From 83f6a11381ce1baa19715422a1b26fe67628f7e4 Mon Sep 17 00:00:00 2001 From: Hongwei Qin Date: Tue, 3 Feb 2015 16:12:58 +0800 Subject: [PATCH 1/2] minor typos --- classification.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/classification.md b/classification.md index 8b6fe056..809fdb38 100644 --- a/classification.md +++ b/classification.md @@ -281,4 +281,4 @@ Here are some (optional) links you may find interesting for further reading: - [A Few Useful Things to Know about Machine Learning](http://homes.cs.washington.edu/~pedrod/papers/cacm12.pdf), where especially section 6 is related but the whole paper is a warmly recommended reading. -- [Recognizing and Learning Object Categories](http://people.csail.mit.edu/torralba/shortCourseRLOC/index.html), a short course of object categorization at ICCV 2015 +- [Recognizing and Learning Object Categories](http://people.csail.mit.edu/torralba/shortCourseRLOC/index.html), a short course of object categorization at ICCV 2005. From 83be4daffad7035af10d71f2128809278d76b8a1 Mon Sep 17 00:00:00 2001 From: Hongwei Qin Date: Thu, 5 Feb 2015 14:29:40 +0800 Subject: [PATCH 2/2] correct a typo --- linear-classify.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/linear-classify.md b/linear-classify.md index 0091b9f0..56601aab 100644 --- a/linear-classify.md +++ b/linear-classify.md @@ -57,7 +57,7 @@ Notice that a linear classifier computes the score of a class as a weighted sum
An example of mapping an image to class scores. For sake of visualization we assume the image only has 4 pixels and that we have 3 classes (red, blue, green class). We stretch the image pixels into a column and perform matrix multiplication to get the scores for each class. Note that this particular set of weights W is not good at all: the weights assign our cat image a very low cat score. In particular, this set of weights seems convinced that it's looking at a dog.
-**Analogy of images as high-dimensional points.** Since the images are stretched into high-dimensional column vectors, we can interpret each image as a single point in this space (e.g. each image in CIFAR-10 is a point in 3072-dimensional space of 32x32x3 images). Analogously, the entire dataset is a (labeled) set of points. +**Analogy of images as high-dimensional points.** Since the images are stretached into high-dimensional column vectors, we can interpret each image as a single point in this space (e.g. each image in CIFAR-10 is a point in 3072-dimensional space of 32x32x3 images). Analogously, the entire dataset is a (labeled) set of points. Since we defined the score of each class as a weighted sum of all image pixels, each class score is a linear function over this space. We cannot visualize 3072-dimensional spaces, but if we imagine squashing all those dimensions into only two dimensions, then we can try to visualize what the classifier might be doing: @@ -113,7 +113,7 @@ For example, going back to the example image of a cat and its scores for the cla #### Multiclass Support Vector Machine loss -There are several ways to define the details of the loss function. As a first example we will first develop a commonly used loss called the **Multiclass Support Vector Machine** (SVM) loss. The SVM loss is set up so that the SVM "wants" the correct class for each image to a have a score higher than the incorrect classes by some fixed margin \\(\Delta\\). Notice that it's sometimes helpful to antropomorphise the loss functions as we did above: The SVM "wants" a certain outcome in the sense that the outcome would yield a lower loss (which is good). +There are several ways to define the details of the loss function. As a first example we will first develop a commonly used loss called the **Multiclass Support Vector Machine** (SVM) loss. The SVM loss is set up so that the SVM "wants" the correct class for each image to a have a score higher than the incorrect classes by some fixed margin \\(\Delta\\). Notice that it's sometimes helpful to anthropomorphise the loss functions as we did above: The SVM "wants" a certain outcome in the sense that the outcome would yield a lower loss (which is good). Lets now get more precise. Recall that for the i-th example we are given the pixels \\( x\_i \\) and the label \\( y\_i \\) that specifies the index of the correct class. The score function takes the pixels and computes the vector \\( f(x\_i, W) \\) of class scores. For example, the score for the j-th class is the j-th element: \\( f(x\_i, W)\_j \\). The Multiclass SVM loss for the i-th example is then formalized as follows: