iccv iccv2013 iccv2013-352 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Oisin Mac Aodha, Gabriel J. Brostow
Abstract: Typical approaches to classification treat class labels as disjoint. For each training example, it is assumed that there is only one class label that correctly describes it, and that all other labels are equally bad. We know however, that good and bad labels are too simplistic in many scenarios, hurting accuracy. In the realm of example dependent costsensitive learning, each label is instead a vector representing a data point’s affinity for each of the classes. At test time, our goal is not to minimize the misclassification rate, but to maximize that affinity. We propose a novel example dependent cost-sensitive impurity measure for decision trees. Our experiments show that this new impurity measure improves test performance while still retaining the fast test times of standard classification trees. We compare our approach to classification trees and other cost-sensitive methods on three computer vision problems, tracking, descriptor matching, and optical flow, and show improvements in all three domains.
Reference: text
sentIndex sentText sentNum sentScore
1 In the realm of example dependent costsensitive learning, each label is instead a vector representing a data point’s affinity for each of the classes. [sent-9, score-0.204]
2 We propose a novel example dependent cost-sensitive impurity measure for decision trees. [sent-11, score-0.65]
3 Our experiments show that this new impurity measure improves test performance while still retaining the fast test times of standard classification trees. [sent-12, score-0.62]
4 We compare our approach to classification trees and other cost-sensitive methods on three computer vision problems, tracking, descriptor matching, and optical flow, and show improvements in all three domains. [sent-13, score-0.306]
5 , C} is its corresponding class label, the test-time goal of classification is to label an unseen feature vector x∗ with one of C discrete class labels. [sent-25, score-0.238]
6 The disjoint formulation of the classification problem is well suited to scenarios where each feature vector can be assigned a discrete class label, e. [sent-27, score-0.211]
7 Cost-sensitive learning is concerned with the situation where the classification task may not be disjoint [9, 30, 6]. [sent-30, score-0.196]
8 For example, when computing the optical flow field between a pair of images, we may have access to several different algorithms, each with differing strengths and weaknesses. [sent-31, score-0.169]
9 Each specialist (or in this case algorithm) is said to have a task score, a measure of their competence at performing that task, evaluated against known ground truth (available only at training time). [sent-34, score-0.654]
10 A lone specialist might have a significantly higher task score in certain scenarios, while in others, multiple specialists could be comparably accurate. [sent-35, score-0.897]
11 The key here is that we are not only interested in specialists that score well, but more importantly, yn the differences between them. [sent-36, score-0.397]
12 More specifically, in costsensitive classification we are presented with a set of specialists S, where C = |S|, and a set of training examples yn ? [sent-37, score-0.492]
13 label vector is a continuous value, 0 ≤ ≤ 1, representing specialist c’s task score. [sent-45, score-0.628]
14 More concretely, for a given task instance x we wish to find the specialist c ∈ S that produces the maximum task score. [sent-47, score-0.707]
15 yn Lcs (c, f(c, x)) = 1 − f(c, x) , (1) where f(c, x) is the task score for specialist c on task instance x, with a best possible task score of 1, and 0 as the worst. [sent-49, score-0.944]
16 Given a new at test time, we wish to assign a proportionally higher suitability probability to specialists that give superior task scores. [sent-50, score-0.453]
17 We propose a novel impurity measure for decision trees, which takes task (i. [sent-51, score-0.653]
18 Our experiments show how computer vision tasks such as tracking, descriptor matching and optical flow estimation can be posed as example dependent cost-sensitive learning x∗ problems. [sent-55, score-0.327]
19 Our novel impurity measure has the benefits of higher accuracy at test time, simpler decision boundaries, and fast test time performance, at the expense of a moderate increase in training time. [sent-56, score-0.689]
20 In CCS, costs are defined using a cost matrix and all misclassifications for a given class are considered equal e. [sent-64, score-0.174]
21 In ECS, different costs are associated with misclassifying each individual datapoint e. [sent-67, score-0.217]
