.096, 'weight': 0.723, 'content': [{'end': 322.678, 'text': 'Well Okay, let me make a straight line like this and suppose If I have a point somewhere here, Okay.', 'start': 314.096, 'duration': 8.582}, {'end': 325.199, 'text': 'If I have a point somewhere here, this is my plane.', 'start': 322.918, 'duration': 2.281}, {'end': 326.28, 'text': 'Okay This is my plane.', 'start': 325.42, 'duration': 0.86}, {'end': 327.901, 'text': 'I can just write it as this is my plane.', 'start': 326.36, 'duration': 1.541}, {'end': 332.443, 'text': "Okay And with respect to this particular plane, I'll have some coefficients, some W value.", 'start': 328.321, 'duration': 4.122}, {'end': 334.404, 'text': "Right So I'll have some W value.", 'start': 332.503, 'duration': 1.901}, {'end': 336.605, 'text': 'Right I hope it is pretty much clear.', 'start': 335.004, 'duration': 1.601}, {'end': 338.246, 'text': 'We will have some coefficient value.', 'start': 336.645, 'duration': 1.601}, {'end': 346.01, 'text': 'Now, if I want to find out the distance between this particular point and the plane by the help of linear algebra,', 'start': 338.866, 'duration': 7.144}, {'end': 354.629, 'text': 'we usually write the equation as WT of X plus B, divided by the truth value of w.', 'start': 346.01, 'duration': 8.619}, {'end': 361.097, 'text': 'okay?. Now, if we consider this w as a unit vector, this exactly becomes 1, right?', 'start': 354.629, 'duration': 6.468}, {'end': 368.886, 'text': "And apart from this, since the line is passing through the origin, which I'm considering it okay, I'm going to make this b value as 0..", 'start': 361.617, 'duration': 7.269}, {'end': 370.628, 'text': 'So this is nothing but wt of x.', 'start': 368.886, 'duration': 1.742}, {'end': 383.177, 'text': 'Now you can say that Wt of x is nothing, but it is the distance of this particular point, that is my x and this particular plane.', 'start': 372.267, 'duration': 10.91}], 'summary': 'Explaining the concept of distance between a point and a plane using linear algebra with coefficients and equations.', 'duration': 69.081, 'max_score': 314.096, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw314096.jpg'}, {'end': 621.12, 'src': 'embed', 'start': 578.146, 'weight': 4, 'content': [{'end': 584.048, 'text': 'Now what I do is that I will apply a formula wherein I will multiply y multiplied by Wt of x.', 'start': 578.146, 'duration': 5.902}, {'end': 587.055, 'text': 'Understand this particular point, guys.', 'start': 585.515, 'duration': 1.54}, {'end': 593.317, 'text': 'when I multiply Y multiplied by WT of X, it is going to become greater than 0.', 'start': 587.055, 'duration': 6.262}, {'end': 599.718, 'text': 'That basically indicates that if I have this kind of scenario, it is getting easily classified, right?', 'start': 593.317, 'duration': 6.401}, {'end': 606.24, 'text': 'So whenever my Y value and WT of X, that is, the distance within the plane, is positive, right?', 'start': 599.978, 'duration': 6.262}, {'end': 613.022, 'text': "I'm getting a positive value and I know, since I am getting a positive value, this Y of I is properly classified.", 'start': 606.52, 'duration': 6.502}, {'end': 614.042, 'text': 'This is my positive point.', 'start': 613.022, 'duration': 1.02}, {'end': 616.398, 'text': 'I hope you are understanding this.', 'start': 615.037, 'duration': 1.361}, {'end': 619.539, 'text': 'Now understand about the case 2.', 'start': 617.138, 'duration': 2.401}, {'end': 621.12, 'text': 'So I am going to discuss about my case 2.', 'start': 619.539, 'duration': 1.581}], 'summary': 'Using a formula to classify scenarios based on positive values of y and wt of x.', 'duration': 42.974, 'max_score': 578.146, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw578146.jpg'}], 'start': 106.324, 'title': 'Logistic regression and assumptions', 'summary': 'Delves into logistic regression, focusing on finding the best fit line for linearly separating classification points and discussing assumptions, distance calculation, and coefficient calculation methods. it includes specific examples and classifications.', 'chapters': [{'end': 222.672, 'start': 106.324, 'title': 'Logistic regression and best fit line', 'summary': 'Discusses the concept of logistic regression, emphasizing the need to find the best fit line to linearly separate classification points and the methods to calculate the coefficients for the best fit line.', 'duration': 116.348, 'highlights': ['The need to find the best fit line to linearly separate the classification points is emphasized. It is crucial to find the best fit line that can linearly separate the classification points.', 'Discussion on the methods to calculate the coefficients for the best fit line. The chapter explains the various methods, including understanding the coefficients and modifying them to find the best fit line.', 'Explanation of the equation for the best fit line: y = mx + c, y = beta 0 + beta 1 * x, and y = wt x + b. The equation for the best fit line is explained, including variations such as y = mx + c, y = beta 0 + beta 1 * x, and y = wt x + b.']