Interpretable Feature

Decision trees are widely recognized for their interpretability and computational efficiency. However, the choice of impurity function-typically entropy or Gini impurity-can significantly influence model performance, especially in highdimensional or imbalanced data settings. We propose Adaptive Weighted Impurity (AWI), a novel impurity criterion that dynamically integrates entropy and Gini impurity through an adaptive, data-driven weighting mechanism. AWI retains the transparency of classical decision trees while enhancing classification accuracy, scalability, and robustness across diverse datasets. Extensive experiments on benchmark datasets (Iris, Titanic, MNIST) demonstrate that AWI consistently improves classification performance, reduces training time, and simplifies resulting models. Notably, AWI introduces no additional hyperparameters and can be seamlessly incorporated into existing decision tree frameworks. This makes it particularly suitable for resource-constrained environments and applications requiring low-latency inference, such as financial analytics, healthcare diagnostics, and embedded AI systems. Impact Statement-The impurity criterion used in decision trees has a direct impact on model accuracy, training efficiency, and generalization. This work introduces Adaptive Weighted Impurity (AWI)-a hybrid impurity function that combines entropy and Gini via adaptive weighting. AWI consistently improves decision tree performance across a range of dataset sizes and class imbalances, without compromising interpretability. The proposed approach is especially valuable for real-world deployments in domains like medical diagnosis and financial risk modeling, where decision transparency, speed, and accuracy are critical.

Low-dimensional representations, or embeddings, of a graph's nodes facilitate several practical data science and data engineering tasks. As such embeddings rely, explicitly or implicitly, on a similarity measure among nodes, they require the computation of a quadratic similarity matrix, inducing a tradeoff between space complexity and embedding quality. To date, no graph embedding work combines (i) linear space complexity, (ii) a nonlinear transform as its basis, and (iii) nontrivial quality guarantees. In this paper we introduce FREDE (FREquent Directions Embedding), a graph embedding based on matrix sketching that combines those three desiderata. Starting out from the observation that embedding methods aim to preserve the covariance among the rows of a similarity matrix, FREDE iteratively improves on quality while individually processing rows of a nonlinearly transformed PPR similarity matrix derived from a stateof-the-art graph embedding method and provides, at any iteration, column-covariance approximation guarantees in due course almost indistinguishable from those of the optimal approximation by SVD. Our experimental evaluation on variably sized networks shows that FREDE performs almost as well as SVD and competitively against state-of-the-art embedding methods in diverse data science tasks, even when it is based on as little as 10% of node similarities.

Typical graph embeddings may not capture type-specific bipartite graph features that arise in such areas as recommender systems, data visualization, and drug discovery. Machine learning methods utilized in these applications would be better served with specialized embedding techniques. We propose two embeddings for bipartite graphs that decompose edges into sets of indirect relationships between node neighborhoods. When sampling higher-order relationships, we reinforce similarities through algebraic distance on graphs. We also introduce ensemble embeddings to combine both into a “best of both worlds” embedding. The proposed methods are evaluated on link prediction and recommendation tasks and compared with other state-of-the-art embeddings. Our embeddings are found to perform better on recommendation tasks and equally competitive in link prediction. Although all considered embeddings are beneficial in particular applications, we demonstrate that none of those considered is clearly s...

Typical graph embeddings may not capture type-specific bipartite graph features that arise in such areas as recommender systems, data visualization, and drug discovery. Machine learning methods utilized in these applications would be better served with specialized embedding techniques. We propose two embeddings for bipartite graphs that decompose edges into sets of indirect relationships between node neighborhoods. When sampling higher-order relationships, we reinforce similarities through algebraic distance on graphs. We also introduce ensemble embeddings to combine both into a "best of both worlds" embedding. The proposed methods are evaluated on link prediction and recommendation tasks and compared with other state-of-the-art embeddings. Our embeddings are found to perform better on recommendation tasks and equally competitive in link prediction. Although all considered embeddings are beneficial in particular applications, we demonstrate that none of those considered is clearly superior (in contrast to what is claimed in many papers). Therefore, we discuss the trade offs among them, noting that the methods proposed here are robust for applications relying on same-typed comparisons.

Typical graph embeddings may not capture type-specific bipartite graph features that arise in such areas as recommender systems, data visualization, and drug discovery. Machine learning methods utilized in these applications would be better served with specialized embedding techniques. We propose two embeddings for bipartite graphs that decompose edges into sets of indirect relationships between node neighborhoods. When sampling higher-order relationships, we reinforce similarities through algebraic distance on graphs. We also introduce ensemble embeddings to combine both into a "best of both worlds" embedding. The proposed methods are evaluated on link prediction and recommendation tasks and compared with other state-of-the-art embeddings. Our embeddings are found to perform better on recommendation tasks and equally competitive in link prediction. Although all considered embeddings are beneficial in particular applications, we demonstrate that none of those considered is clearly superior (in contrast to what is claimed in many papers). Therefore, we discuss the trade offs among them, noting that the methods proposed here are robust for applications relying on same-typed comparisons.

