This paper proposes a client-server decision tree learning method for outsourced private data. The privacy model is anatomization fragmentation: the server sees data values, but the link between sensitive and identifying information is encrypted with a key known only to clients. Clients have limited processing and storage capability. Both sensitive and identifying information thus are stored on the server. The approach presented also retains most processing at the server, and client-side processing is amortized over predictions made by the clients. Experiments on various datasets show that the method produces decision trees approaching the accuracy of a non-private decision tree, while substantially reducing the client's computing resource requirements.
There have been studies in how to mine anonymized data. @cite_27 give a top-down specialization method (TDS) for anonymization so that the anonymized data allows accurate decision trees. @cite_5 and @cite_3 address the frequent itemset mining problem. proposes a clustering algorithm that handles the anonymized data as uncertain information @cite_9 . propose a hierarchical density based clustering method using fuzzy objects @cite_26 . discusses the problem of distance calculation for uncertain objects @cite_7 . Nearest Neighbor classification using generalized data is investigated by Martin @cite_19 . studies Naive Bayes using partially specified data @cite_23 . studies decision tree classifier with random substitutions @cite_0 . proposes a new Support Vector classification and Nearest Neighbor classification that deals with anonymized data @cite_8 . They extend the generalization based anonymization scheme to keep all necessary statistics and use these statistics to build effective classifiers. investigate learning C4.5 decision trees from datasets that satisfy differential privacy @cite_17 . propose a tree classifier based on random forests that is built from differentially private data @cite_13 .
@cite_26 @cite_7 @cite_8 @cite_9 @cite_3 @cite_0 @cite_19 @cite_27 @cite_23 @cite_5 @cite_13 @cite_17
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The nearestor near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search index structures for performing similarity search over high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. Unfortunately, all known techniques for solving this problem fall prey to the of dimensionality." That is, the data structures scale poorly with data dimensionality; in fact, if the number of dimensions exceeds 10 to 20, searching in k-d trees and related structures involves the inspection of a large fraction of the database, thereby doing no better than brute-force linear search. It has been suggested that since the selection of features and the choice of a distance metric in typical applications is rather heuristic, determining an approximate nearest neighbor should su ce for most practical purposes. In this paper, we examine a novel scheme for approximate similarity search based on hashing. The basic idea is to hash the points Supported by NAVY N00014-96-1-1221 grant and NSF Grant IIS-9811904. Supported by Stanford Graduate Fellowship and NSF NYI Award CCR-9357849. Supported by ARO MURI Grant DAAH04-96-1-0007, NSF Grant IIS-9811904, and NSF Young Investigator Award CCR9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and or special permission from the Endowment. Proceedings of the 25th VLDB Conference, Edinburgh, Scotland, 1999. from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. We provide experimental evidence that our method gives signi cant improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition. Experimental results also indicate that our scheme scales well even for a relatively large number of dimensions (more than 50). Privacy-preserving data publishing addresses the problem of disclosing sensitive data when mining for useful information. Among the existing privacy models, ∈-differential privacy provides one of the strongest privacy guarantees and has no assumptions about an adversary's background knowledge. Most of the existing solutions that ensure ∈-differential privacy are based on an interactive model, where the data miner is only allowed to pose aggregate queries to the database. In this paper, we propose the first anonymization algorithm for the non-interactive setting based on the generalization technique. The proposed solution first probabilistically generalizes the raw data and then adds noise to guarantee ∈-differential privacy. As a sample application, we show that the anonymized data can be used effectively to build a decision tree induction classifier. Experimental results demonstrate that the proposed non-interactive anonymization algorithm is scalable and performs better than the existing solutions for classification analysis. Objectives: To investigate whether (1) machine learning classifiers can help identify nonrandomized studies eligible for full-text screening by systematic reviewers; (2) classifier performance varies with optimization; and (3) the number of citations to screen can be reduced. Methods: We used an open-source, data-mining suite to process and classify biomedical citations that point to mostly nonrandomized studies from 2 systematic reviews. We built training and test sets for citation portions and compared classifier performance by considering the value of indexing, various feature sets, and optimization. We conducted our experiments in 2 phases. The design of phase I with no optimization was: 4 classifiersx3 feature setsx3 citation portions. Classifiers included k-nearest neighbor, naive Bayes, complement naive Bayes, and evolutionary support vector machine. Feature