}, {'end': 643.349, 'start': 222.672, 'title': 'Logistic regression assumptions and distance calculation', 'summary': 'Discusses the major assumptions made in logistic regression, including denoting positive points as plus one and negative points as minus one, and explains the calculation of distance between points and the plane using wt of x, with specific examples and classifications.', 'duration': 420.677, 'highlights': ['The major assumptions made in logistic regression involve denoting positive points as plus one and negative points as minus one, which determines the classification of points. The major assumptions made in logistic regression involve denoting positive points as plus one and negative points as minus one, which determines the classification of points.', 'The explanation of calculating the distance between points and the plane using WT of X, where above the plane the distance is positive and below the plane the distance is negative, with specific examples and classifications. The explanation of calculating the distance between points and the plane using WT of X, where above the plane the distance is positive and below the plane the distance is negative, with specific examples and classifications.', 'The application of a formula where multiplying Y by WT of X results in a positive value, indicating proper classification of positive points. The application of a formula where multiplying Y by WT of X results in a positive value, indicating proper classification of positive points.']}], 'duration': 537.025, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw106324.jpg', 'highlights': ['The need to find the best fit line to linearly separate the classification points is emphasized. It is crucial to find the best fit line that can linearly separate the classification points.', 'Discussion on the methods to calculate the coefficients for the best fit line. The chapter explains the various methods, including understanding the coefficients and modifying them to find the best fit line.', 'Explanation of the equation for the best fit line: y = mx + c, y = beta 0 + beta 1 * x, and y = wt x + b. The equation for the best fit line is explained, including variations such as y = mx + c, y = beta 0 + beta 1 * x, and y = wt x + b.', 'The major assumptions made in logistic regression involve denoting positive points as plus one and negative points as minus one, which determines the classification of points. The major assumptions made in logistic regression involve denoting positive points as plus one and negative points as minus one, which determines the classification of points.', 'The explanation of calculating the distance between points and the plane using WT of X, where above the plane the distance is positive and below the plane the distance is negative, with specific examples and classifications.', 'The application of a formula where multiplying Y by WT of X results in a positive value, indicating proper classification of positive points. The application of a formula where multiplying Y by WT of X results in a positive value, indicating proper classification of positive points.']}, {'end': 927.09, 'segs': [{'end': 716.642, 'src': 'embed', 'start': 686.604, 'weight': 3, 'content': [{'end': 687.244, 'text': 'Because understand.', 'start': 686.604, 'duration': 0.64}, {'end': 688.625, 'text': 'This is a negative value.', 'start': 687.604, 'duration': 1.021}, {'end': 690.225, 'text': 'This is a negative value.', 'start': 689.105, 'duration': 1.12}, {'end': 692.406, 'text': 'Negative value multiplied by negative value.', 'start': 690.586, 'duration': 1.82}, {'end': 693.767, 'text': 'Will be a positive value.', 'start': 692.646, 'duration': 1.121}, {'end': 696.088, 'text': 'Now understand one more thing.', 'start': 694.727, 'duration': 1.361}, {'end': 697.028, 'text': 'Again here.', 'start': 696.388, 'duration': 0.64}, {'end': 701.41, 'text': 'Since the multiplication of this particular value is greater than zero.', 'start': 697.528, 'duration': 3.882}, {'end': 706.896, 'text': 'At that time what is happening? This particular point is getting classified correctly.', 'start': 702.253, 'duration': 4.643}, {'end': 710.338, 'text': 'Because we are able to classify this point.', 'start': 707.936, 'duration': 2.402}, {'end': 712.799, 'text': 'Since this particular point is minus 1.', 'start': 710.638, 'duration': 2.161}, {'end': 714.781, 'text': 'Understand in this particular way guys.', 'start': 712.799, 'duration': 1.982}, {'end': 716.642, 'text': 'Now suppose let me take another case.', 'start': 715.021, 'duration': 1.621}], 'summary': 'Negative values multiplied result in a positive value, aiding in correct classification of points.', 'duration': 30.038, 'max_score': 686.604, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw686604.jpg'}, {'end': 789.859, 'src': 'embed', 'start': 748.956, 'weight': 2, 'content': [{'end': 759.923, 'text': 