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Automation of the construction of knowledge-based systems. Modeling human learning mechanisms. A Learning [5] Strategy is a basic form of learning characterized by the employment of a certain type of inference like deduction, induction or analogy and a certain type of computational or representational mechanism like rules, trees, neural networks, etc. The first task is supervised learning [11]. The goal is to learn a mapping from supervised learning x to y, given a training set made of pairs xi, yi.

Here, the yi Y are called the labels or targets of the examples xi. If the labels are numbers, [Abbildung in dieser Leseprobe nicht enthalten] denotes the column vector of labels. The task is well defined, since a mapping can be evaluated through its predictive performance on test examples. When [Abbildung in dieser Leseprobe nicht enthalten] or more generally, when the labels are continuous , the task is called regression.

Mostly of this will focus on classification there is some work on regression in, i. Supervised learning aims to learn a mapping function f: X Y, where X and Y are input and output spaces, respectively e. The process of learning the mapping function is called training and the set of labelled objects used is called the training data or the training set. The mapping, once learned, can be used to predict the labels of the objects that were not seen during the training phase. Several pattern recognition [13], [14] and machine learning [1] textbooks discuss supervised learning extensively.

A brief overview of supervised learning algorithms is presented in this section. Supervised learning methods can be broadly divided into generative or discriminative approaches. Generative models assume that the data is independently and identically distributed and is generated by a parameterized probability density function.

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Probabilistic methods could further be divided into frequent list or Bayesian. Frequent list methods estimate parameters based on the observed data alone, while Bayesian methods allow for inclusion of prior knowledge about the unknown parameters. Examples of this approach include the Naive Bayes classifier, Bayesian linear and quadratic discriminants to name a few.

Instead of modelling the data generation process, discriminative methods directly model the decision boundary between the classes. The decision boundary is represented as a parametric function of data, and the parameters are learned by minimizing the classification error on the training set [12].

This is largely the approach taken by Neural Networks [14] and Logistic Regression [13]. As opposed to probabilistic methods, these do not assume any specific distribution on the generation of data, but model the decision boundary directly. Most methods following the ERM principle suffer from poor generalization performance.

This led to the development of Support Vector Machines SVMs which regularize the complexity of classifiers while simultaneously minimizing the empirical error. The second one is unsupervised learning. Let [Abbildung in dieser Leseprobe nicht enthalten] be a set of n examples unsupervised learning or points , where xi X for all [Abbildung in dieser Leseprobe nicht enthalten].

Typically it is assumed that the points are drawn i. The goal of unsupervised learning [Abbildung in dieser Leseprobe nicht enthalten] is to find interesting structure in the data X. It has been argued that the problem of unsupervised learning is fundamentally that of estimating a density which is likely to have generated X.

However, there are also weaker forms of unsupervised learning, such as quantile estimation, clustering, outlier detection, and dimensionality reduction. Unsupervised learning or clustering is a significantly more difficult problem than classification because of the absence of labels on the training data. Given a set of objects, or a set of pair wise similarities between the objects, the goal of clustering is to find natural groupings clusters in the data.

The mathematical definition of what is considered a natural grouping defines the clustering algorithm. A very large number of clustering algorithms have already been published, and new ones continue to appear [15,17].

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We broadly divide the clustering algorithms into groups based on their fundamental assumptions, and discuss a few representative algorithms in each group, ignoring minor variations within the group. K-means [15,17], arguably, is the most popular and widely used clustering algorithm. K- means is an example of a sum of squared error SSE minimization algorithm. Each cluster is represented by its centroid. The goal of K-means is to find the centroids and the cluster labels for the data points such that the sum-of-squared error between each data point and its closest centroid is minimized.

K-means is initialized with a set of random cluster centers that are iteratively updated by assigning the closest data point to each center, and recomputing the centroids. Parametric mixture models are well known in statistics and machine learning communities [20]. A mixture of parametric distributions, in particular, GMM [21,22], has been extensively used for clustering. GMMs are limited by the assumption that each component is homogeneous, unimodal, and generated using a Gaussian density. Latent Dirichlet Allocation[23] is a multinomial mixture model that has become the de facto standard for text clustering.