Theoretical background How can syntactic structures vary from one language to another, or from one stage to another in the history of a single language? The strongest version of the cartographic approach to syntax says, in effect, that they cannot: "if some language provides evidence for […] a particular functional head […], then that head […] must be present in every other language, whether the language offers overt evidence for it or not" (Cinque & Rizzi 2008: 45). Under this view, all surface syntactic variation arises through movement, and any seemingly absent head is merely syntactically and phonologically inert (attracting no specifier and having no over spellout). In principle, this is a strong claim about the universality of functional structure, but it is not easy to test: to falsify it, one must show not just that language Y shows no sign of a projection XP known to exist in language Z, but that Y cannot be analyzed as having XP. In contrast to this view, we pursue what we will call a neoparametric approach-one that admits of variation in how formal features are grouped into projections, while still holding to the Borer-Chomsky conjecture that the lexicon is the source of variability (Borer 1984; Chomsky 1995; Baker 2008) rather than positing parameters in the older sense of Chomsky (1981). This position follows from Chomsky's (2000: 100) assumption that each language selects a subset [F] of the universal set of features, making a one-time assembly of the elements of [F] into a lexicon. As Cowper (2005) points out, intrinsic semantic entailments between features restrict both their combination into lexical items and the selectional requirements of those lexical items. Bobaljik & Thráinsson (1998) offer evidence for the neoparametric approach from variation: several correlated typological properties of Germanic languages follow from differences in the number of projections in the Infl system. Cowper & Hall (2011) make a similar case based on diachronic changes in English voice and aspect, showing that the replacement of the passival by the progressive passive (among other changes) is most elegantly explained by positing a reorganization of features from one head to two. In this paper, we show that the neoparametric approach also offers an elegant account of the diachronic development of the English modals.

Representation learning is one of the foundations of Deep Learning and allowed important improvements on several Machine Learning tasks, such as Neural Machine Translation, Question Answering and Speech Recognition. Recent works have proposed new methods for learning representations for nodes and edges in graphs. Several of these methods are based on the SkipGram algorithm, and they usually process a large number of multi-hop neighbors in order to produce the context from which node representations are learned. In this paper, we propose an effective and also efficient method for generating node embeddings in graphs that employs a restricted number of permutations over the immediate neighborhood of a node as context to generate its representation, thus ego-centric representations. We present a thorough evaluation showing that our method outperforms state-of-the-art methods in six different datasets related to the problems of link prediction and node classification, being one to three orders of magnitude faster than baselines when generating node embeddings for very large graphs.

Heterogeneous information network (HIN) are becoming popular across multiple applications in forms of complex large-scaled networked data such as social networks, bibliographic networks, biological networks, etc. Recently, information network embedding (INE) has aroused tremendously interests from researchers due to its effectiveness in information network analysis and mining tasks. From recent views of INE, community is considered as the mesoscopic preserving network’s structure which can be combined with traditional approach of network’s node proximities (microscopic structure preserving) to leverage the quality of network’s representation. Most of contemporary INE models, like as: HIN2Vec, Metapath2Vec, HINE, etc. mainly concentrate on microscopic network structure preserving and ignore the mesoscopic (intra-community) structure of HIN. In this paper, we introduce a novel approach of topic-driven meta-path-based embedding, namely W-Com2Vec (Weighted intra-community to vector). Ou...

Layer-wise relevance propagation (LRP) heatmaps aim to provide graphical explanation for decisions of a classifier. This could be of great benefit to scientists for trusting complex black-box models and getting insights from their data. The LRP heatmaps tested on benchmark datasets are reported to correlate significantly with interpretable image features. In this work, we investigate these claims and propose to refine them.

Graphs, such as social networks, word co-occurrence networks, and communication networks, occur naturally in various real-world applications. Analyzing these networks yields insight into the structure of society, language, and different patterns of communications. Many approaches have been proposed to perform the analysis. Recently, many researchers are interested on methods which use the representation of graph nodes in vector. In this research, we provide a comprehensive and structured analysis of an integrated platform to evaluate graph embedding techniques. We will first explain our platform and then evaluate many techniques of graph embedding on a few common datasets and compare their performance against one another. We have implemented graph embedding techniques on an integrated platform and further evaluated the performance of each technique.