'Right. So if I multiply Y, multiplied by WT of X, this particular value, considering this, will be less than zero, because I have minus one over here,', 'start': 748.956, 'duration': 10.967}, {'end': 761.044, 'text': 'and this is a positive value.', 'start': 759.923, 'duration': 1.121}, {'end': 764.967, 'text': 'Negative value into a positive value will be less than zero.', 'start': 761.645, 'duration': 3.322}, {'end': 772.412, 'text': 'Now, when we have this particular value less than zero at that time, what will happen? Understand this thing is this value.', 'start': 765.927, 'duration': 6.485}, {'end': 775.154, 'text': 'You can see that this red point is incorrectly classified.', 'start': 772.852, 'duration': 2.302}, {'end': 776.654, 'text': 'Right Now.', 'start': 775.854, 'duration': 0.8}, {'end': 782.917, 'text': 'this basically indicates that whenever you do this multiplication of Y and WT of X, if you are getting a negative value,', 'start': 776.654, 'duration': 6.263}, {'end': 786.858, 'text': 'that basically indicates that this is not a correctly classified point.', 'start': 782.917, 'duration': 3.941}, {'end': 788.019, 'text': 'OK, take this particular example.', 'start': 786.878, 'duration': 1.141}, {'end': 789.859, 'text': 'Now, one more example can be this.', 'start': 788.499, 'duration': 1.36}], 'summary': 'Multiplying y by wt of x yields incorrectly classified points if less than zero.', 'duration': 40.903, 'max_score': 748.956, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw748956.jpg'}, {'end': 879.998, 'src': 'embed', 'start': 834.773, 'weight': 0, 'content': [{'end': 843.517, 'text': 'i is equal to 1 to n, w of i multiplied by x of i should be maximum as possible.', 'start': 834.773, 'duration': 8.744}, {'end': 851.601, 'text': 'If I want to create this straight line, the best fit line, which linearly separates to this particular points,', 'start': 844.478, 'duration': 7.123}, {'end': 858.525, 'text': 'I have to make sure that the summation of all the points, along with the distance, should be maximum.', 'start': 851.601, 'duration': 6.924}, {'end': 866.711, 'text': 'Because this indicates when it is greater than 0, all the time when it is greater than 0,, it is correctly classifying all the points,', 'start': 860.187, 'duration': 6.524}, {'end': 868.331, 'text': 'both the positive and the negative points.', 'start': 866.711, 'duration': 1.62}, {'end': 876.476, 'text': 'But if the value of the multiplication of w and wt of x is less than 0, it is not classifying the points properly.', 'start': 869.032, 'duration': 7.444}, {'end': 879.998, 'text': 'So this is basically my cost function.', 'start': 877.416, 'duration': 2.582}], 'summary': 'Maximize summation of w and x to classify points properly.', 'duration': 45.225, 'max_score': 834.773, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw834773.jpg'}], 'start': 644.266, 'title': 'Classification and cost function', 'summary': 'Explains the classification process through multiplication of yi value with wt of x, and discusses linear classification cost function, emphasizing the need to maximize the sum of product of weights and input variables for proper classification.', 'chapters': [{'end': 730.577, 'start': 644.266, 'title': 'Classification and multiplication', 'summary': 'Explains the classification process based on the multiplication of the yi value with the wt of x, leading to correct classification due to negative value multiplication resulting in a positive value.', 'duration': 86.311, 'highlights': ['The yi value is determined to be -1, and when computing WT of X, it becomes less than 0, resulting in a negative value.', 'The multiplication of Y and WT of X yields a value greater than zero due to the negative value multiplied by negative value, resulting in a positive value, leading to correct classification of the point.', 'Explanation of the correct classification process based on the multiplication of negative values and its impact on the classification of specific points.']}, {'end': 927.09, 'start': 730.978, 'title': 'Linear classification cost function', 'summary': 'Discusses the cost function of linear classification, emphasizing the need to maximize the sum of the product of weights and input variables for proper classification, with examples of correctly and incorrectly classified points.', 'duration': 196.112, 'highlights': ['The importance of maximizing the sum of the product of weights and input variables for proper classification The cost function aims to maximize the sum of the product of weights and input variables, ensuring proper classification of points.', 'Examples of correctly and incorrectly classified points based on the multiplication of Y and WT of X Demonstrates how points are correctly or incorrectly classified based on the result of multiplying Y and WT of X, with negative values indicating incorrect classification.', 'The need to update coefficients to achieve maximum summation of all points for proper classification Emphasizes the necessity of updating coefficient weights to achieve the maximum summation of all points, which ensures proper classification.']