This chapter considers unsupervised learning methods for clustering analysis when the data samples in the given dataset are no longer labeled, including the K-means method and Gaussian mixture model. The K-means algorithm is straight forward in theory and simple to implement. Based on a set of K randomly initialized seeds assumed to be the mean vectors of some K clusters, the algorithm keeps on modifying them iteratively until they become stabilized. The drawback of this method is that the resulting clusters are only characterized by their means, while the shapes of their distribution are not considered. If the distributions of the actual clusters in the dataset are not spherical, they will not be properly represented. This problem can be addressed if the dataset is modeled as a mixture of Gaussian distributions, each characterized by its means and covariance, which are to be estimated iteratively by the expectation maximization (EM) method. The resulting Gaussian clusters reveal the structure of the dataset much more accurately. The k-means and Gaussian mixture methods are analogous, respectively, to the discriminative minimum-distance classifier and the generative Bayesian classifier. Following the same idea of GMM, the last section of this chapter also considers the algorithm of Bernoulli mixture model for clustering of binary data.

This chapter reviews the basic numerical methods for solving equation systems, including fixed-point iteration that will be used while discussing reinforcement learning, and the Newton-Raphson method for solving both univariate and multivariate systems, which is closely related to methods for solving optimization problems to be discussed in the following chapters. Newton’s method is based on the approximation of the function in question by the first two constant and linear terms of its Taylor expansion at an initial guess of the root, which is then iteratively improved to approach the true root where the function is equal to zero. The appendices of the chapter further discuss some important computational issues such as the order of convergence of these methods which may be of interest to more advanced readers.

This chapter considers a set of algorithms for statistic pattern classification, including two simple classifiers based on nearest neighbors and minimum distances, and two more powerful methods of naïve Bayes and adaptive boosting (AdaBoost). The Bayes classifier is a typical generative method based on the assumption that in the training set all data points of the same class are samples from the same Gaussian distribution, and, it classifies any unlabeled data samples into one of the classes with the highest posterior probability of the class given the sample, proportional to the product of the likelihood and prior probability. Differently, the AdaBoost classifier is a typical boosting algorithm (ensemble learning) that iteratively improves a set of weak classifiers.

Zooarchaeological research is guided by the scientific method. Zooarchaeologists distinguish between primary data, which are descriptive observations, and secondary data, which are analytical products derived from primary data. As much primary data as possible should be clearly recorded during the initial study, and these data should be accessible to future researchers.

The ultimate goal of zooarchaeological analysis is to use animal remains, alongside other evidence, to make inferences regarding the biological, cultural, and ecological behavior of people in the past. Secondary data, which are often mathematically derived from primary data, link primary observations about zooarchaeological specimens to larger cultural and ecological processes.

This chapter discusses a two-layer competitive learning network for unsupervised clustering based on a competitive learning rule. The weights of each node of the output layer are treated as a vector, in the same space for the input vectors. Given an input, all nodes compete to become the sole winner (winner-take-all) with the highest output value, so that its weights can be modified in such a way that it will be more likely to win when the same input is presented to the input layer next time. By the end of this iterative learning process, each weight vector is gradually moved toward the center of one of the clusters in the space, thereby representing the cluster. The chapter further considers the self organizing map (SOM), a network based on the same competitive learning rule, but modified in such a way that nodes in the neighborhood of the winner learn along with the winner by modifying their weights as well but to a lesser extent. Once fully trained, the SOM achieves the effect that neighboring nodes learn to respond to similar inputs, mimicking a typical behavior of certain visual and auditory cortex in the brain.

This chapter first introduces a simple two-layer perceptron network based on some straight forward learning rule. This perceptron network can be used as a linear classifier capable of multiclass classification if the classes are linearly separable, which can be further generalized for nonlinear classification when the kernel method is introduced into the algorithm. The main algorithm discussed in this chapter is the multi-layer (3 or more) back propagation network which is a supervised method most widely used for classification, and also serves as one of the building blocks of the much more powerful deep learning method and other artificial intelligence methods. Based on the labeled sample in the training set, the weights of the back propagation network are sequentially modified in the training process in such a way that the error, the difference between the actual out and the desired outputs, the ground truth labeling of its input, is reduced by the gradient descent method. Based on the same training process, this network can be modified to serve as an autoencoder for dimensionality reduction, similar to what the PCA can do.

This chapter discusses the basic methods for solving unconstrained optimization problems, which plays an important role in ML, as many learning problems are solved by either maximizing or minimizing some objective function. The solution of an optimization problem, the point at which the given function is minimized, can be typically found by either gradient descent or Newton’s method. The gradient descent method approaches the solution iteratively from an initial guess by moving in the opposite direction of the gradient, while Newton’s method finds the solution based on the second order derivative as well as the first order, the gradient. It is therefore a more effective method than the gradient method due to the extra piece of information, with a higher computational cost for calculating the second order derivatives. In fact, Newton’s method for minimizing a function is essentially solving an equation resulting from setting the derivative of the function to zero, i.e., it is essentially the same method used for solving equations considered previously. The chapter also considers some variants of Newton’s method, including the quasi-Newton methods and the conjugate gradient method requiring fewer iteration steps.

This chapter considers some basic concepts of essentail importance in supervised learning, of which the fundamental task is to model the given dataset (training set) so that the model prediction matches the given data optimally in certain sense. As typically the form of the model is predetermined, the task of supervised learning is essentially to find the optimal parameters of the model in either of two ways: (a) the least squares estimation (LSE) method that minimizes the squared error between the model prediction and observed data, or (b) the maximum A posteriori (MAP) method that maximizes the posterior probability of the model parameters given the data is maximized. The chapter further considers some important issues including overfitting, underfitting, and bias-variance tradeoff, faced by all supervised learning methods based on noisy data, and then some specific methods to address such issues, including cross-validation, regularization, and ensemble learning.

A key dimension of human–animal relationships is predation. People pursue animal resources that support life and health, while ensuring that the costs required to find, catch, transport, process, distribute, and consume these foods do not exceed the benefits they offer. Animals play a key role in human subsistence strategies, and their use and meaning is woven into all other facets of human life, from the sacred to the profane.

This chapter discusses the most basic frequentist method, the linear least squares (LLS) regression, for obtaining the optimal weights for the linear regression model that minimizes the squared error between the model prediction and observation. The chapter also considers how the goodness of its results can be evaluated quantitatively by the coefficient of determination (R-squared). The chapter then further discusses some variations of LLS, including ridge regression with an extra regularization term to make proper tradeoff between overfitting and underfitting, and linear method based on basis functions for nonlinear regression problems. Finally the last section of the chapter briefly discusses the Bayes methods that maximizes the likelihood and the posterior probability of the parameters of the linear regression model. This section serves to prepare the reader for discussion of various Bayesian learning algorithms in future chapters.

Knowledge drawn from ecology, the study of interactions between organisms and their environments, is critical to zooarchaeological interpretation. Using theories and methods common in modern ecology, zooarchaeological research demonstrates the profound impact of human behavior on ecosystems across space and time. Ecological understanding allows zooarchaeologists to understand how humans shaped ecosystems in the past, how those systems shaped us, and how we may adapt to ecological changes in the future.

Taphonomy is the study of the transformation of archaeological deposits from deposition, to recovery, and analysis. These changes occur prior to excavation (first-order changes), and during excavation and analysis (second-order changes). The taphonomic histories of assemblages vary greatly from site to site, and may not be completely knowable, even using multiple lines of evidence.