Random Forests and Ferns 随机树和随机蕨的讲解.pdf

发布时间：2022-06-13 发布人：admin 分类：说明书资料大小：5.73M 资料格式：pdf 举报版权申诉

67f773ff-a89a-4686-8272-351f6b075ce4.pdf-第1页.png

第1页 / 共40页

67f773ff-a89a-4686-8272-351f6b075ce4.pdf-第2页.png

第2页 / 共40页

67f773ff-a89a-4686-8272-351f6b075ce4.pdf-第3页.png

第3页 / 共40页

67f773ff-a89a-4686-8272-351f6b075ce4.pdf-第4页.png

第4页 / 共40页

67f773ff-a89a-4686-8272-351f6b075ce4.pdf-第5页.png

第5页 / 共40页

67f773ff-a89a-4686-8272-351f6b075ce4.pdf-第6页.png

第6页 / 共40页

67f773ff-a89a-4686-8272-351f6b075ce4.pdf-第7页.png

第7页 / 共40页

67f773ff-a89a-4686-8272-351f6b075ce4.pdf-第8页.png

第8页 / 共40页

文本预览

Random Forests and Ferns David Capel

The Multi-class Classiﬁcation Problem Fergus, Zisserman and Perona 276 276 Fergus, Zisserman and Perona Training: Labelled exemplars representing multiple classes Handwritten digits Planes Faces Cars Cats 276 Fergus, Zisserman and Perona Classifying: to which class does this new example belong? ? ? Figure 1. Some sample images from the datasets. Note the large variation in scale in, for example, the cars (rear) database. These datasets are from both http://www.vision. caltech.edu/html-ﬁles/archive.html and http://www.robots. ox.ac.uk vgg/data/, except for the Cars (Side) from (http://l2r.cs.uiuc.edu/ cogcomp/ index research.html) and Spotted Cats from the Corel Image library. A Powerpoint presentation of the ﬁgures Figure 1. Some sample images from the datasets. Note the large variation in scale in, for example, the cars (rear) database. These datasets are from both http://www.vision. caltech.edu/html-ﬁles/archive.html and http://www.robots. ox.ac.uk vgg/data/, except for the Cars (Side) from (http://l2r.cs.uiuc.edu/ cogcomp/ index research.html) and Spotted Cats from the Corel Image library. A Powerpoint presentation of the ﬁgures

The Multi-class Classiﬁcation Problem • A classiﬁer is a mapping H from feature vectors f to discrete class labels C f = (f1, f2, ..., fN) C ∈ {c1, c2, ..., cK} H : f → C P (C = ci|f1, f2, ..., fN) • Numerous choices of feature space F are possible, e.g. H(f) = arg max P (C = ci|f1, f2, ..., fN) i Dm = (f m, Cm) for m = 1...M Raw pixel values Gij = Texton histograms 1 2! 1 n"k (d2 ik + d2 kj) − d2 ij − Color histograms Oriented ﬁlter banks kl# d2 1 n2"kl

C ∈ {c1, c2, ..., cK} H : f → C The Multi-class Classiﬁcation Problem P (C = ci|f1, f2, ..., fN) • We have a (large) database of labelled exemplars P (C = ci|f1, f2, ..., fN) H(f) = arg max i Dm = (f m, Cm) for m = 1...M • Problem: Given such training data, learn the mapping H 1 Gij = • Even better: learn the posterior distribution over class label H(f) = arg max conditioned on the features: ..and obtain classiﬁer H as the mode of the posterior: 1 kl# d2 f = (f1, f2, ..., fN) 2! 1 n"k n2"kl C ∈ {c1, c2, ..., cK} kj) − d2 ik + d2 (d2 ij − H : f → C f = (f1, f2, ..., fN) P (C = ci|f1, f2, ..., fN) C ∈ {c1, c2, ..., cK} f = (f1, f2, ..., fN) err(y) ="ij $Gij − y!i yj%2 C ∈ {c1, c2, ..., cK} i P (C = ck|f1, f2, ..., fN) P (C = ck|f1, f2, ..., fN) yαi =&λαvαi 2! 1 n"k P (C = ci|f1, f2, ..., fN) H : f → C H : f → C P (C = ck|f1, f2, ..., fN) for m = 1...M P (C = ck|f1, f2, ..., fN) for m = 1...M 1 kj) − d2 Dm = (f m, Cm) ik + d2 n2"kl H(f) = argmax Dm = (f m, Cm) H(f) = argmax k for α =1,2,...,d ij − (d2 k kl# d2 1 Gij =

How do we represent and learn the mapping? In Bishop’s book, we saw numerous ways to build multi-class classiﬁers, e.g. • Direct, non-parametric learning of class posterior (histograms) • K-Nearest Neighbours • Fisher Linear Discriminants • Relevance Vector Machines • Multi-class SVMs y t i s n e n t f1 i l i e x p e g d E Class A Class B 0.2 0.4 0.6 0.8 1 1 ! Specificity (c) Center pixel intensity Direct, non-parametric f2 (d) k-Nearest Neighbours

Binary Decision Trees • Decision trees classify features by a series of Yes/No questions • At each node, the feature space is split according to the outcome of some binary decision criterion • The leaves are labelled with the class C corresponding the feature reached via that path through the tree B1(f)=True? No Yes B2(f)=True? B3(f)=True? No Yes No Yes c1 c2 c1 c1

Binary Decision Trees • Decision trees classify features by a series of Yes/No questions • At each node, the feature space is split according to the outcome of some binary decision criterion • The leaves are labelled with the class C corresponding the feature reached via that path through the tree f B1(f)=True? B1(f)=True? No Yes B2(f)=True? B3(f)=True? No Yes No Yes c1 c2 c1 c1

Binary Decision Trees • Decision trees classify features by a series of Yes/No questions • At each node, the feature space is split according to the outcome of some binary decision criterion • The leaves are labelled with the class C corresponding the feature reached via that path through the tree f B1(f)=True? B1(f)=True? No Yes Yes B2(f)=True? B3(f)=True? B3(f)=True? No Yes No Yes c1 c2 c1 c1

分享到：

赞收藏

资料库

Random Forests and Ferns 随机树和随机蕨的讲解.pdf

相关推荐

课程资源

热门标签

最新资料