}], 'duration': 282.824, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw644266.jpg', 'highlights': ['The need to update coefficients to achieve maximum summation of all points for proper classification', 'The importance of maximizing the sum of the product of weights and input variables for proper classification', 'Demonstrates how points are correctly or incorrectly classified based on the result of multiplying Y and WT of X, with negative values indicating incorrect classification', 'Explanation of the correct classification process based on the multiplication of negative values and its impact on the classification of specific points', 'The multiplication of Y and WT of X yields a value greater than zero due to the negative value multiplied by negative value, resulting in a positive value, leading to correct classification of the point', 'The yi value is determined to be -1, and when computing WT of X, it becomes less than 0, resulting in a negative value']}, {'end': 1227.911, 'segs': [{'end': 980.988, 'src': 'embed', 'start': 951.894, 'weight': 0, 'content': [{'end': 954.055, 'text': 'right, pretty much simple guys, understand.', 'start': 951.894, 'duration': 2.161}, {'end': 954.835, 'text': 'one more thing.', 'start': 954.055, 'duration': 0.78}, {'end': 961.398, 'text': "i'll just revise and give, give you an idea about it, and i've referred many, many materials to understand this.", 'start': 954.835, 'duration': 6.563}, {'end': 965.941, 'text': 'you know, when i started learning logistic regression, my understanding was completely different.', 'start': 961.398, 'duration': 4.543}, {'end': 969.362, 'text': 'then, as time moved on, i learned more new, new things.', 'start': 965.941, 'duration': 3.421}, {'end': 973.044, 'text': 'then i got to know the proper algorithm, how it actually works.', 'start': 969.362, 'duration': 3.682}, {'end': 976.266, 'text': 'But still we have not come to a sigmoid function.', 'start': 973.564, 'duration': 2.702}, {'end': 978.287, 'text': 'that will try to understand just after this.', 'start': 976.266, 'duration': 2.021}, {'end': 980.988, 'text': 'But the main aim is that this is my cost function.', 'start': 978.567, 'duration': 2.421}], 'summary': 'Learning logistic regression, understanding the cost function.', 'duration': 29.094, 'max_score': 951.894, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw951894.jpg'}, {'end': 1081.631, 'src': 'embed', 'start': 1055.636, 'weight': 2, 'content': [{'end': 1066.002, 'text': 'we have already found out that the main aim in logistic regression is actually to find out max of summation of i is equal to 1 to n w multiplied by wt of x,', 'start': 1055.636, 'duration': 10.366}, {'end': 1073.186, 'text': 'and this particular value based on the updation of weight, which is giving the maximum value that will actually be used to create the best fit line.', 'start': 1066.002, 'duration': 7.184}, {'end': 1081.631, 'text': 'Now understand one thing guys, what will happen if we have some outliers in logistic regression? Now suppose I have these two data points.', 'start': 1073.786, 'duration': 7.845}], 'summary': 'Logistic regression aims to find the maximum value for creating the best fit line.', 'duration': 25.995, 'max_score': 1055.636, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw1055636.jpg'}, {'end': 1126.213, 'src': 'embed', 'start': 1098.3, 'weight': 1, 'content': [{'end': 1103.903, 'text': 'Now understand one thing, guys there is an outlier that basically means this particular point is somewhere populated over here,', 'start': 1098.3, 'duration': 5.603}, {'end': 1105.363, 'text': 'and this is basically my outlier.', 'start': 1103.903, 'duration': 1.46}, {'end': 1110.446, 'text': 'Now what I told is that we need to find out the summation of Y of I, WT of X of I.', 'start': 1105.924, 'duration': 4.522}, {'end': 1116.769, 'text': 'And remember the positive points is basically given as plus 1, the negative point is basically given as minus 1.', 'start': 1110.446, 'duration': 6.323}, {'end': 1118.77, 'text': 'Now considering this particular thing.', 'start': 1116.769, 'duration': 2.001}, {'end': 1126.213, 'text': 'guys, what we will now find out is that whenever I am trying to find out the distance And let me consider that this all distance are somewhere around 2..', 'start': 1118.77, 'duration': 7.443}], 'summary': 'Identifying outliers and summing y of i, wt of x of i, using +1 for positive and -1 for negative points, considering distances around 2.', 'duration': 27.913, 'max_score': 1098.3, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw1098300.jpg'}, {'end': 1216.057, 'src': 'heatmap', 'start': 1186.341, 'weight': 0.748, 'content': [{'end': 1191.064, 'text': 'Now when I am adding this, this minus 2 will get multiplied by Y.', 'start': 1186.341, 'duration': 4.723}, {'end': 1192.305, 'text': 'So it is nothing but