Automated Marketing Research Using Online Customer Reviews

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[3] Phrase clustering We cluster the vectors (the matrix rows) so that all phrases describing the same product attribute are grouped together. More formally, given the phrase � word matrix(i,j) over the set of I phrases and the set of words J, we seek to separate phrases into a set C of k mutually exclusive and exhaustive clusters We use the cosine measure of angular distance between vectors to calculate similarity. The cosine measure is then applied to the phrase � word matrix using the K-means clustering algorithm. As noted earlier, while any number of clustering algorithms is acceptable, we selected K-means for its simplicity and its familiarity to both the text-mining and marketing communities. The quality, QC, of a K-means clustering, C, is calculated by the sum of the distances from each vector in a cluster to that vector's centroid. Following (Zhao and Karypis 2002), this metric is more simply defined as the sum of the length of the composite vectors: �v centroid�c �� composite�c � � � cos i � QC � , �ci�C�v�ci�ci�C where composite �ci � � �v (1) �v� Because K-means is known to be extremely sensitive to its initial conditions, we repeat the algorithm ten times, beginning with a new, random set of k centers and pick the solution that maximizes QC. [4] Attributes and their dimensions A critical step in our approach is to discover not only what product attributes customers are discussing but also the granularity with which those attributes are discussed. Specifically, we seek to elicit the attribute dimensions that customers use in their reviews. To discover attributes, we assume that each phrase corresponds to a distinct product attribute. To discover attribute dimensions, we will assume that each word in the phrase corresponds to a distinct dimension. Discovering attributes then reduces to the assignment of particular words to attribute dimensions. ci i 4
Conceptually, we model this process as a constrained optimization problem. Abusing our previous notation slightly, assume a set of phrases I composed from the set of words J and a set of attribute dimensions D. We have J � D binary decision variables Xjd where Xjd is 1 if word j is assigned to dimension d. There are I � J {0, 1} variables representing a constraint matrix where Yij is 1 or 0 depending upon whether word j appears in phrase i. Thus, our objective is to: max s. t. � X � �i Y * X � 1 X jd jd J ij binary The graph partitioning algorithm used to set the parameters I, J, and D and the constrained logic program (CLP) by which we solve the optimization are implemented in Python and detailed next. [5] Graph representations To discover attributes, we assume that each customer review phrase corresponds to a distinct product attribute. To discover attribute dimensions, we assume that each word in the phrase corresponds to a distinct dimension. Discovering attribute dimensions then reduces to the assignment of particular words to attribute dimensions. But how do we know how many dimensions there are in the assignment problem? Is it possible that the assignment optimization has no feasible solution because of conflicting constraints due to noise from the vagaries of human language? To solve this problem, we generate a graph of all words in the cluster. Each word is a node and arcs are defined by the co-occurrence of two words in the same phrase. We partition the graph into (possibly overlapping) sub-graphs by searching for maximal cliques. Intuitively, each sub-graph represents a maximal subset of words and phrases for which an optimal solution exists. The size of the maximal clique sets the number of attributes |D|. The sub- graph (words J and phrases I) define the optimization. jd 5
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