Several mixture models have been extended to their non-parametric form by taking the number of components to infinity in the limit [24,25,26]. A non-parametric prior is used in the generative process of these infinite models e.

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Dirichlet Process for clustering in [24]. One of the key advantages offered by the non-parametric prior based approaches is that they adjust their complexity to fit the data by choosing the appropriate number of parametric components. Hierarchical Topic Models [25] are clustering approaches that have seen huge success in clustering text data. Kernel K-means is a related kernel based algorithm, which generalizes the Euclidean distance based K-means to arbitrary. Metrics in the feature space.

Using the kernel trick, the data is first mapped into a higher dimensional space using a possibly non-linear map, and a K-means clustering is performed in the higher dimensional space. In [30], the explicit relation equivalence for a particular choice of normalization of the kernel between Kernel K-means, Spectral Clustering and Normalized Cut was established. Non-parametric density based methods are popular in the data mining community. Meanshift clustering [31] is a widely used non-parameteric density based clustering algorithm.

The objective of Mean-shift is to identify the modes in the kernel-density, seeking the nearest mode for each point in the input space. Several density based methods like DBSCAN also rely on empirical probability estimates, but their performance degrades heavily when the data is high dimensional. A recent segmentation algorithm [32] uses a hybrid mixture model, where each mixture component is a convex combination of a parametric and non-parametric density estimates.

Hierarchical clustering algorithms are popular non-parametric algorithms that iteratively build a cluster tree from a given pairwise similarity matrix Agglomerative algorithms such as Single Link, Complete Link, Average Link [16,17], Bayesian Hierarchical Clustering [33],start with each data point in a single cluster, and merge them succesively into larger clusters based on different similarity criteria at each iteration. Divisive algorithms start with a single cluster, and successively divide the clusters at each iteration.

A decision tree is one of the earliest classifier , which can handle a variety of data with a mix of both real, nominal, missing features and multiple classes. It also provides interpretable classifiers, which give a user an insight about which features are contributing for a particular class being predicted for a given input example. Decision trees could produce complex decision rules, and are sensitive to noise in the data.

Their complexity can be controlled by using approaches like pruning; however, in practice classifiers like SVM or Nearest Neighbour have been shown to outperform decision trees on vector data. Supervised learning expects training data that is completely labeled.

On the other extreme, unsupervised learning is applied on completely unlabeled data. Unsupervised learning is more difficult problem than supervised learning due to the lack of a well- defined user-independent objective [15,16]. For this reason, it is usually considered an ill- posed problem that is exploratory in nature that is, the user is expected to validate the output of the unsupervised learning process. Devising a fully automatic unsupervised learning algorithm that is applicable in a variety of data settings is an extremely difficult problem, and possibly infeasible.

On the other hand, supervised learning is a relatively easier task compared to unsupervised learning. The ease comes with an added cost of creating a labeled training set. Has uncertainty about the level of detail : the labels of objects change with the granularity at which the user looks at the object. For example, speech signals and images have to be accurately segmented into syllables and objects, respectively before labeling can be performed.

Can be ambiguous : objects might have non-unique labelings or the labelings themselves may be unreliable due to a disagreement among experts. Uses limited vocabulary: Typical labeling setting involves selecting a label from a list of pre-specified labels which may not completely or precisely describe an object. As an example labeled image collections usually come with a pre-specified vocabulary that can describe only the images that are already present in the training and testing data.

Unlabeled data is available in abundance, but it is difficult to learn the underlying structure of the data. Labeled data is scarce but is easier to learn from Semi-supervised learning is designed to alleviate the problems of supervised and unsupervised learning problems, and has gained significant interest in the machine learning research community. Semi-supervised learning SSL is halfway between supervised and unsupervised learning.