minus 1.', 'start': 1191.064, 'duration': 1.241}, {'end': 1195.612, 'text': 'So this will also become plus 2.', 'start': 1192.305, 'duration': 3.307}, {'end': 1198.833, 'text': 'right. so total value over here you can see that it is 20.', 'start': 1195.612, 'duration': 3.221}, {'end': 1203.754, 'text': 'but we need to still add this this blue point is basically negative 1, right.', 'start': 1198.833, 'duration': 4.921}, {'end': 1208.175, 'text': 'so negative 1 into 500 is nothing but minus 500.', 'start': 1203.754, 'duration': 4.421}, {'end': 1216.057, 'text': 'right now, when i am doing the summation of all these things, this is 20 minus 500, which is actually giving me minus 480.', 'start': 1208.175, 'duration': 7.882}], 'summary': 'The total value is 20, and after adding the negative value of 500, it becomes -480.', 'duration': 29.716, 'max_score': 1186.341, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw1186341.jpg'}], 'start': 927.09, 'title': 'Logistic regression', 'summary': 'Covers logistic regression basics, emphasizing positive and negative values, unit vector use, and learning evolution, alongside logistic regression optimization, focusing on cost function, optimization process, and the need for further optimization.', 'chapters': [{'end': 973.044, 'start': 927.09, 'title': 'Logistic regression basics', 'summary': 'Explains logistic regression, highlighting the importance of positive and negative values, the use of a unit vector, and the evolution of understanding through learning and research.', 'duration': 45.954, 'highlights': ['Logistic regression uses a unit vector and classifies positive values as plus 1 and negative values as minus 1.', 'Understanding of logistic regression evolved through learning and research, leading to a grasp of the proper algorithm.', 'Initial understanding of logistic regression was different, but evolved over time through learning and research.']}, {'end': 1227.911, 'start': 973.564, 'title': 'Logistic regression optimization', 'summary': 'Explains the cost function and optimization process for logistic regression, aiming to find the maximum summation of product of y with w to create the best fit line, considering outliers and the need for further optimization.', 'duration': 254.347, 'highlights': ['The main aim in logistic regression is actually to find out max of summation of i is equal to 1 to n w multiplied by wt of x, and this particular value based on the updation of weight, which is giving the maximum value that will actually be used to create the best fit line. The main goal of logistic regression is to maximize the summation of product of Y with W to create the best fit line.', 'The need to consider outliers in logistic regression and their impact on the distance calculation and summation of Y of I and WT of X, as demonstrated by the example with outlier points. Outliers in logistic regression can impact the distance calculation and summation of Y of I and WT of X, as shown in the example.', 'Illustration of the calculation of the summation of Y of I and WT of X, considering positive and negative points, and the impact of outliers on the overall summation. The example demonstrates the calculation of the summation of Y of I and WT of X, considering positive and negative points and the impact of outliers on the overall summation.']}], 'duration': 300.821, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw927090.jpg', 'highlights': ['Understanding of logistic regression evolved through learning and research, leading to a grasp of the proper algorithm.', 'The need to consider outliers in logistic regression and their impact on the distance calculation and summation of Y of I and WT of X, as demonstrated by the example with outlier points.', 'The main aim in logistic regression is actually to find out max of summation of i is equal to 1 to n w multiplied by wt of x, and this particular value based on the updation of weight, which is giving the maximum value that will actually be used to create the best fit line.']}, {'end': 1401.716, 'segs': [{'end': 1296.951, 'src': 'embed', 'start': 1267.336, 'weight': 2, 'content': [{'end': 1269.958, 'text': 'First of all, let me just rub all this particular value.', 'start': 1267.336, 'duration': 2.622}, {'end': 1273.52, 'text': 'Now suppose I calculate the distance between this point and this point.', 'start': 1270.778, 'duration': 2.742}, {'end': 1277.625, 'text': 'Now suppose I calculate this is plus 1.', 'start': 1274.841, 'duration': 2.784}, {'end': 1278.726, 'text': 'This is plus 1.', 'start': 1277.625, 'duration': 1.101}, {'end': 1284.128, 'text': 'This is plus 1 plus 1, 2 plus 3 plus 4 plus 5 plus 6.', 'start': 1278.726, 'duration': 5.402}, {'end': 1285.729, 'text': "I'm calculating the distance like this.", 'start': 1284.128, 'duration': 1.601}, {'end': 1288.97, 'text': 'Okay Suppose this is my distance like this.', 'start': 1286.429, 'duration': 2.541}, {'end': 1293.733, 'text': 'Okay Similarly, if I calculate a distance like this, it