22 Different approaches have been proposed to solve the example dependent cost-sensitive learning problem, such as reweighting the training examples based on their cost [10, 2]. [sent-71, score-0.191]
23 There are three main ways in which cost information can be incorporated into decision trees during training. [sent-80, score-0.216]
24 A variant of their method is illustrated on an ensemble of trees where each tree samples with replacement from the training data, and samples are drawn proportionately to their cost. [sent-84, score-0.254]
25 The next option is to alter the class distribution at each node so it is cost aware. [sent-85, score-0.283]
26 [6] alter the node posterior by weighting it by the cost vector for each class (the cost vector is the sum across each column of the cost matrix for the class of interest). [sent-87, score-0.5]
27 A drawback of both methods is that they will create the same trees for different cost matrices if summing the cost matrix columns happens to produce the same totals. [sent-89, score-0.187]
28 This perhaps explains the similar performance for multiclass classification when compared to standard classification in [23]. [sent-90, score-0.168]
29 The last option, the one being employed in this paper, is to create a novel impurity measure that is designed specifically for the example cost-sensitive case. [sent-91, score-0.494]
30 This lack of data meant that experimental validation was typically performed by artificially generating cost matrices for standard machine learning datasets based on class frequency in the training set e. [sent-95, score-0.159]
31 However, increasingly there are classification problems in which these example dependent costs are available naturally [13, 18]. [sent-102, score-0.228]
32 Cost-Sensitive Discriminative Classifier We propose a novel multi-class example dependent costsensitive classification algorithm, which takes into account the full label vector information when building the classifier. [sent-107, score-0.278]
33 Random Forests To review, a Random Forest is an ensemble of decision trees [6], where each tree is trained independently on a random subset of the data. [sent-112, score-0.284]
34 Trees are grown recursively from the root node where at each node, P, a set of random splitting decisions is proposed that attempt to separate the datapoints landing at the node into its left (L) and right (R) child nodes. [sent-113, score-0.409]
35 Decision trees greedily minimize a loss function at each node to partition the data. [sent-114, score-0.233]
36 To compute the information gain of (2), we need to calculate the impurity I(·) at each node. [sent-120, score-0.46]
37 The goal of the impurity measure is to determine how much disagreement there is among the datapoint labels at that node. [sent-121, score-0.597]
38 For classification, a node has minimum impurity when all the data points at the node belong to the same class, and maximum when they are all equally different. [sent-122, score-0.745]
39 As illustrated in Section 4, we use Igini as the representative cost-oblivious impurity measure when growing a forest of classification decision trees. [sent-131, score-0.784]
40 (6) N∗ is the subset of datapoints N that landed at the node, and μy is the mean label value in N∗ . [sent-135, score-0.234]
41 Cost-Sensitive Impurity Measure Standard classification impurity measures cannot utilize the task scores at training time. [sent-139, score-0.699]
42 We could ignore the task scores (see the CLRF baseline) and set the class label for a given example to the specialist that produces the highest task score, c = arg maxc ycn. [sent-141, score-0.814]
43 Gini-impurity Cost-Sensitive Random Forest (GCSRF): The simplest way to use the task scores would be to adapt the C dimensional class posterior p at each xn node. [sent-143, score-0.281]
44 Instead of counting the number of examples from each class that lands at a node (N∗), we could use their task scores directly to weight the normalized frequency for each class. [sent-144, score-0.332]
45 This altering of the class posterior at the node has been explored for class dependent cost-sensitive learning [23, 6]. [sent-145, score-0.353]
46 For this class dependent version, each element of the modified node posterior is computed as = ? [sent-146, score-0.302]
47 k=1 We can now use these new posteriors in any of the standard classification impurity measures, and use Gini for this baseline, for better comparison to the Gini-based CLRF. [sent-153, score-0.534]
48 PairWise Cost-Sensitive Random Forest (PWCSRF): In practice, we are interested not in the absolute task scores for each datapoint, but in the relative difference for each specialist’s score for that example. [sent-154, score-0.207]
