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Top1. Introduction
Clustering techniques, traditionally as primary tools in exploratory data analytics have received notably attention due to the fact that identifying similar objects allows for categorization, which simplifies the input space. By conventional clustering methods the implicit emphasis is that all attributes have the same importance. However, this assumption is not reliable for several reasons (Garcia-Escudero & Gordaliza, 2007). Firstly, adding non-relevant attributes to a feature space leads to different similarities. Secondly, the magnitude of attributes plays a crucial role, i.e. while two instances maybe similar on the whole feature space, considering a new attribute can lead to a significant dissimilarity 1. Nevertheless, an incorrect understanding of the underlying similarity can cause a flawed understanding of the data. We shall illustrate this point by mentioning an example: Assume several cars from several brands, each of which is characterized by horsepower, consumption, weight and number of doors with the car price as output. Since prices vary, the goal may be to cluster cars by price. One might think of a price clustering, however, a price clustering could indeed lead to the clustering of very dissimilar cars, e.g. a large car may be in the same group as a small and speedy car since both are in the same price range. The simple reason is that projecting an object specified by features to a one-dimensional space (output) leads to information lost. Note that in a straightforward manner response can be integrated in the feature space, and immediately the clustering techniques can be conducted, however, when the price as a factor is taken into account the simple clustering approach cannot sparkle its effect correctly. The simple reason is that the price effect thanks to the other input factors can be ignored, especially in the light of the large number of input attributes the effect can be neglected.
More concretely, we are aiming at clustering the articles from fashion products regarding the number of sales. One of the challenging tasks of fashion retailers is to estimate approximately the number of orders w.r.t. several products for the next season or even the next year. Due to the costs associated with purchasing and transferring, typically apparel retailers refrain from ordering more than two times per year. Seen from this perspective, an accurate sales-forecasting is required and prevents reordering. Accounting for the fact that each product is characterized by several qualitative and quantitative attributes, the goal is to find established patterns in the sales records on the use of a reliable ordering. A conventional solution is addressed under fitting a regression curve based on available sales data, however, in the presence of outliers a simple regression model delivers poor results. To overcome this problem our idea refers to identify the products which have similar characteristic in terms of the number of sales. We should again emphasize that thresholding solely based on the regression output may lead to the wrong conclusion, namely thresholding on the number of sales sacrifices a part of information, i.e., while a product is highly sold due to a low price a trendy product my sell well due to its trendiness. To cope with this inconsistency, the model should incorporate the response with other input factors, which leads to a more robust solution. In this regard, we modify the conventional clustering approach by integrating the response into the model, which at the core of the idea lies a proper weighting approach. Another drawback of the conventional clustering is to assume the same weights for all input factors, which indeed leads to a poor clustering, due to the fact that irrelevant input factors easily contribute to the model, even more in the case that all input factors are relevant, they are incorporating in different manners.
This paper is organized as follows: in the next section we give an overview on existing semi-supervised clustering approaches. In Section 3 we discuss comprehensive about conventional clustering. Section 4 is dedicated to our proposal. In Section 5 the algorithm is presented and in Section 7 the first preliminary results are shown. Finally, in Section 8 the concluding remarks and future horizon are discussed.