In addition to unlabeled data, the algorithm is provided with some supervision information - but not necessarily for all examples. Often, this information will be the targets associated with some of the examples. In this case, the data standard setting of SSL set [Abbildung in dieser Leseprobe nicht enthalten]can be divided into two parts: the points [Abbildung in dieser Leseprobe nicht enthalten] which labels [Abbildung in dieser Leseprobe nicht enthalten] are provided, and the points [Abbildung in dieser Leseprobe nicht enthalten] the labels of which are not known.

Semi-supervised learning SSL works in situations where the available information in data is in between those considered by the supervised and unsupervised learners; i. Various sources of side-information considered in the literature are summarized in Table 2. Semi-supervised classification algorithms train a classifier given both labeled and unlabeled data.

A special case of this is the well-known transductive learning [35], where the goal is to label only the unlabeled data available during training. Semi-supervised classification can also be viewed as an unsupervised learning problem with only a small amount of labeled training data. While semi-supervised classification is a relatively new field, the idea of using unlabeled samples to augment labeled examples for prediction was conceived several decades ago. An earlier work by Robbins and Monro [37] on sequential learning can also be viewed as related to semi-supervised learning.

The filled dots show the unlabeled data. The gray region depicts the data distribution obtained from the unlabeled data. Given a set of labeled data, a decision boundary may be learned using any of the supervised learning methods Fig. When a large number of unlabeled data is provided in addition to the labeled data, the true structure of each class is revealed through the distribution of the unlabeled data Fig.

The task now is no longer just limited to separating the labeled data, but to separate the regions to which the labeled data belong. Existing semi-supervised classification algorithms may be classified into two categories based on their underlying assumptions. An algorithm is said to satisfy the manifold assumption if it utilizes the fact that the data lie on a low-dimensional manifold in the input space.

Usually, the underlying geometry of the data is captured by representing the data as a graph, with samples as the vertices, and the pair wise similarities between the samples as edge- weights. Several graph based algorithms such as Label propagation [39], Markov random walks [40], Graph cut algorithms [41], Spectral graph transducer [42], and Low density separation [43] proposed in the literature are based on this assumption. The second assumption is called the cluster assumption [44].

It states that the data. Clustering is an ill-posed problem, and it is difficult to come up with a general purpose objective function that works satisfactorily with an arbitrary dataset [16]. If any side information is available, it must be exploited to obtain a more useful or relevant clustering of the data.

The pairwise constraints are of two types: must-link and cannot-link constraints. The clustering algorithm must try to assign the same label to the pair of points participating in a must-link constraint, and assign different labels to a pair of points participating in a cannot-link constraint.

These pairwise constraints may be specified by a user to encode his preferred clustering. Pairwise constraints can also be automatically inferred from the structure of the data, without a user having to specify them. As an example, web pages that are linked to one another may be considered as participating in a must-link constraint.

Feature selection can be performed for both supervised and unsupervised settings depending on the data available. Unsupervised feature selection is difficult for the same reasons that make clustering difficult, lack of a clear objective apart from the model assumptions. Supervised feature selection has the same limitations as classification, i.

Semi-supervised feature selection aims to utilize pair wise constraints in order to identify a possibly superior subset of features for the task. Many other learning tasks, apart from classification and clustering have their semisupervised Counterparts as well e. For example, page ranking algorithms used by search engines can utilize existing partial ranking information on the data to obtain a final ranking based on the query.

Generative models are perhaps the oldest semi-supervised learning method. With large amount of unlabeled data, the mixture components can be identified; then ideally we only need one labeled example per component to fully determine the mixture distribution, see Figure 2. Nigam et al.

They showed the resulting classifiers perform better than those trained only from L. Baluja uses the same algorithm on a face orientation discrimination task. Fujino et al. One has to pay attention to a few things:. The mixture model ideally should be identifiable. If the model family is identifiable, in theory with infinite U one can learn up to a permutation of component indices.