sets included bag of words, and 2- and 3-term n-grams. Citation portions included titles, titles and abstracts, and full citations with metadata. Phase II with optimization involved a subset of the classifiers, as well as features extracted from full citations, and full citations with overweighted titles. We optimized features and classifier parameters by manually setting information gain thresholds outside of a process for iterative grid optimization with 10-fold cross-validations. We independently tested models on data reserved for that purpose and statistically compared classifier performance on 2 types of feature sets. We estimated the number of citations needed to screen by reviewers during a second pass through a reduced set of citations. Results: In phase I, the evolutionary support vector machine returned the best recall for bag of words extracted from full citations; the best classifier with respect to overall performance was k-nearest neighbor. No classifier attained good enough recall for this task without optimization. In phase II, we boosted performance with optimization for evolutionary support vector machine and complement naive Bayes classifiers. Generalization performance was better for the latter in the independent tests. For evolutionary support vector machine and complement naive Bayes classifiers, the initial retrieval set was reduced by 46 and 35 , respectively. Conclusions: Machine learning classifiers can help identify nonrandomized studies eligible for full-text screening by systematic reviewers. Optimization can markedly improve performance of classifiers. However, generalizability varies with the classifier. The number of citations to screen during a second independent pass through the citations can be substantially reduced. In this paper, we study the problem of constructing private classifiers using decision trees, within the framework of differential privacy. We first present experimental evidence that creating a differentially private ID3 tree using differentially private low-level queries does not simultaneously provide good privacy and good accuracy, particularly for small datasets. In search of better privacy and accuracy, we then present a differentially private decision tree ensemble algorithm based on random decision trees. We demonstrate experimentally that this approach yields good prediction while maintaining good privacy, even for small datasets. We also present differentially private extensions of our algorithm to two settings: (1) new data is periodically appended to an existing database and (2) the database is horizontally or vertically partitioned between multiple users. A major challenge in indexing unstructured hypertext databases is to automatically extract meta-data that enables structured search using topic taxonomies, circumvents keyword ambiguity, and improves the quality of search and profile-based routing and filtering. Therefore, an accurate classifier is an essential component of a hypertext database. Hyperlinks pose new problems not addressed in the extensive text classification literature. Links clearly contain high-quality semantic clues that are lost upon a purely term-based classifier, but exploiting link information is non-trivial because it is noisy. Naive use of terms in the link neighborhood of a document can even degrade accuracy. Our contribution is to propose robust statistical models and a relaxation labeling technique for better classification by exploiting link information in a small neighborhood around documents. Our technique also adapts gracefully to the fraction of neighboring documents having known topics. We experimented with pre-classified samples from Yahoo! 1 and the US Patent Database 2 . In previous work, we developed a text classifier that misclassified only 13 of the documents in the well-known Reuters benchmark; this was comparable to the best results ever obtained. This classifier misclassified 36 of the patents, indicating that classifying hypertext can be more difficult than classifying text. Naively using terms in neighboring documents increased error to 38 ; our hypertext classifier reduced it to 21 . Results with the Yahoo! sample were more dramatic: the text classifier showed 68 error, whereas our hypertext classifier reduced this to only 21 . We study the problem of selecting a subset of big data to train a classifier while incurring minimal performance loss. We show the connection of submodularity to the data likelihood functions for Naive Bayes (NB) and Nearest Neighbor (NN) classifiers, and formulate the data subset selection problems for these classifiers as constrained submodular maximization. Furthermore, we apply this framework to active learning and propose a novel scheme called filtered active submodular selection (FASS), where we combine the uncertainty sampling method with a submodular data subset selection framework. We extensively evaluate the proposed framework on text categorization and handwritten digit recognition tasks with four different classifiers, including deep neural network (DNN) based classifiers. Empirical results indicate that the proposed framework yields significant improvement over the state-of-the-art algorithms on all classifiers. We present a new method for clustering based on compression. The method does not use subject-specific features or background knowledge, and works as follows: First, we determine a parameter-free, universal, similarity distance, the normalized compression distance or NCD, computed from the lengths of compressed data files (singly and in pairwise concatenation). Second, we apply a hierarchical clustering method. The NCD is not restricted to a specific application