Link prediction of a scale-free network has become relevant for problems relating to social network analysis, recommendation system, and in the domain of bioinformatics. In recently proposed approaches, the sampling of nodes of a network is done by simulating random walk. The generated node samples are used to train a neural network to learn the contextual information through an embedding vector. This method has gained popularity as the embedding vector is produced from the primitive node adjacency information and has achieved an outstanding performance. In this article, a naive and scalable approach for generating the node samples based on the principle of goal-oriented greedy searching has been proposed. The generated node samples have low noisy structures, which can represent the relation of edges of the network in a better way, compared to the state-of-the-art methods. Consequently, better representation of feature embedding of nodes of the network is generated from the samples. The learned feature vectors are used for solving the link prediction problem using a pairwise kernel support vector machine (SVM) classifier, which is computationally and spatially expensive in nature. Therefore, as an alternative, we have chosen to deploy a random forest (RF) classifier with a new algebraic operation to obtain the symmetric pairwise feature representation of a node pair. We demonstrated the efficacy of the proposed Topo2vec by testing it against the state-of-the-art network context generation algorithms in several real-world networks. Altogether, the proposed Topo2vec algorithm is a new method for solving the link prediction problem with entirely different settings.

In real-world, our DNA is unique but many people share names. is phenomenon o en causes erroneous aggregation of documents of multiple persons who are namesake of one another. Such mistakes deteriorate the performance of document retrieval, web search, and more seriously, cause improper a ribution of credit or blame in digital forensic. To resolve this issue, the name disambiguation task is designed which aims to partition the documents associated with a name reference such that each partition contains documents pertaining to a unique real-life person. Existing solutions to this task substantially rely on feature engineering, such as biographical feature extraction, or construction of auxiliary features from Wikipedia. However, for many scenarios, such features may be costly to obtain or unavailable due to the risk of privacy violation. In this work, we propose a novel name disambiguation method. Our proposed method is non-intrusive of privacy because instead of using a ributes pertaining to a real-life person, our method leverages only relational data in the form of anonymized graphs. In the methodological aspect, the proposed method uses a novel representation learning model to embed each document in a low dimensional vector space where name disambiguation can be solved by a hierarchical agglomerative clustering algorithm. Our experimental results demonstrate that the proposed method is signi cantly be er than the existing name disambiguation methods working in a similar se ing.

Network embedding aims to learn vector representations of vertices, that preserve both network structures and properties. However, most existing embedding methods fail to scale to large networks. A few frameworks have been proposed by extending existing methods to cope with network embedding on large-scale networks. These frameworks update the global parameters iteratively or compress the network while learning vector representation. Such network embedding schemes inevitably lead to a high cost of either high communication overhead or sub-optimal embedding quality. In this paper, we propose a novel decentralized large-scale network embedding framework called DeLNE. As the name suggests, DeLNE divides a network into smaller partitions and learn vector representation in a distributed fashion, avoiding any unnecessary communication overhead. Our proposed framework uses Variational Graph Convolution Auto-Encoders to embed the structure and properties of each sub-network. Secondly, we propose an embedding aggregation mechanism, that captures the global properties of each node. Thirdly, we propose an alignment function, that reconciles all subnetworks embedding into the same vector space. Due to the parallel nature of DeLNE, it scales well on large clustered environments. Through extensive experimentation on realistic datasets, we show that DeLNE produces high-quality embedding and outperforms existing large-scale network embeddings frameworks, in terms of both efficiency and effectiveness.

Heterogenous information network embedding aims to embed heterogenous information networks (HINs) into low dimensional spaces, in which each vertex is represented as a low-dimensional vector, and both global and local network structures in the original space are preserved. However, most of existing heterogenous information network embedding models adopt the dot product to measure the proximity in the low dimensional space, and thus they can only preserve the first-order proximity and are insufficient to capture the global structure. Compared with homogenous information networks, there are multiple types of links (i.e., multiple relations) in HINs, and the link distribution w.r.t relations is highly skewed. To address the above challenging issues, we propose a novel heterogenous information network embedding model PME based on the metric learning to capture both first-order and second-order proximities in a unified way. To alleviate the potential geometrical inflexibility of existing...

This work proposes a novel deep neural network (DNN) architecture, Implicit Segmentation Neural Network (ISNet), to solve the task of image segmentation followed by classification. It substitutes the common pipeline of two DNNs with a single model. We designed the ISNet for high flexibility and performance: it allows virtually any classification neural network architecture to analyze a common image as if it had been previously segmented. Furthermore, in relation to the original classifier, the ISNet does not cause any increment in computational cost at run-time. We implement an ISNet based on a DenseNet121 classifier to solve the task of COVID-19 detection in chest X-rays. The ISNet precisely ignored the image regions outside of the lungs; it achieved 94.5 +/-4.1% mean accuracy with an external test database, surpassing the performances of state-of-the-art DNNs (U-Net segmenter followed by DenseNet121 and standalone DenseNet121) by 6 to 7.9%. ISNet presents an accurate, fast, and li...

