The two clusters of modality X are shown on the left of the figure with one cluster containing crosses and the other circles. The two clusters of modality Y are shown in the center of the figure with one cluster containing blue points and the other red points. We consider the subgroup made from C x and C y marked on figure.
From this, we would conclude that the subgroup formed by C x and C y is interesting, and there is a dependence between the two modalities. Classification is a supervised learning task. In contrast to clustering, meaningful groupings of the data are known a priori and are provided as labels. The task is to be able to accurately predict the labels, given the data.
This mapping is chosen to minimize the prediction error. As an example, from a hearing aid manufacturer, there may be a fixed number of styles of device available completely-in-the-canal, in-the-ear, behind-the-ear, etc. For existing users, we know which style of device the user has ideally further qualified by some measure of benefit , and so we can analyze to see whether particular audiogram patterns are associated with each style of device.
A simplistic task would then be to build a classification model to predict which style is most likely to be suitable for a new user on the basis of their audiogram alone. In this example, for didactic purposes only, we have ignored some of the more real-world qualifiers that may further influence device choice such as the dexterity of the user or cost. Each decision tree functions as a classifier, or regressor, based on decision rules expressed within a tree-like structure; the branch structure develops as a product of the dimensions available from obeying each of a string of rules.
An example decision tree is shown in Figure 3. The final decision of the branching is represented by a leaf. Example decision tree. The input data point, x , enters at the top of the tree. This process repeats until a leaf node is reached. The leaf node states the prediction y for the input x. The actual decision nodes shown are illustrative and not intended to represent a practical classifier. In addition, the candidate dimensions for splitting at each node are a random subset of the total set of dimensions. The generation of each tree in the forest by the use of bagging and random subsets of candidate dimensions decreases the statistical dependence between trees, thereby improving the estimate of the final, aggregated, decision from the forest.
The smaller the value of the Gini impurity, the better the decision separates the data with respect to the labels. It is zero when there is only one category in the node. An equation defining the Gini impurity is given in the Supplementary Material. The training data are partitioned or clustered by the learned decision tree, with each leaf representing a partition or cluster.
Random forests are robust to the scaling of data, and so transformations of the data can be less important than in other methods. A more in-depth discussion of decision trees and Random forests can be found in Flach For example, whereas classification is appropriate for predicting the type of device behind-the-ear, completely-in-the-canal, etc. Gaussian processes are a popular model that can be used for both classification and regression tasks. They are a probabilistic model, and so one of their great strengths is in quantifying uncertainty.
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That is, not only will the model provide a prediction, but it can also provide a measure of confidence in the prediction. One practical application in audiology is that the uncertainty measure can be useful in detecting outliers within a data set: The outlier represents an highly unexpected setting or operation that may warrant further investigation as to the cause. Here, we provide a brief overview of Gaussian processes with respect to the regression task. Assuming Gaussian noise on the observations and a Gaussian process prior on the function to be learned, the posterior is also given by a Gaussian process.
Spectral Feature Selection for Data Mining (Open Access) - Zheng Alan Zhao, Huan Liu - Google Buku
That is, for a new input, the Gaussian process provides a distribution of potential values. This distribution provides an estimate of the uncertainty for the predictions made. The values of the diagonal of the covariance the variance of the posterior give an indicator of how uncertain is the prediction for that input.
The lower the variance, the more confident is the prediction. Equations for defining the posterior are given in the Supplementary Material, while Rasmussen and Williams give a thorough treatise of Gaussian processes. The form of the covariance function determines the type of functions that are considered.
These covariance functions can even be combined through addition or multiplication. For instance, a Gaussian process with a covariance function that is the sum of a linear covariance function and a squared-exponential covariance function might model a smoothly varying function to be approximated that has a general linearly increasing trend.
The computational cost of obtaining the posterior distribution is of the order of N 3 , where N is the number of examples in the data set. For large data sets, this is prohibitively expensive. As long as the number of inducing points, M , is small and appropriately chosen, then the method can be applied to very large data sets.
An illustration of the effects of the number and spacing of inducing points, as well as the choice of kernel, is given in Figure 4. Again, further investigation as to a possible cause may then be warranted. An example of Gaussian process regression to model a data set similar to an audiogram. The abscissa in each plot can be taken as frequency in kHz, while the ordinate represents threshold in dB HL.
The blue lines show the mean prediction of the Gaussian process, and the shaded blue areas show the associated confidence regions. The top plots show the use of a squared-exponential RBF kernel, and the bottom plots show a linear kernel.
Application of Data Mining to “Big Data” Acquired in Audiology: Principles and Potential
The leftmost plots show the use of a single inducing point, depicted by a red marker on the x -axis. The middle plots show the use of 10 inducing points, and the rightmost plots show the use of inducing points. The solid black line shows the function to be approximated. Use of either an inappropriate number or spacing of inducing points, or insufficiently flexible kernel, leads to poor fitting blue line lying outside of the black line.
Data mining may offer great promise at finding novel and complex relationships within data sets, but because of the size of the data sets, and the number of comparisons made during mining, many of these may be spurious. Beside statistical confidence, expert interpretation and validation will always be required in order to provide context and to extract potential value from the findings. Unexpected findings, if they can lead to the generation of rational hypotheses, may prompt new areas of targeted research. Elements of the data set that were either discarded or partly resynthesized in order to overcome missing values may introduce a bias into analyses.
Experimental rigor demands the understanding and possible quantification of such bias. For a task such as classification or regression, the objective is the predictive power of the learned model on new instances of data, which prompts several questions: a where does a newly acquired data set fit into the patterns from historic data sets and, if it does not, b does the model need updating, and finally, c how does that affect our decisions on patient management?
The performance of a model should therefore be evaluated on data that are separate to the data used to train or update the model.
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The estimated performance of the model based on the training data will be overconfident because the model can be adapted to fit the seen data specifically and hence may overfit the data. This will produce N unbiased estimates of performance. If estimates of performance derived from the training data are high while the testing estimates are low, then the model has overfit the data and has not generalized well. The splitting of data for a threefold cross-validation is visualized in Figure 5. A visualization of splitting data in a threefold cross-validation. Each row shows a different split of the data, where a single fold is used as test data, and the contents of the remaining folds are used as training data for the classification or regression model.
We have presented an overview of the field of data mining where we have. Classification is the task of predicting the label or category of a new observation from a set of labels or categories , given a training set of data containing observations or instances whose labels are already known.
Clustering is the task of grouping observations or instances into groups known as clusters, given a training set of data containing observations. The goal is that instances in the same cluster should be more similar to each other than to instances in other clusters. Unlike with classification, no labels are provided beforehand. Dimension is a synonym for an attribute or feature. An example entry, or instance, in the data set will be described by a set of dimensions. Examples of dimensions are height, gender, and age, or a measure of absolute threshold at a single frequency.
Domain is a high-level modality, where the concept is broader in nature. For example, a clinical audiogram is typically specified by thresholds at eight different frequencies.
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When the dimensions together describe a single concept, such as an audiogram, we term this a modality. Regression is the task of predicting the continuous response to an input variable, given a set of training data containing observations whose continuous response is already known. This prediction of a continuous response is as opposed to classification where solely a discrete label or category is predicted. Subgroup discovery is the task of finding a subset of instances in a data set for which some relationship or dependency holds.
This is as opposed to classification, regression, and clustering that provide some prediction or description of the whole data set. The authors wish to thank an anonymous hearing aid manufacturer for the effort in preparing this data set for release for independent research.
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