Here is an example showing the problem with unidentifiable models. The model p x y is uniform for[Abbildung in dieser Leseprobe nicht enthalten]. Assuming with large amount of un-labeled data U we know p x is uniform in [0, 1]. We also have 2 labeled data points [Abbildung in dieser Leseprobe nicht enthalten]. With our assumptions we cannot distinguish the following two models:. Even if we known p x top are a mixture of two uniform distributions, we cannot uniquely identify the two components. If the mixture model assumption is correct, unlabeled data is guaranteed to improve accuracy.

However if the model is wrong, unlabeled data may actually hurt accuracy. Figure 3 shows an example. This has been observed by multiple researchers. Cozman et al. It is thus important to carefully construct the mixture model to reflect reality. For example in text categorization a topic may contain several subtopics, and will be better modeled by multiple multinomials instead of a single one. Another solution is to down-weighing unlabeled data, which is also used by Nigam et al.

For example, a is clearly not generated from two Gaussian. If we insist that each class is a single Gaussian, b will have higher probability than c. Even if the mixture model assumption is correct, in practice mixture components are identified by the Expectation-Maximization EM algorithm EM is prone to local maxima. If a local maximum is far from the global maximum, unlabeled data may again hurt learning. Remedies include smart choice of starting point by active learning. We shall also mention that instead of using a probabilistic generative mixture model, some approaches employ various clustering algorithms to cluster the whole dataset, and then label each cluster with labeled data.

Although they can perform well if the particular clustering algorithms match the true data distribution, these approaches are hard to analyze due to their algorithmic nature. Another approach for semi-supervised learning with generative models is to convert data into a feature representation determined by the generative model. The new feature representation is then fed into a standard discriminative classifier. First a generative mixture model is trained, one component per class. At this stage the unlabeled data can be incorporated via EM, which is the same as in previous subsections.

However instead of directly using the generative model for classification, each labeled example is converted into a fixed-length Fisher score vector, i. These Fisher score vectors are then used in a discriminative classifier like an SVM, which empirically has high accuracy. Self-training is a commonly used technique for semi-supervised learning.

In self-training a classifier is first trained with the small amount of labeled data. The classifier is then used to classify the unlabeled data. Typically the most confident unlabeled points, together with their predicted labels, are added to the training set. The classifier is re- trained and the procedure repeated. Note the classifier uses its own predictions to teach itself.

The procedure is also called self-teaching or bootstrapping not to be confused with the statistical procedure with the same name. One can imagine that a classification mistake can reinforce itself. Self-training has been applied to several natural language processing tasks. Yarowsky uses self- training for word sense disambiguation, e. Riloff et al.

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Maeireizo et al. Self-training has also been applied to parsing and machine translation. Rosenberg et al. Self-training is a wrapper algorithm, and is hard to analyze in general. Initially two separate classifiers are trained with the labeled data, on the two sub feature sets respectively. Each classifier is retrained with the additional training examples given by the other classifier, and the process repeats. With this assumption the high confident data points in x1 view, represented by circled labels, will be randomly scattered in x2 view.

This is advantageous if they are to be used to teach the classifier in x2 view. In co-training, unlabeled data helps by reducing the version space size. In other words, the two classifiers or hypotheses must agree on the much larger unlabeled data as well as the labeled data. We need the assumption that sub-features are sufficiently good, so that we can trust the labels by each learner on U.

Figure 4 visualizes the assumption. Nigam and Ghani perform extensive empirical experiments to compare co-training with generative mixture models and EM. Their result shows co-training performs well if the conditional independence assumption indeed holds. In addition, it is better to probabilistically label the entire U, instead of a few most confident data points. They name this paradigm co-EM. Finally, if there is no natural feature split, the authors create artificial split by randomly break the feature set into two subsets.

They show co-training with artificial feature split still helps, though not as much as before. Collins and Singer ; Jones used co-training, co-EM and other related methods for information extraction from text. Balcan and Blum show that co-training can be quite effective, that in the extreme case only one labeled point is needed to learn the classifier.

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