Network embedding that encodes structural information of graphs into a low-dimensional vector space has been proven to be essential for network analysis applications, including node classification and community detection. Although recent methods show promising performance for various applications, graph embedding still has some challenges; either the huge size of graphs may hinder a direct application of the existing network embedding method to them, or they suffer compromises in accuracy from locality and noise. In this paper, we propose a novel Network Embedding method, NECL, to generate embedding more efficiently or effectively. Our goal is to answer the following two questions: 1) Does the network Compression significantly boost Learning? 2) Does network compression improve the quality of the representation? For these goals, first, we propose a novel graph compression method based on the neighborhood similarity that compresses the input graph to a smaller graph with incorporatin...

Sampling a network is an important prerequisite for unsupervised network embedding. Further, random walk has widely been used for sampling in previous studies. Since random walk based sampling tends to traverse adjacent neighbors, it may not be suitable for heterogeneous network because in heterogeneous networks two adjacent nodes often belong to different types. Therefore, this paper proposes a K-hop random walk based sampling approach which includes a node in the sample list only if it is separated by K hops from the source node. We exploit the samples generated using K-hop random walker for network embedding using skip-gram model (word2vec). Thereafter, the performance of network embedding is evaluated on co-authorship prediction task in heterogeneous DBLP network. We compare the efficacy of network embedding exploiting proposed sampling approach with recently proposed best performing network embedding models namely, Metapath2vec and Node2vec. It is evident that the proposed sampling approach yields better quality of embeddings and out-performs baselines in majority of the cases.

The potential for machine learning systems to amplify social inequities and unfairness is receiving increasing popular and academic attention. Much recent work has focused on developing algorithmic tools to assess and mitigate such unfairness. However, there is little work on enhancing fairness in graph algorithms. Here, we develop a simple, effective and general method, CrossWalk, that enhances fairness of various graph algorithms, including influence maximization, link prediction and node classification, applied to node embeddings. CrossWalk is applicable to any random walk based node representation learning algorithm, such as DeepWalk and Node2Vec. The key idea is to bias random walks to cross group boundaries, by upweighting edges which (1) are closer to the groups’ peripheries or (2) connect different groups in the network. CrossWalk pulls nodes that are near groups’ peripheries towards their neighbors from other groups in the embedding space, while preserving the necessary str...

Network embedding that encodes structural information of graphs into a low-dimensional vector space has been proven to be essential for network analysis applications, including node classification and community detection. Although recent methods show promising performance for various applications, graph embedding still has some challenges; either the huge size of graphs may hinder a direct application of the existing network embedding method to them, or they suffer compromises in accuracy from locality and noise. In this paper, we propose a novel Network Embedding method, NECL, to generate embedding more efficiently or effectively. Our goal is to answer the following two questions: 1) Does the network Compression significantly boost Learning? 2) Does network compression improve the quality of the representation? For these goals, first, we propose a novel graph compression method based on the neighborhood similarity that compresses the input graph to a smaller graph with incorporatin...

Graph representation learning aims to represent the structural and semantic information of graph objects as dense real value vectors in low dimensional space by machine learning. It is widely used in node classification, link prediction, and recommendation systems. However, directly computing the embeddings for original graphs is prohibitively inefficient, especially for large-scale graphs. To address this issue, we present the GSE (Graph Summarization Embedding) model, a more efficient model that computes the nodes' embeddings based on graph summarization. Specifically, the model first searches for the minimum information entropy of k groups to transform the original graph into a hypergraph with higherorder structural features. Next, the summarization graph's connection probabilities are used to determine the biased random walks on the hypergraph, which then generates the sequences of the super-nodes. Finally, the node sequences are fed into the skip-gram to generate the vectors of these nodes. Our proposed model improves the efficiency of graph embedding on big data graphs and effectively alleviates the local optimal problem caused by the random walks. Experimental results demonstrate that GSE outperforms main existing clustering baselines, such as K_Means Clustering, Affinity Propagation Clustering, Canopy Clustering, and ACP Clustering. Moreover, our model can be coupled with the main graph embedding methods and improves the Macro-F1 scores and Micro-F1 scores for classification tasks on a variety of real-world graph data. INDEX TERMS Graph embedding, graph summarization, graph coarsening, random walks.

Representation learning is one of the foundations of Deep Learning and allowed important improvements on several Machine Learning tasks, such as Neural Machine Translation, Question Answering and Speech Recognition. Recent works have proposed new methods for learning representations for nodes and edges in graphs. Several of these methods are based on the SkipGram algorithm, and they usually process a large number of multi-hop neighbors in order to produce the context from which node representations are learned. In this paper, we propose an effective and also efficient method for generating node embeddings in graphs that employs a restricted number of permutations over the immediate neighborhood of a node as context to generate its representation, thus ego-centric representations. We present a thorough evaluation showing that our method outperforms state-of-the-art methods in six different datasets related to the problems of link prediction and node classification, being one to three...

This paper investigates how working of Convolutional Neural Network (CNN) can be explained through visualization in the context of machine perception of autonomous vehicles. We visualize what type of features are extracted in different convolution layers of CNN that helps to understand how CNN gradually increases spatial information in every layer. Thus, it concentrates on region of interests in every transformation. Visualizing heat map of activation helps us to understand how CNN classifies and localizes different objects in image. This study also helps us to reason behind low accuracy of a model helps to increase trust on object detection module.

