From Clustering to Cluster Explanations via Neural Networks

Abstract

A recent trend in machine learning has been to enrich learned models with the ability to explain their own predictions. The emerging field of explainable AI (XAI) has so far mainly focused on supervised learning, in particular, deep neural network classifiers. In many practical problems, however, the label information is not given and the goal is instead to discover the underlying structure of the data, for example, its clusters. While powerful methods exist for extracting the cluster structure in data, they typically do not answer the question why a certain data point has been assigned to a given cluster. We propose a new framework that can, for the first time, explain cluster assignments in terms of input features in an efficient and reliable manner. It is based on the novel insight that clustering models can be rewritten as neural networks-or "neuralized." Cluster predictions of the obtained networks can then be quickly and accurately attributed to the input features. Several showcases demonstrate the ability of our method to assess the quality of learned clusters and to extract novel insights from the analyzed data and representations.

Identifying dominant industrial sectors in market states of the S&P 500 financial data

“…[4] for the problems that can arise from this fact in practical applications). The XAI algorithm from [21] is well-suited to deal with such dependencies because of its holistic approach: it starts with the prediction of the k -means algorithm and goes backwards through the algorithmic structure until it arrives at the input layer, where it distributes the prediction relevance on all input variables (here: correlations) simultaneously. I.e.…”

“…While most of the above clustering analyses use a hierarchical k -means clustering, we use regular k -means clustering. This has a big advantage because it can be reformulated to allow the use of XAI, which can analyse the decisions of the clustering algorithm [21]. This allows us to reveal the dominant factors of the different market states and to compare the market states quantitatively, thereby improving the qualitative comparison depicted in figure 2 of [26].…”

“…Because the analyses [26,40,48] unanimously revealed eight market states for the time period analysed in this article, we set the number of clusters for the k -means algorithm to eight. In contrast to the procedure in the literature, however, regular kmeans clustering is used instead of a hierarchical binary k -means clustering in order to make the cluster centres amenable to the XAI method suggested in [21]. The regular k -means clustering method starts with a predefined number of k clusters and randomly selects k initial cluster centres before iteratively assigning each daily correlation matrix to its nearest cluster centre and updating the centres by setting them as the cluster's centroid until their centroid positions converge [27].…”

“…However, these comparisons were purely qualitative via plotting and comparing heat maps of the clusters' centroids and thus, there has not yet been a quantitative analysis of what differentiates these market states from each other. In this article our goal is to identify the dominant factors within the different economic states in the framework of [26,40,48] by using a method [21] from the emerging field of explainable artificial intelligence (XAI) which can be understood as a collection of methods that shed light on the black box that most AI methods seem to be from the user's perspective [34,43]. XAI allows a quantitative ranking of how much a given observable has influenced the decision algorithm (here: clustering algorithm) and therefore gives us deeper insights into the differences between the market states than the analysis in [26].…”

Tensorial Multi-Linear Multi-View Clustering via Schatten-p Norm

“…Clustering [1], [2], [3] is an essential research subject in machine learning and computer vision, whose purpose is to classify samples into different categories in the light of their similarity. In recent years, numerous clustering methods have emerged endlessly.…”