area, and works across application area boundaries. A theoretical precursor, the normalized information distance, co-developed by one of the authors, is provably optimal. However, the optimality comes at the price of using the noncomputable notion of Kolmogorov complexity. We propose axioms to capture the real-world setting, and show that the NCD approximates optimality. To extract a hierarchy of clusters from the distance matrix, we determine a dendrogram (ternary tree) by a new quartet method and a fast heuristic to implement it. The method is implemented and available as public software, and is robust under choice of different compressors. To substantiate our claims of universality and robustness, we report evidence of successful application in areas as diverse as genomics, virology, languages, literature, music, handwritten digits, astronomy, and combinations of objects from completely different domains, using statistical, dictionary, and block sorting compressors. In genomics, we presented new evidence for major questions in Mammalian evolution, based on whole-mitochondrial genomic analysis: the Eutherian orders and the Marsupionta hypothesis against the Theria hypothesis. Today, the publication of microdata poses a privacy threat: anonymous personal records can be re-identified using third data sources. Past research has tried to develop a concept of privacy guarantee that an anonymized data set should satisfy before publication, culminating in the notion of t-closeness. To satisfy t-closeness, the records in a data set need to be grouped into Equivalence Classes (ECs), such that each EC contains records of indistinguishable quasi-identifier values, and its local distribution of sensitive attribute (SA) values conforms to the global table distribution of SA values. However, despite this progress, previous research has not offered an anonymization algorithm tailored for t-closeness. In this paper, we cover this gap with SABRE, a SA Bucketization and REdistribution framework for t-closeness. SABRE first greedily partitions a table into buckets of similar SA values and then redistributes the tuples of each bucket into dynamically determined ECs. This approach is facilitated by a property of the Earth Mover's Distance (EMD) that we employ as a measure of distribution closeness: If the tuples in an EC are picked proportionally to the sizes of the buckets they hail from, then the EMD of that EC is tightly upper-bounded using localized upper bounds derived for each bucket. We prove that if the t-closeness constraint is properly obeyed during partitioning, then it is obeyed by the derived ECs too. We develop two instantiations of SABRE and extend it to a streaming environment. Our extensive experimental evaluation demonstrates that SABRE achieves information quality superior to schemes that merely applied algorithms tailored for other models to t-closeness, and can be much faster as well. Automatic integration of bibliographical data from various sources is a really critical task in the field of digital libraries. One of the most important challenges for this process is the author name disambiguation. In this paper, we applied supervised learning approach and proposed a set of features that can be used to assist training classifiers in disambiguating Vietnamese author names. In order to evaluate efficiency of the proposed features set, we did experiments on five supervised learning methods: Random Forest, Support Vector Machine (SVM), k-Nearest Neighbors (kNN), C4.5 (Decision Tree), Bayes. The experiment dataset collected from three online digital libraries such as Microsoft Academic Search, ACM Digital Library, IEEE Digital Library. Our experiments shown that kNN, Random Forest, C4.5 classifier outperform than the others. The average accuracy archived with kNN approximates 94.55 , random forest is 94.23 , C4.5 is 93.98 , SVM is 91.91 and Bayes is lowest with 81.56 . Summary, we archived the highest accuracy 98.39 for author name disambiguation problem with the proposed feature set in our experiments on the Vietnamese authors dataset. In this paper, we address the incremental classifier learning problem, which suffers from catastrophic forgetting. The main reason for catastrophic forgetting is that the past data are not available during learning. Typical approaches keep some exemplars for the past classes and use distillation regularization to retain the classification capability on the past classes and balance the past and new classes. However, there are four main problems with these approaches. First, the loss function is not efficient for classification. Second, there is unbalance problem between the past and new classes. Third, the size of pre-decided exemplars is usually limited and they might not be distinguishable from unseen new classes. Forth, the exemplars may not be allowed to be kept for a long time due to privacy regulations. To address these problems, we propose (a) a new loss function to combine the cross-entropy loss and distillation loss, (b) a simple way to estimate and remove the unbalance between the old and new classes , and (c) using Generative Adversarial Networks (GANs) to generate historical data and select representative exemplars during generation. We believe that the data generated by GANs have much less privacy issues than real images because GANs do not directly copy any real image patches. We evaluate the proposed method on CIFAR-100, Flower-102, and MS-Celeb-1M-Base datasets and extensive experiments demonstrate the effectiveness of our method. Publishing data for analysis from a table containing personal records, while maintaining individual privacy, is a problem of increasing importance