boundary-defining points of another label should be maximized as much as possible alsothe boundaries do not have to be linear--we can use nonlinear kernels to more flexibly separate the data neural networks we can learn representations of the data using neural networkswhich are composed of an input layerseveral hidden layersand an output layer the input layer uses the featuresand the output layer tries to match the response variable the hidden layers are nested hierarchy of concepts--each layer (or conceptis trying to understand how the previous layer relates to the output layer using this hierarchy of conceptsthe neural network is able to learn complicated concepts by building them out of simpler ones neural networks are one of the most powerful approaches to function approximation but are prone to overfitting and are hard to interpretshortcomings that we will explore in greater detail later in the book closer look at unsupervised algorithms we will now turn our attention to problems where we do not have labels instead of trying to make predictionsunsupervised learning algorithms will try to learn the underlying structure of the data dimensionality reduction one family of algorithms--known as dimensionality reduction algorithms--projects the original high-dimensional input data to low-dimensional spacefiltering out the not-so-relevant features and keeping as much of the interesting ones as possible dimensionality reduction allows unsupervised learning ai to more effectively identify patterns and more efficiently solve large-scalecomputationally expensive problems (often involving imagesvideospeechand textlinear projection there are two major branches of dimensionality--linear projection and nonlinear dimensionality reduction we will start with linear projection first principal component analysis (pcaone approach to learning the underlying structure of data is to identify which features out of the full set of features are most important in explaining the variability among the instances in the data not all features are equal for more on neutral networkscheck out deep learning (lowyoshua bengioand aaron courville (mit pressa closer look at unsupervised algorithms