will be also same.', 'start': 1289.391, 'duration': 4.342}, {'end': 1296.951, 'text': '6, 5, 4, 3, 2, 1.', 'start': 1293.753, 'duration': 3.198}], 'summary': 'Calculating distances between points, resulting in a consistent value of 6.', 'duration': 29.615, 'max_score': 1267.336, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw1267336.jpg'}, {'end': 1410.341, 'src': 'embed', 'start': 1381.008, 'weight': 0, 'content': [{'end': 1386.35, 'text': "Now you can understand guys, when we are doing this max of this, I'm getting a positive value over here.", 'start': 1381.008, 'duration': 5.342}, {'end': 1391.132, 'text': 'But with respect to this best fit line, I got a negative value of 480.', 'start': 1386.71, 'duration': 4.422}, {'end': 1393.913, 'text': 'So what will happen? This particular best fit line will get selected.', 'start': 1391.132, 'duration': 2.781}, {'end': 1396.234, 'text': 'And this is the impact of an outlier.', 'start': 1394.453, 'duration': 1.781}, {'end': 1398.475, 'text': 'This is all because of this particular outlier.', 'start': 1396.574, 'duration': 1.901}, {'end': 1401.716, 'text': "What is happening? For this particular case, I've got plus 2.", 'start': 1398.515, 'duration': 3.201}, {'end': 1405.077, 'text': "But for this particular case, I've got minus 480.", 'start': 1401.716, 'duration': 3.361}, {'end': 1410.341, 'text': 'Right So how do we prevent this? How do we prevent this? That is the most important thing.', 'start': 1405.077, 'duration': 5.264}], 'summary': 'Impact of outlier: +2 vs -480, importance of prevention', 'duration': 29.333, 'max_score': 1381.008, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw1381008.jpg'}], 'start': 1228.491, 'title': "Outliers' impact", 'summary': 'Explores the influence of outliers on best fit lines, highlighting distance calculation and the selection of the best fit line, leading to a positive value of 2 despite a negative value of 480.', 'chapters': [{'end': 1401.716, 'start': 1228.491, 'title': 'Impact of outliers on best fit line', 'summary': 'Discusses the impact of outliers on best fit lines, explaining the distance calculation and the influence of outliers on the selection of the best fit line, resulting in a positive value of 2 despite a negative value of 480.', 'duration': 173.225, 'highlights': ['The impact of outliers on best fit lines is illustrated through the calculation of distances, resulting in a positive value of 2 despite a negative value of 480, leading to the selection of the best fit line.', 'The distance calculation involves the summation of distances between points, with positive and negative values, ultimately resulting in a selection based on the presence of an outlier.', 'The chapter emphasizes the influence of outliers on the selection of the best fit line, demonstrating the significant impact of outliers on the overall decision-making process.']}], 'duration': 173.225, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw1228491.jpg', 'highlights': ['The impact of outliers on best fit lines is illustrated through the calculation of distances, resulting in a positive value of 2 despite a negative value of 480, leading to the selection of the best fit line.', 'The chapter emphasizes the influence of outliers on the selection of the best fit line, demonstrating the significant impact of outliers on the overall decision-making process.', 'The distance calculation involves the summation of distances between points, with positive and negative values, ultimately resulting in a selection based on the presence of an outlier.']}, {'end': 1695.511, 'segs': [{'end': 1430.455, 'src': 'embed', 'start': 1401.716, 'weight': 1, 'content': [{'end': 1405.077, 'text': "But for this particular case, I've got minus 480.", 'start': 1401.716, 'duration': 3.361}, {'end': 1410.341, 'text': 'Right So how do we prevent this? How do we prevent this? That is the most important thing.', 'start': 1405.077, 'duration': 5.264}, {'end': 1420.248, 'text': 'For this we just modify this equation by applying a f function around this and we actually calculate the max.', 'start': 1411.281, 'duration': 8.967}, {'end': 1426.972, 'text': 'Now what is this f function? This f function is nothing but sigmoid function.', 'start': 1421.468, 'duration': 5.504}, {'end': 1430.455, 'text': 'Sigmoid function.', 'start': 1429.494, 'duration': 0.961}], 'summary': 'In this case, the loss is -480, and to prevent it, we apply a sigmoid function to modify the equation and calculate the maximum.', 'duration': 28.739, 'max_score': 1401.716, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw1401716.jpg'}, {'end': 1491.809, 'src': 'embed', 'start': 1458.307, 'weight': 0, 'content': [{'end': 1459.087, 'text': 'Let me just consider.', 'start': 1458.307, 'duration': 0.78}, {'end': 1466.852, 'text': 'This is my Z and This particular value is represented as Z, and we will try to place this over here.', 'start': 1459.127, 'duration': 7.725}, {'end': 1469.635, 'text': 'now, What is the speciality of sigmoid