Αναλύουµε το φαινόµενο του «Αναδιπλασιασµού Προσδιοριστικού ∆είκτη» (Determiner Spreading) µε βάση την διαπίστωση πως έχει κατηγορηµατική ερµηνεία. Προσφέρουµε µία ανάλυση του φαινοµένου αυτού ως κατηγορηµατικών δοµών Φράσης Προσδιοριστικού ∆είκτη µέσα στην οποία µία ελλειπτική Φράση Π∆ αποτελεί είτε το υποκείµενο είτε το κατηγορούµενο. Τέλος, προσκοµίζουµε ψυχογλωσσολογικά δεδοµένα από το πεδίο της γλωσσικής κατάκτησης προς υποστήριξη της ανάλυσής µας.

Determiner Spreading (DS) occurs in adjectivally modified nominal phrases comprising more than one definite article, a phenomenon that has received considerable attention and has been extensively described in Greek. This paper discusses the syntactic properties of DS in detail and argues that DS structures are both arguments and predication configurations involving two DPs. This account successfully captures the word-order facts and the distinctive interpretation of DS, while also laying the groundwork towards unifying it with other structures linking two DPs in a predicative relation.

Multi-graph clustering aims to improve clustering accuracy by leveraging information from different domains, which has been shown to be extremely effective for achieving better clustering results than single graph based clustering algorithms. Despite the previous success, existing multi-graph clustering methods mostly use shallow models, which are incapable to capture the highly non-linear structures and the complex cluster associations in multigraph, thus result in sub-optimal results. Inspired by the powerful representation learning capability of neural networks, in this paper, we propose an end-to-end deep learning model to simultaneously infer cluster assignments and cluster associations in multi-graph. Specifically, we use autoencoding networks to learn node embeddings. Meanwhile, we propose a minimum-entropy based clustering strategy to cluster nodes in the embedding space for each graph. We introduce two regularizers to leverage both within-graph and cross-graph dependencies. An attentive mechanism is further developed to learn cross-graph cluster associations. Through extensive experiments on a variety of datasets, we observe that our method outperforms state-of-the-art baselines by a large margin. CCS CONCEPTS • Information systems → Clustering.

(pre-final version, January 2022, accepted to Syntax, )
On the basis of original data from Moksha Mordvin (Finno-Ugric), I argue that some languages have nominal concord even though modifiers of the noun generally do not show inflection. Evidence for the presence of concord comes from nominal ellipsis, under which inflection is phonologically realized and restricted in the same way as regular nominal concord. To account for the distribution of concord exponents, I develop a model that allows features to be present in syntax but avoid realization. In particular, I propose that (i) Spell-Out applies to a node as soon as its Merge and Agree features are satisfied; (ii) Agree features are by default ineligible at PF and need to undergo Probe Conversion in order to get accessible to PF processes. The distribution of features then follows from the respective timing of Spell-Out and Probe Conversion. Keywords: concord, nominal ellipsis, Moksha Mordvin, Spell-Out, Agree, interpretabil- ity, PF, Probe Conversion

Graph embedding has become a key component of many data mining and analysis systems. Current graph embedding approaches either sample a large number of node pairs from a graph to learn node embeddings via stochastic optimization or factorize a high-order node proximity/adjacency matrix via computationally intensive matrix factorization techniques. These approaches typically require significant resources for the learning process and rely on multiple parameters, which limits their applicability in practice. Moreover, most of the existing graph embedding techniques operate effectively in one specific metric space only (e.g., the one produced with cosine similarity), do not preserve higher-order structural features of the input graph and cannot automatically determine a meaningful number of dimensions for the embedding space. Typically, the produced embeddings are not easily interpretable, which complicates further analyses and limits their applicability. To address these issues, we propose DAOR, a highly efficient and parameter-free graph embedding technique producing metric space-robust, compact and interpretable embeddings without any manual tuning. Compared to a dozen state-of-the-art graph embedding algorithms, DAOR yields competitive results on both node classification (which benefits form high-order proximity) and link prediction (which relies on low-order proximity mostly). Unlike existing techniques, however, DAOR does not require any parameter tuning and improves the embeddings generation speed by several orders of magnitude. Our approach has hence the ambition to greatly simplify and speed up data analysis tasks involving graph representation learning. Index Terms-parameter-free graph embedding, unsupervised learning of network representation, automatic feature extraction, interpretable embeddings, scalable graph embedding.

Heads can be spelled out higher than their merge-in position. The operation that the transformationalist generative literature uses to model this is called head movement. Government and Binding posited that the operation in question involves adjunction of a lower head to a higher head in narrow syntax. It has been noted early on, however, that this approach is highly problematic because head-adjunction violates several well-motivated constraints on syntactic structures.