today. The traditional approach of de-identifying records is to remove identifying fields such as social security number, name etc. However, recent research has shown that a large fraction of the US population can be identified using non-key attributes (called quasi-identifiers) such as date of birth, gender, and zip code [15]. Sweeney [16] proposed the k-anonymity model for privacy where non-key attributes that leak information are suppressed or generalized so that, for every record in the modified table, there are at least k−1 other records having exactly the same values for quasi-identifiers. We propose a new method for anonymizing data records, where quasi-identifiers of data records are first clustered and then cluster centers are published. To ensure privacy of the data records, we impose the constraint that each cluster must contain no fewer than a pre-specified number of data records. This technique is more general since we have a much larger choice for cluster centers than k-Anonymity. In many cases, it lets us release a lot more information without compromising privacy. We also provide constant-factor approximation algorithms to come up with such a clustering. This is the first set of algorithms for the anonymization problem where the performance is independent of the anonymity parameter k. We further observe that a few outlier points can significantly increase the cost of anonymization. Hence, we extend our algorithms to allow an e fraction of points to remain unclustered, i.e., deleted from the anonymized publication. Thus, by not releasing a small fraction of the database records, we can ensure that the data published for analysis has less distortion and hence is more useful. Our approximation algorithms for new clustering objectives are of independent interest and could be applicable in other clustering scenarios as well. Given dissimilarity data on pairs of objects in a set, we study the problem of fitting a tree metric to this data so as to minimize additive error (i.e. some measure of the difference between the tree metric and the given data). This problem arises in constructing an M-level hierarchical clustering of objects (or an ultrametric on objects) so as to match the given dissimilarity data - a basic problem in statistics. Viewed in this way, the problem is a generalization of the correlation clustering problem (which corresponds to M = 1). We give a very simple randomized combinatorial algorithm for the M-level hierarchical clustering problem that achieves an approximation ratio of M+2. This is a generalization of a previous factor 3 algorithm for correlation clustering on complete graphs. The problem of fitting tree metrics also arises in phylogeny where the objective is to learn the evolution tree by fitting a tree to dissimilarity data on taxa. The quality of the fit is measured by taking the l sub p norm of the difference between the tree metric constructed and the given data. Previous results obtained a factor 3 approximation for finding the closest tree tree metric under the l spl infin norm. No nontrivial approximation for general l sub p norms was known before. We present a novel LP formulation for this problem and obtain an O((log n log log n) sup 1 p ) approximation using this. Enroute, we obtain an O((log n log log n) sup 1 p ) approximation for the closest ultrametric under the l sub p norm. Our techniques are based on representing and viewing an ultrametric as a hierarchy of clusterings, and may be useful in other contexts. We explore a new approach to shape recognition based on a virtually infinite family of binary features (queries) of the image data, designed to accommodate prior information about shape invariance and regularity. Each query corresponds to a spatial arrangement of several local topographic codes (or tags), which are in themselves too primitive and common to be informative about shape. All the discriminating power derives from relative angles and distances among the tags. The important attributes of the queries are a natural partial ordering corresponding to increasing structure and complexity; semi-invariance, meaning that most shapes of a given class will answer the same way to two queries that are successive in the ordering; and stability, since the queries are not based on distinguished points and substructures. No classifier based on the full feature set can be evaluated, and it is impossible to determine a priori which arrangements are informative. Our approach is to select informative features and build tree classifiers at the same time by inductive learning. In effect, each tree provides an approximation to the full posterior where the features chosen depend on the branch that is traversed. Due to the number and nature of the queries, standard decision tree construction based on a fixed-length feature vector is not feasible. Instead we entertain only a small random sample of queries at each node, constrain their complexity to increase with tree depth, and grow multiple trees. The terminal nodes are labeled by estimates of the corresponding posterior distribution over shape classes. An image is classified by sending it down every tree and aggregating the resulting distributions. The method is applied to classifying handwritten digits and synthetic linear and nonlinear deformations of three hundred L AT E X symbols. Stateof-the-art error rates are achieved on the National Institute of Standards and Technology database of digits. The principal goal of the experiments on L AT E X symbols is to analyze invariance, generalization error and related issues, and a comparison with artificial neural networks methods is presented in this context. The performance of