function?', 'start': 1466.852, 'duration': 2.783}, {'end': 1475.7, 'text': 'Remember, guys, this distance that you see right over here from here to this particular point right?', 'start': 1470.295, 'duration': 5.405}, {'end': 1477.682, 'text': 'Sorry, from here to this particular point.', 'start': 1475.72, 'duration': 1.962}, {'end': 1482.807, 'text': 'We saw that it is 500 Right now because of this particular outlier.', 'start': 1478.022, 'duration': 4.785}, {'end': 1491.809, 'text': 'there was a bigger impact wherein we skipped our best fit line, and Now, when we are actually multiplying W of I, WT of X of I,', 'start': 1482.807, 'duration': 9.002}], 'summary': 'Discussion on sigmoid function and impact of outlier on best fit line.', 'duration': 33.502, 'max_score': 1458.307, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw1458307.jpg'}, {'end': 1596.027, 'src': 'embed', 'start': 1571.979, 'weight': 3, 'content': [{'end': 1578.044, 'text': 'but just understand, a sigmoid function will actually transform all your summation between 0 to 1, not summation.', 'start': 1571.979, 'duration': 6.065}, {'end': 1585.209, 'text': 'this multiplication between 0 to 1 now, when it is doing that, it is removing the effect of outlier.', 'start': 1578.044, 'duration': 7.165}, {'end': 1592.965, 'text': 'it is the removing the effect of outlier, And that is where this sigmoid function is actually used.', 'start': 1585.209, 'duration': 7.756}, {'end': 1594.966, 'text': 'Remember this particular stuff guys.', 'start': 1593.365, 'duration': 1.601}, {'end': 1596.027, 'text': 'This is the diagram.', 'start': 1595.047, 'duration': 0.98}], 'summary': 'Sigmoid function transforms summation between 0 to 1, removing outlier effect.', 'duration': 24.048, 'max_score': 1571.979, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw1571979.jpg'}, {'end': 1668.441, 'src': 'embed', 'start': 1642.368, 'weight': 4, 'content': [{'end': 1651.835, 'text': 'The main funda of actually finding the best fit line is basically doing this multiplication and then applying this particular activation function,', 'start': 1642.368, 'duration': 9.467}, {'end': 1657.798, 'text': "updating this W value, unless and until you don't get a best fit line that can classify this point.", 'start': 1651.835, 'duration': 5.963}, {'end': 1661.141, 'text': 'And always remember guys, this max is pretty much important.', 'start': 1657.859, 'duration': 3.282}, {'end': 1668.441, 'text': 'Summation of all this particular stuff, all these particular points, along with this distance should be maximum.', 'start': 1662.293, 'duration': 6.148}], 'summary': 'Finding best fit line involves multiplication, activation function, updating w value for classification.', 'duration': 26.073, 'max_score': 1642.368, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw1642368.jpg'}], 'start': 1401.716, 'title': 'Sigmoid function in outlier detection', 'summary': 'Explores the application of sigmoid function in outlier detection, achieving a distance reduction of 500 units and transforming multiplication values between 0 to 1 in logistic regression for classification.', 'chapters': [{'end': 1482.807, 'start': 1401.716, 'title': 'Outlier detection with sigmoid function', 'summary': 'Discusses preventing outliers by modifying an equation with a sigmoid function, resulting in a max calculation and a distance reduction of 500 units due to the outlier.', 'duration': 81.091, 'highlights': ['The use of a sigmoid function to modify the equation resulted in a calculation of the max value.', 'The sigmoid function, represented by 1 / (1 + e^(-X)), was applied to the values passed from the equation, leading to a distance reduction of 500 units due to the outlier.', 'The discussion emphasized the importance of preventing outliers in the given case, where an outlier caused a decrease of 480 units prior to modification.']}, {'end': 1695.511, 'start': 1482.807, 'title': 'Logistic regression and sigmoid function', 'summary': 'Explains the use of sigmoid function in logistic regression to transform the multiplication values between 0 to 1, removing the effect of outliers and finding the best fit line for classification.', 'duration': 212.704, 'highlights': ['The sigmoid function transforms the multiplication values between 0 to 1, removing the effect of outliers and finding the best fit line for classification.', 'The main goal of logistic regression is to find the best fit line by doing multiplication and applying the activation function, ensuring the summation of all points is maximum for accurate classification.', 'The impact of skipping the best fit line resulted in a very high negative value leading to the need for transformation using a sigmoid function.', 'The sigmoid function equation is given by 1 plus e to the power of minus z, transforming values between 0 to 1, effectively handling any number of outliers.']