Recently, a technique called Layer-wise Relevance Propagation (LRP) was shown to deliver insightful explanations in the form of input space relevances for understanding feed-forward neural network classification decisions. In the present work, we extend the usage of LRP to recurrent neural networks. We propose a specific propagation rule applicable to multiplicative connections as they arise in recurrent network architectures such as LSTMs and GRUs. We apply our technique to a word-based bi-directional LSTM model on a five-class sentiment prediction task, and evaluate the resulting LRP relevances both qualitatively and quantitatively, obtaining better results than a gradient-based related method which was used in previous work.

Layer-wise relevance propagation (LRP) is a recently proposed technique for explaining predictions of complex non-linear classifiers in terms of input variables. In this paper, we apply LRP for the first time to natural language processing (NLP). More precisely, we use it to explain the predictions of a convolutional neural network (CNN) trained on a topic categorization task. Our analysis highlights which words are relevant for a specific prediction of the CNN. We compare our technique to standard sensitivity analysis, both qualitatively and quantitatively, using a ``word deleting'' perturbation experiment, a PCA analysis, and various visualizations. All experiments validate the suitability of LRP for explaining the CNN predictions, which is also in line with results reported in recent image classification studies.

Graphs, such as social networks, word co-occurrence networks, and communication networks, occur naturally in various real-world applications. Analyzing them yields insight into the structure of society, language, and different patterns of communication. Many approaches have been proposed to perform the analysis. Recently, methods which use the representation of graph nodes in vector space have gained traction from the research community. In this survey, we provide a comprehensive and structured analysis of various graph embedding techniques proposed in the literature. We first introduce the embedding task and its challenges such as scalability, choice of dimensionality, and features to be preserved, and their possible solutions. We then present three categories of approaches based on factorization methods, random walks, and deep learning, with examples of representative algorithms in each category and analysis of their performance on various tasks. We evaluate these state-of-the-art methods on a few common datasets and compare their performance against one another and versus non-embedding based models. Our analysis concludes by suggesting some potential applications and future directions. We finally present the open-source Python library, named GEM (Graph Embedding Methods), we developed that provides all presented algorithms within a unified interface, to foster and facilitate research on the topic.

The structure of demonstrative expressions in Modern Greek serves as our looking glass into the broader structure of the nominal domain. Concentrating on the different positions of demonstratives and the obligatory co-occurrence of the definite article (“demonstrative doubling”), the proposal integrates issues of anti-locality into the nominal domain, where apparent articles doubling the demonstrative are analyzed as the spelled out copy of an otherwise illicitly moved demonstrative.

Deep neural networks (DNNs) have demonstrated impressive performance in complex machine learning tasks such as image classification or speech recognition. However, due to their multilayer nonlinear structure, they are not transparent, i.e., it is hard to grasp what makes them arrive at a particular classification or recognition decision, given a new unseen data sample. Recently, several approaches have been proposed enabling one to understand and interpret the reasoning embodied in a DNN for a single test image. These methods quantify the "importance" of individual pixels with respect to the classification decision and allow a visualization in terms of a heatmap in pixel/input space. While the usefulness of heatmaps can be judged subjectively by a human, an objective quality measure is missing. In this paper, we present a general methodology based on region perturbation for evaluating ordered collections of pixels such as heatmaps. We compare heatmaps computed by three dif...

—Deep Neural Networks (DNNs) have demonstrated impressive performance in complex machine learning tasks such as image classification or speech recognition. However, due to their multi-layer nonlinear structure, they are not transparent, i.e., it is hard to grasp what makes them arrive at a particular classification or recognition decision given a new unseen data sample. Recently, several approaches have been proposed enabling one to understand and interpret the reasoning embodied in a DNN for a single test image. These methods quantify the " importance " of individual pixels wrt the classification decision and allow a visualization in terms of a heatmap in pixel/input space. While the usefulness of heatmaps can be judged subjectively by a human, an objective quality measure is missing. In this paper we present a general methodology based on region perturbation for evaluating ordered collections of pixels such as heatmaps. We compare heatmaps computed by three different methods on the SUN397, ILSVRC2012 and MIT Places data sets. Our main result is that the recently proposed Layer-wise Relevance Propagation (LRP) algorithm qualitatively and quantitatively provides a better explanation of what made a DNN arrive at a particular classification decision than the sensitivity-based approach or the deconvolution method. We provide theoretical arguments to explain this result and discuss its practical implications. Finally, we investigate the use of heatmaps for unsupervised assessment of neural network performance.

