**Logistic regression** is an algorithm for binary classification. Here's an example of a binary classification problem. You might have an input of an image and want to output a label to recognize this image as either being a cat, in which case you output 1, or not-cat in which case you output 0, and we're going to use y to denote the output label.

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In a binary classification problem** , the result is a discrete value output.

For example

- account hacked (1) or compromised (0)

- a tumor malign (1) or benign (0)

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Let's look at how an image** is represented in a computer. To store an image your computer stores three separate matrices corresponding to the red, green, and blue color channels of this image.

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So if your input image** is 64 pixels by 64 pixels, then you would have 3 - 64 by 64 matrices corresponding to the red, green and blue pixel intensity values for your images.

** So to turn these pixel intensity values** - Into a feature vector, we unroll all of these pixel values into an input feature vector x. To unroll all these pixel intensity values into Feature vector, we define a feature vector x corresponding to this image as follows.

** We're just going to take all the red pixels** , then eventually blue and green pixels. If this image is a 64 by 64 image, the total dimension of this vector x will be 64 * 64 * 3 = 12288 because that's the total numbers we have in all of these matrixes.

**Thus n**_{x}=12288 to represent the dimension of the input features x. So in binary classification, our goal is to learn a classifier that can input an image represented by this feature vector x. And predict whether the corresponding label y is 1 or 0, that is, whether this is a cat image or a non-cat image.