Nearest Neighbor (NN) classifier is known to be sensitive to the distance (or similarity) function used in classifying a test instance. Another major disadvantage of NN is that it uses all training instances in the generalization phase. This can cause slow execution speed and high storage requirement when dealing with large datasets. In the past research, many solutions have been proposed to handle one or both of the above problems. In the scheme proposed in this paper, we tackle both of these problems by assigning a weight to each training instance. The weight of a training instance is used in the generalization phase to calculate the distance (or similarity) of a query pattern to that instance. The basic NN classifier can be viewed as a special case of this scheme that treats all instances equally (by assigning equal weight to all training instances). Using this form of weighted similarity measure, we propose a learning algorithm that attempts to maximize the leave-one-out (LV1) classification rate of the NN rule by adjusting the weights of the training instances. At the same time, the algorithm reduces the size of the training set and can be viewed as a powerful instance reduction technique. An instance having zero weight is not used in the generalization phase and can be virtually removed from the training set. We show that our scheme has comparable or better performance than some recent methods proposed in the literature for the task of learning the distance function and or prototype reduction. We introduce a new probabilistic proximity search algorithm for range and A"-nearest neighbor (A"-NN) searching in both coordinate and metric spaces. Although there exist solutions for these problems, they boil down to a linear scan when the space is intrinsically high dimensional, as is the case in many pattern recognition tasks. This, for example, renders the A"-NN approach to classification rather slow in large databases. Our novel idea is to predict closeness between elements according to how they order their distances toward a distinguished set of anchor objects. Each element in the space sorts the anchor objects from closest to farthest to it and the similarity between orders turns out to be an excellent predictor of the closeness between the corresponding elements. We present extensive experiments comparing our method against state-of-the-art exact and approximate techniques, both in synthetic and real, metric and nonmetric databases, measuring both CPU time and distance computations. The experiments demonstrate that our technique almost always improves upon the performance of alternative techniques, in some cases by a wide margin. With recent technological advances, shared memory parallel machines have become more scalable, and offer large main memories and high bus bandwidths. They are emerging as good platforms for data warehousing and data mining. In This work, we focus on shared memory parallelization of data mining algorithms. We have developed a series of techniques for parallelization of data mining algorithms, including full replication, full locking, fixed locking, optimized full locking, and cache-sensitive locking. Unlike previous work on shared memory parallelization of specific data mining algorithms, all of our techniques apply to a large number of popular data mining algorithms. In addition, we propose a reduction-object-based interface for specifying a data mining algorithm. We show how our runtime system can apply any of the techniques we have developed starting from a common specification of the algorithm. We have carried out a detailed evaluation of the parallelization techniques and the programming interface. We have experimented with apriori and fp-tree-based association mining, k-means clustering, k-nearest neighbor classifier, and decision tree construction. The main results from our experiments are as follows: 1) Among full replication, optimized full locking, and cache-sensitive locking, there is no clear winner. Each of these three techniques can outperform others depending upon machine and dataset parameters. These three techniques perform significantly better than the other two techniques. 2) Good parallel efficiency is achieved for each of the four algorithms we experimented with, using our techniques and runtime system. 3) The overhead of the interface is within 10 percent in almost all cases. 4) In the case of decision tree construction, combining different techniques turned out to be crucial for achieving high performance. We propose a novel approach to performing efficient similarity search and classification in high dimensional data. In this framework, the database elements are vectors in a Euclidean space. Given a query vector in the same space, the goal is to find elements of the database that are similar to the query. In our approach, a small number of independent "voters" rank the database elements based on similarity to the query. These rankings are then combined by a highly efficient aggregation algorithm. Our methodology leads both to techniques for computing approximate nearest neighbors and to a conceptually rich alternative to nearest neighbors.One instantiation of our methodology is as follows. Each voter projects all the vectors (database elements and the query) on a random line (different for each voter), and ranks the database elements based on the proximity of the projections to the projection of the query. The aggregation rule picks the database element that has the best median rank. This combination has several appealing features. On the theoretical side, we prove that with high probability, it produces a result that is a (1 + e) factor approximation to the Euclidean