Nonlinear methods such as Deep Neural Networks (DNNs) are the gold standard for various challenging machine learning problems such as image recognition. Although these methods perform impressively well, they have a significant disadvantage, the lack of transparency, limiting the interpretability of the solution and thus the scope of application in practice. Especially DNNs act as black boxes due to their multilayer nonlinear structure. In this paper we introduce a novel methodology for interpreting generic multilayer neural networks by decomposing the network classification decision into contributions of its input elements. Although our focus is on image classification, the method is applicable to a broad set of input data, learning tasks and network architectures. Our method called deep Taylor decomposition efficiently utilizes the structure of the network by backpropagating the explanations from the output to the input layer. We evaluate the proposed method empirically on the MNIST and ILSVRC data sets.

We summarize the main concepts behind a recently proposed method for explaining neural network predictions called deep Taylor decomposition. For conciseness, we only present the case of simple neural networks of ReLU neurons organized in a directed acyclic graph. More struc-tured networks with special layers are discussed in the original paper (Montavon et al., 2015).

The Layer-wise Relevance Propagation (LRP) algorithm explains a classifier's prediction specific to a given data point by attributing relevance scores to important components of the input by using the topology of the learned model itself. With the LRP Toolbox we provide platform-agnostic implementations for explaining the predictions of pre-trained state of the art Caffe networks and stand-alone implementations for fully connected Neural Network models. The implementations for Matlab and python shall serve as a playing field to familiarize oneself with the LRP algorithm and are implemented with readability and transparency in mind. Models and data can be imported and exported using raw text formats, Matlab's .mat files and the .npy format for numpy or plain text.

We state some key properties of the recently proposed Layer-wise Relevance Propagation (LRP) method, that make it particularly suitable for model analysis and validation. We also review the capabilities and advantages of the LRP method on empirical data, that we have observed in several previous works.

Fisher vector (FV) classifiers and Deep Neural Networks (DNNs) are popular and successful algorithms for solving image classification problems. However, both are generally considered 'black box' predictors as the non-linear transformations involved have so far prevented transparent and interpretable reasoning. Recently, a principled technique, Layer-wise Relevance Propagation (LRP), has been developed in order to better comprehend the inherent structured reasoning of complex nonlinear classification models such as Bag of Feature models or DNNs. In this paper we (1) extend the LRP framework also for Fisher vector classifiers and then use it as analysis tool to (2) quantify the importance of context for classification, (3) qualitatively compare DNNs against FV classifiers in terms of important image regions and (4) detect potential flaws and biases in data. All experiments are performed on the PASCAL VOC 2007 and ILSVRC 2012 data sets.

Layer-wise relevance propagation is a framework which allows to decompose the prediction of a deep neural network computed over a sample, e.g. an image, down to relevance scores for the single input dimensions of the sample such as subpixels of an image. While this approach can be applied directly to generalized linear mappings, product type non-linearities are not covered. This paper proposes an approach to extend layer-wise relevance propagation to neural networks with local renormalization layers, which is a very common product-type non-linearity in convolutional neural networks. We evaluate the proposed method for local renormalization layers on the CIFAR-10, Imagenet and MIT Places datasets.

We present a comparison of the perception of input images for classification of the state of the art deep convolutional neural networks and high performing Fisher Vector predic-tors. Layer-wise Relevance Propagation (LRP) is a method to compute scores for the components of input points denoting their contribution to the prediction of the classifier for one particular test point. We demonstrate the impact of different choices of decomposition cutoff points during the LRP-process, controlling the degree of detail and resolution of the heatmap on test images from the PASCAL VOC 2007 test data set.

Deep Neural Networks (DNNs) have demonstrated impressive performance in complex machine learning tasks such as image classification or speech recognition. However, due to their multi-layer nonlinear structure, they are not transparent, i.e., it is hard to grasp what makes them arrive at a particular classification or recognition decision given a new unseen data sample. Recently, several approaches have been proposed enabling one to understand and interpret the reasoning embodied in a DNN for a single test image. These methods quantify the "importance" of individual pixels wrt the classification decision and allow a visualization in terms of a heatmap in pixel/input space. While the usefulness of heatmaps can be judged subjectively by a human, an objective quality measure is missing. In this paper we present a general methodology based on region perturbation for evaluating ordered collections of pixels such as heatmaps. We compare heatmaps computed by three different methods on the SUN397, ILSVRC2012 and MIT Places data sets. Our main result is that the recently proposed Layer-wise Relevance Propagation (LRP) algorithm qualitatively and quantitatively provides a better explanation of what made a DNN arrive at a particular classification decision than the sensitivity-based approach or the deconvolution method. We provide theoretical arguments to explain this result and discuss its practical implications. Finally, we investigate the use of heatmaps for unsupervised assessment of neural network performance.