49 With this aim, we define an impurity measure based on the pairwise difference between the task scores in the label vector, i. [sent-156, score-0.689]
50 how much better is one specialist than another, Ics=C21− Ci? [sent-158, score-0.484]
51 (8) The pairwise specialist empirical frequency fi→j is com- puted between every pair of classes for every datapoint in N∗, resulting in C2 − C comparisons of fi→j=n∈? [sent-162, score-0.637]
52 We will refer to the standard classification Random Forest with Igini impurity measure as CLRF, the example dependent cost-sensitive forest with Gini impurity using the cost aware posterior of (7) as GCSRF, and our forest with pairwise cost-sensitive impurity measure as PWCSRF. [sent-168, score-2.001]
53 Insight Into Proposed Impurity Measure Figure 1 illustrates the node-impurity binary classification curves for different classification impurity measures. [sent-170, score-0.608]
54 195 Again, during training, potential splits are accepted or rejected for a node in a tree on the basis of the node impurity. [sent-171, score-0.327]
55 Also displayed are the impurity scores for two example sets of datapoints, N1and N2. [sent-172, score-0.511]
56 The label vectors along with impurity values for both sets in this toy example are presented in Table 1. [sent-173, score-0.528]
57 Both sets contain four datapoints, the only difference being that in N2 one of the datapoints has a very similar task score for the two specialists (red and green). [sent-174, score-0.556]
58 For N1, which contains disjoint labels, our newly proposed cost-sensitive measure Ics simply produces the same impurity as Igini and Icsg (Gini impurity using the cost aware posterior of (7)). [sent-175, score-1.118]
59 Ics exploits the fact that the red specialist will give a high task score for the whole set. [sent-177, score-0.64]
60 This is because for three observations, the red specialist scores best, and has a very similar score to the green specialist for the fourth observation. [sent-178, score-1.093]
61 Unlike our Ics, alternative impurity measures can overlook a good split because they are over-sensitive to negligible differences in the label vector (see Table 1). [sent-179, score-0.522]
62 It is unable to look at pairwise differences, producing a high impurity even when the difference between specialists is negligible. [sent-181, score-0.739]
63 Comparison of node-impurity binary classification curves for different impurity measures (note that both Ics and Ient are scaled) for the binary classification problem. [sent-196, score-0.608]
64 Low impurity indicates a good grouping of the data. [sent-198, score-0.46]
65 Outside the graph, solid colored discs represent datapoints best described by one of two specialists (red or green), while a disc with a colored cross indicates only a slight preference for one over the other. [sent-199, score-0.492]
66 Ics and Igini return the same impurity for the standard binary classification task N1, while in the non-disjoint case, N2, Ics recognizes that the red specialist achieves a relatively high task score, resulting in a much lower impurity. [sent-200, score-1.182]
67 Synthetic Example In the toy example of Figure 2, we generate datapoints at random from an underlying known distribution. [sent-203, score-0.197]
68 Here we have two specialists, where datapoints in the green region are best described by the first specialist (yn = (1, 0)), in the red by the second specialist (yn = observations N1 and N2, each containing four datapoints. [sent-205, score-1.111]
69 y represents the label vector, while y is the index of the specialist with the best task score. [sent-207, score-0.606]
70 For the white region, the color of the cross in the center represents the specialist that is marginally better (may require zooming in). [sent-213, score-0.505]
71 At test time, we evaluate the probability of each location in the feature space and illustrate the posterior specialist suitability probability for each example. [sent-214, score-0.615]
72 For this illustrative example, we chose the following pa- rameters: 500 training points, 10 trees, 60 random tests at each node, and a minimum node count of 3. [sent-215, score-0.293]
73 We grow trees down to a maximum specified depth, unless the minimum sample count at a node is reached, and there is no pruning of the final trees. [sent-225, score-0.271]
74 A) Ground truth distribution from which training data points are randomly of the feature space where one of the two specialists is superior. [sent-263, score-0.289]
75 Red and green regions indicate areas If an example comes from the white region it is close to equally well represented by either specialist (white points with colored crosses). [sent-265, score-0.557]
