رگرسیون خطی خوشه ای
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|24146||2002||7 صفحه PDF||سفارش دهید||4128 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Knowledge-Based Systems, Volume 15, Issue 3, March 2002, Pages 169–175
Clustered linear regression (CLR) is a new machine learning algorithm that improves the accuracy of classical linear regression by partitioning training space into subspaces. CLR makes some assumptions about the domain and the data set. Firstly, target value is assumed to be a function of feature values. Second assumption is that there are some linear approximations for this function in each subspace. Finally, there are enough training instances to determine subspaces and their linear approximations successfully. Tests indicate that if these approximations hold, CLR outperforms all other well-known machine-learning algorithms. Partitioning may continue until linear approximation fits all the instances in the training set — that generally occurs when the number of instances in the subspace is less than or equal to the number of features plus one. In other case, each new subspace will have a better fitting linear approximation. However, this will cause over fitting and gives less accurate results for the test instances. The stopping situation can be determined as no significant decrease or an increase in relative error. CLR uses a small portion of the training instances to determine the number of subspaces. The necessity of high number of training instances makes this algorithm suitable for data mining applications.
Approximating the values of continuous functions is called regression and it is one of the main research issues in machine learning, while approximating the values of functions that have categorical values is called as classification. In that respect, classification is a subcategory of regression. Some researchers emphasized this relation by describing regression as ‘learning how to classify among continuous classes’ . For both these problems, we have also two types of solutions: eager learning and lazy learning. In eager learning, models are constructed according to the given training instances in training part. Such methods can obtain the interpretation of the underlying data. Constructing models in training leads long training times for eager learning methods. On the other hand, in lazy learning methods, all the work is done during testing, so they require much longer test times. Lazy learning methods do not construct models by using training data, so they cannot enable interpretation of training data. CLR, an extension of linear regression, is an eager learning approach. Although most of the real life applications are classification problem, there are also very important regression problems such as problems involving time-series. Regression techniques can also be applicable to the classification problems. For example, neural networks are often applied to classification problems  The traditional approach for regression problem is the classical linear least-squares regression. This old, yet effective, method has been widely used in real-world applications. However, this simple method has deficiency of linear methods in general. Advances in computational technology bring us the advantage of using new sophisticated non-linear regression algorithms. Among eager learning regression systems, CART , RETIS , M5  and DART/HYESS  induces regression trees; FORS  uses inductive logic programming for regression and RULE  induces regression rules, projection pursuit regression , neural network models and MARS  produces mathematical models. Among lazy learning methods, locally weighted regression (LWR)  produces local parametric functions according to the query instances, and k-NN ,  and  algorithm is the most popular non-parametric instance-based approach for regression problems . Regression by feature projections (RFP) method is an advanced k-NN method that uses feature projections based knowledge representation. This research uses the local weight and feature projection concepts and combines them with the traditional k-NN method. Using local weight with feature projection may cause losing the relation between the features; however, this new method eliminates the most common problems of regression, such as curse of dimensionality, dealing with missing feature values, robustness (dealing with noisy feature values), information loss because of disjoint partitioning of data, irrelevant features, computational complexity of test and training, missing local information at query positions and requirement for normalization. CLR is an extension of linear regression algorithm. CLR approximates on the subspaces, and therefore, it can give accurate results for non-linear regression functions. Also, irrelevant features are eliminated easily. Robustness can be achieved by having large number of training instances. CLR can eliminate effects of noise as well.