Understanding and interpreting classification decisions of automated image classification systems is of high value in many applications as it allows to verify the reasoning of the system and provides additional information to the human expert. Although machine learning methods are solving very successfully a plethora of tasks, they have in most cases the disadvantage of acting as a black box, not providing any information about what made them arrive at a particular decision. This work proposes a general solution to the problem of understanding classification decisions by pixel-wise decomposition of non- linear classifiers. We introduce a methodology that allows to visualize the contributions of single pixels to predictions for kernel-based classifiers over Bag of Words features and for multilayered neural networks. These pixel contributions can be visualized as heatmaps and are provided to a human expert who can intuitively not only verify the validity of the classification decision, but also focus further analysis on regions of potential interest. We evaluate our method for classifiers trained on PASCAL VOC 2009 images, synthetic image data containing geometric shapes, the MNIST handwritten digits data set and for the pre-trained ImageNet model available as part of the Caffe open source package.

Deep Neural Networks (DNNs) have demonstrated impressive performance in complex machine learning tasks such as image classification or speech recognition. However, due to their multi-layer nonlinear structure, they are not transparent, i.e., it is hard to grasp what makes them arrive at a particular classification or recognition decision given a new unseen data sample. Recently, several approaches have been proposed enabling one to understand and interpret the reasoning embodied in a DNN for a single test image. These methods quantify the "importance" of individual pixels wrt the classification decision and allow a visualization in terms of a heatmap in pixel/input space. While the usefulness of heatmaps can be judged subjectively by a human, an objective quality measure is missing. In this paper we present a general methodology based on region perturbation for evaluating ordered collections of pixels such as heatmaps. We compare heatmaps computed by three different methods on the SUN397, ILSVRC2012 and MIT Places data sets. Our main result is that the recently proposed Layer-wise Relevance Propagation (LRP) algorithm qualitatively and quantitatively provides a better explanation of what made a DNN arrive at a particular classification decision than the sensitivity-based approach or the deconvolution method. We provide theoretical arguments to explain this result and discuss its practical implications. Finally, we investigate the use of heatmaps for unsupervised assessment of neural network performance.

Understanding and interpreting classification decisions of automated image classification systems is of high value in many applications, as it allows to verify the reasoning of the system and provides additional information to the human expert. Although machine learning methods are solving very successfully a plethora of tasks, they have in most cases the disadvantage of acting as a black box, not providing any information about what made them arrive at a particular decision. This work proposes a general solution to the problem of understanding classification decisions by pixel-wise decomposition of nonlinear classifiers. We introduce a methodology that allows to visualize the contributions of single pixels to predictions for kernel-based classifiers over Bag of Words features and for multilayered neural networks. These pixel contributions can be visualized as heatmaps and are provided to a human expert who can intuitively not only verify the validity of the classification decision, but also focus further analysis on regions of potential interest. We evaluate our method for classifiers trained on PASCAL VOC 2009 images, synthetic image data containing geometric shapes, the MNIST handwritten digits data set and for the pre-trained ImageNet model available as part of the Caffe open source package.

With the help of a convolutional neural network (CNN) trained to recognize objects, a scene image is represented as a bag of semantics (BoS). This involves classifying image patches using the network and considering the class posterior probability vectors as locally extracted semantic descriptors. The image BoS is summarized using a Fisher vector (FV) embedding that exploits the properties of the space of these descriptors. The resulting representation is referred to as a semantic Fisher vector. Two implementations of a semantic FV are investigated. First involves modeling the BoS with a Dirichlet Mixture and computing the Fisher gradients for this model. Due to the difficulty of mixture modeling on a non-Euclidean probability simplex, this approach is shown to be unsuccessful. A second implementation is derived using the interpretation of semantic descriptors as parameters of a multinomial distribution. Like the parameters of any exponential family, these can be projected into their natural parameter space. For a CNN, this is shown equivalent to using inputs of its soft-max layer as patch descriptors. A semantic FV is then computed as a Gaussian Mixture FV in the space of these natural parameters. This representation is shown to outperform other alternatives such as FVs of features from the intermediate CNN layers or a classifier obtained by adapting (fine-tuning) the CNN. The proposed FV represents an embedding for object classification probabilities. As an image representation, therefore, it is complementary to the features obtained from a scene classification CNN. A combination of the two representations is shown to achieve state-of-the-art results on MIT Indoor scenes and SUN datasets.

Understanding and interpreting classification decisions of automated image classification systems is of high value in many applications, as it allows to verify the reasoning of the system and provides additional information to the human expert. Although machine learning methods are solving very successfully a plethora of tasks, they have in most cases the disadvantage of acting as a black box, not providing any information about what made them arrive at a particular decision. This work proposes a general solution to the problem of understanding classification decisions by pixel-wise decomposition of nonlinear classifiers. We introduce a methodology that allows to visualize the contributions of single pixels to predictions for kernel-based classifiers over Bag of Words features and for multilayered neural networks. These pixel contributions can be visualized as heatmaps and are provided to a human expert who can intuitively not only verify the validity of the classification decision, but also focus further analysis on regions of potential interest. We evaluate our method for classifiers trained on PASCAL VOC 2009 images, synthetic image data containing geometric shapes, the MNIST handwritten digits data set and for the pre-trained ImageNet model available as part of the Caffe open source package.