}], 'duration': 293.795, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/uFfsSgQgerw/pics/uFfsSgQgerw1401716.jpg', 'highlights': ['The sigmoid function, represented by 1 / (1 + e^(-X)), was applied to the values passed from the equation, leading to a distance reduction of 500 units due to the outlier.', 'The use of a sigmoid function to modify the equation resulted in a calculation of the max value.', 'The discussion emphasized the importance of preventing outliers in the given case, where an outlier caused a decrease of 480 units prior to modification.', 'The sigmoid function transforms the multiplication values between 0 to 1, removing the effect of outliers and finding the best fit line for classification.', 'The main goal of logistic regression is to find the best fit line by doing multiplication and applying the activation function, ensuring the summation of all points is maximum for accurate classification.']}], 'highlights': ['Logistic regression is used for binary classification and can be modified for multi-class classification through topics such as one versus rest and one versus all.', 'The algorithm is applied to problems that are linearly separable, meaning they can be divided with a straight line.', 'The video aims to provide both geometric and mathematical intuition to understand how logistic regression works.', 'The need to find the best fit line to linearly separate the classification points is emphasized.', 'It is crucial to find the best fit line that can linearly separate the classification points.', 'Discussion on the methods to calculate the coefficients for the best fit line.', 'Explanation of the equation for the best fit line: y = mx + c, y = beta 0 + beta 1 * x, and y = wt x + b.', 'The major assumptions made in logistic regression involve denoting positive points as plus one and negative points as minus one, which determines the classification of points.', 'The explanation of calculating the distance between points and the plane using WT of X, where above the plane the distance is positive and below the plane the distance is negative, with specific examples and classifications.', 'The application of a formula where multiplying Y by WT of X results in a positive value, indicating proper classification of positive points.', 'The need to update coefficients to achieve maximum summation of all points for proper classification.', 'The importance of maximizing the sum of the product of weights and input variables for proper classification.', 'Demonstrates how points are correctly or incorrectly classified based on the result of multiplying Y and WT of X, with negative values indicating incorrect classification.', 'Explanation of the correct classification process based on the multiplication of negative values and its impact on the classification of specific points.', 'The multiplication of Y and WT of X yields a value greater than zero due to the negative value multiplied by negative value, resulting in a positive value, leading to correct classification of the point.', 'The yi value is determined to be -1, and when computing WT of X, it becomes less than 0, resulting in a negative value.', 'Understanding of logistic regression evolved through learning and research, leading to a grasp of the proper algorithm.', 'The need to consider outliers in logistic regression and their impact on the distance calculation and summation of Y of I and WT of X, as demonstrated by the example with outlier points.', 'The main aim in logistic regression is actually to find out max of summation of i is equal to 1 to n w multiplied by wt of x, and this particular value based on the updation of weight, which is giving the maximum value that will actually be used to create the best fit line.', 'The impact of outliers on best fit lines is illustrated through the calculation of distances, resulting in a positive value of 2 despite a negative value of 480, leading to the selection of the best fit line.', 'The chapter emphasizes the influence of outliers on the selection of the best fit line, demonstrating the significant impact of outliers on the overall decision-making process.', 'The distance calculation involves the summation of distances between points, with positive and negative values, ultimately resulting in a selection based on the presence of an outlier.', 'The sigmoid function, represented by 1 / (1 + e^(-X)), was applied to the values passed from the equation, leading to a distance reduction of 500 units due to the outlier.', 'The use of a sigmoid function to modify the equation resulted in a calculation of the max value.', 'The discussion emphasized the importance of preventing outliers in the given case, where an outlier caused a decrease of 480 units prior to modification.', 'The sigmoid function transforms the multiplication values between 0 to 1, removing the effect of outliers and finding the best fit line for classification.', 'The main goal of logistic regression is to find the best fit line by doing multiplication and applying the activation function, ensuring the summation of all points is maximum for accurate classification.']}