nearest neighbor. On the practical side, it turns out to be extremely efficient, often exploring no more than 5 of the data to obtain very high-quality results. This method is also database-friendly, in that it accesses data primarily in a pre-defined order without random accesses, and, unlike other methods for approximate nearest neighbors, requires almost no extra storage. Also, we extend our approach to deal with the k nearest neighbors.We conduct two sets of experiments to evaluate the efficacy of our methods. Our experiments include two scenarios where nearest neighbors are typically employed---similarity search and classification problems. In both cases, we study the performance of our methods with respect to several evaluation criteria, and conclude that they are uniformly excellent, both in terms of quality of results and in terms of efficiency. New classifier-independent, dynamic, unsupervised approach for detecting concept drift.Reduced number of false alarms and increased relevance of drift detection.Results comparable to supervised approaches, which require fully labeled streams.Our approach generalizes the notion of margin density, as a signal to detect drifts.Experiments on cybersecurity datasets, show efficacy for detecting adversarial drifts. Classifiers deployed in the real world operate in a dynamic environment, where the data distribution can change over time. These changes, referred to as concept drift, can cause the predictive performance of the classifier to drop over time, thereby making it obsolete. To be of any real use, these classifiers need to detect drifts and be able to adapt to them, over time. Detecting drifts has traditionally been approached as a supervised task, with labeled data constantly being used for validating the learned model. Although effective in detecting drifts, these techniques are impractical, as labeling is a difficult, costly and time consuming activity. On the other hand, unsupervised change detection techniques are unreliable, as they produce a large number of false alarms. The inefficacy of the unsupervised techniques stems from the exclusion of the characteristics of the learned classifier, from the detection process. In this paper, we propose the Margin Density Drift Detection (MD3) algorithm, which tracks the number of samples in the uncertainty region of a classifier, as a metric to detect drift. The MD3 algorithm is a distribution independent, application independent, model independent, unsupervised and incremental algorithm for reliably detecting drifts from data streams. Experimental evaluation on 6 drift induced datasets and 4 additional datasets from the cybersecurity domain demonstrates that the MD3 approach can reliably detect drifts, with significantly fewer false alarms compared to unsupervised feature based drift detectors. At the same time, it produces performance comparable to that of a fully labeled drift detector. The reduced false alarms enables the signaling of drifts only when they are most likely to affect classification performance. As such, the MD3 approach leads to a detection scheme which is credible, label efficient and general in its applicability. A fruitful direction for future data mining research will be the development of techniques that incorporate privacy concerns. Specifically, we address the following question. Since the primary task in data mining is the development of models about aggregated data, can we develop accurate models without access to precise information in individual data records? We consider the concrete case of building a decision-tree classifier from training data in which the values of individual records have been perturbed. The resulting data records look very different from the original records and the distribution of data values is also very different from the original distribution. While it is not possible to accurately estimate original values in individual data records, we propose a novel reconstruction procedure to accurately estimate the distribution of original data values. By using these reconstructed distributions, we are able to build classifiers whose accuracy is comparable to the accuracy of classifiers built with the original data. State-of-the-art image classification methods require an intensive learning training stage (using SVM, Boosting, etc.) In contrast, non-parametric nearest-neighbor (NN) based image classifiers require no training time and have other favorable properties. However, the large performance gap between these two families of approaches rendered NN-based image classifiers useless. We claim that the effectiveness of non-parametric NN-based image classification has been considerably undervalued. We argue that two practices commonly used in image classification methods, have led to the inferior performance of NN-based image classifiers: (i) Quantization of local image descriptors (used to generate "bags-of-words ", codebooks). (ii) Computation of 'image-to-image' distance, instead of 'image-to-class' distance. We propose a trivial NN-based classifier - NBNN, (Naive-Bayes nearest-neighbor), which employs NN- distances in the space of the local image descriptors (and not in the space of images). NBNN computes direct 'image- to-class' distances without descriptor quantization. We further show that under the Naive-Bayes assumption, the theoretically optimal image classifier can be accurately approximated by NBNN. Although NBNN is extremely simple, efficient, and requires no learning training phase, its performance ranks among the top leading learning-based image classifiers. Empirical comparisons are shown on several challenging databases (Caltech-101 ,Caltech-256 and Graz-01).