76 Unless otherwise stated, for bagging we randomly sample with replacement, ensuring an even number of examples from each specialist per tree. [sent-270, score-0.484]
77 Our label vector contains continuous task score values, but for each observation with the CLRF, we set the class label to be the index of the maximum value of Success is determined not in terms of classification score but task score. [sent-271, score-0.539]
78 The classification score would only measure how often the best specialist was chosen, while the task score measures the real benefit of choosing specialists using a given model. [sent-272, score-1.079]
79 Given an image sequence, and a set of motion models used to track features in that sequence, the goal is to choose the motion model which produces the most accurate tracking score for the whole sequence. [sent-278, score-0.175]
80 The task score is the tracking accuracy for that motion model, with higher values indicating better accuracy. [sent-280, score-0.211]
81 In total, there are 117 datapoints and six different motion models: Brownian, Constant Velocity, Right, Left, Forwards and Backwards. [sent-284, score-0.165]
82 For each of the forest based classifiers, we use the following parameters: 50 trees, 10, 000 random tests at each node, and a minimum sample count of 3. [sent-288, score-0.28]
83 Comparison of the different forest based classifiers on the motion model estimation data from [13]. [sent-300, score-0.183]
84 We can see that OSSVR [24] (with C 1000) has superior performance compared to the forest based methods, but at an even larger increase in training time than required for PWCSRF, and a much longer testing time. [sent-336, score-0.171]
85 specialists correspond to ten different image descriptors that could be used to describe the patch. [sent-338, score-0.257]
86 The task scores are the average precision for each descriptor, with 0 being the worst and 1 the best. [sent-339, score-0.158]
87 We set the number of trees to 200, performed 400 random tests at each node, and had a minimum sample count of 2. [sent-349, score-0.232]
88 We also perform a comparison to univariate regression Forests REGRF, where a separate Forest is trained for each specialist and at test time we choose the winning specialist for a datapoint as the one whos regression Forest predicts the best task score. [sent-354, score-1.284]
89 Optical Flow Given an image pair and a set of optical flow algorithms, in an earlier work we attempted to determine the flow algorithm which would result in the lowest error for each pixel [18]. [sent-357, score-0.251]
90 This was posed as a multi-class classification problem and a standard Random Forest was used to learn the pixel-to-algorithm mapping using a feature vector computed from the image and proposed optical flow fields. [sent-358, score-0.29]
91 Here, our specialists correspond to one of C different optical flow algorithms, with the task score representing the end point error (EPE) for a given optical flow vector for each of the algorithms. [sent-359, score-0.773]
92 (11) Table 3 presents results for leave one out optical flow experiments on 22 different sequences from [18] and 8 from [3]. [sent-377, score-0.169]
93 We randomly sample 8, 000 datapoints with replacement from each of the 22 sequences from [18], ensuring an even distribution of wins for each specialist. [sent-378, score-0.21]
94 The optical flow algorithms chosen as specialists were TV [29], FL [27], CN [21] and LD [7]. [sent-379, score-0.426]
95 We used 50 trees with a minimum sample count of 10, 2000 random tests at each node, maximum possible depth of 20, and set λ = 1. [sent-380, score-0.253]
96 Task score results as a function of tree depth for the different forest based classifiers. [sent-481, score-0.298]
97 Conclusion We have presented a novel impurity measure for tree based classifiers for example dependent cost-sensitive classification. [sent-530, score-0.659]
98 We have shown that posing tracking, descriptor selection, and optical flow estimation as cost-sensitive classification tasks usually results in better test time performance when compared to standard classification trees. [sent-532, score-0.397]
99 In the case of optical flow estimation, our new impurity measure achieves a 10% and 7% improvement in flow accuracy over classification and an alternative ensemble of cost-sensitive trees respectively. [sent-533, score-0.936]
100 Crucially, by exploiting all the task score data available at training time, we can build more representative classifiers that better generalize at test time. [sent-534, score-0.236]
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simIndex simValue paperId paperTitle
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