Privacy Preserving Jaccard Similarity by Cloud-Assisted for Classification

Abstract

In the current information era, data mining has been extensively applied in many fields to discover the huge knowledge. It is desirable to design a system to exchange the sensitive data between the data owner and the client during data mining process regardless of the leakage of information. The privacy preserving mechanism is indeed an essential enabler to protect the data being corrupted in the trend of sophisticated cyber-attack. In fact, an approach to secure the data while mining knowledge is appropriate such that both data owners and users are not able to learn anything from each other data. Hence, we target preserving data privacy by mining on encrypted data. In data mining, similarity is the important factor, which either measures how much alike two data objects are, or describes as a distance with dimensions representing features of the objects. In this work, we firstly propose a privacy preserving approach on computing Jaccard similarity by cloud-assisted for data mining scheme. Particularly, our design focuses on the k-nearest neighbors classification, which is a conventional data mining algorithm. Rather, due to the efficient measurement of the Jaccard similarity, we present a solution how to employ the cloud services to preserve the Jaccard computation between the owner’s data and the client’s queries in a secure manner. We also implemented the proposed scheme on the workstation and observed that the computation efficiency of the proposed approach is well-suited in the data mining applications.

Appendix: A Performance of k-NN Algorithm Using Jaccard Similarity

This part describes experiments of using Jaccard similarity to measure distances among data samples when classifying by k-NN algorithm. Data sets for experiments include MNIST, WDBC and DERM:

• 1. MNIST [4] is a public data set of 10 handwritten digits from 0 to 9 (10 classes), available at http://yann.lecun.com/exdb/mnist/. This data set has already been separated into two sets: 60,000 samples of training and 10,000 samples of testing. Figure 6 shows examples of digits in MNIST data set. Each sample is a bitmap image of handwritten digit in size of $28\times 28$. We convert bitmap matrices of images into 784-dimension-vectors and use as inputs for classification. In short, each MNIST data sample is a binary vector of 784 attributes. In each vector, attributes have values of 1s at corresponding positions of digit shape, otherwise, they are 0s.

• 2. WDBC [5] is Breast Cancer Wisconsin Data Set (available at https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Original%29). WDBC includes 699 samples of clinical cases for benign and malignant (two classes). We divide WDBC data set to two sets: 466 samples for training and 233 samples for testing. Originally, each sample has 9 attributes about cells taking integer values in [1, 10]. We express each sample as a binary vector by mapping its attributes to 1s if values is greater than 5, otherwise mapping them to 0s. We divide WDBC data set to two sets: 466 samples for training and 233 samples for testing.

• 3. DERM [6] is Dermatology Data Set (available at https://archive.ics.uci.edu/ml/datasets/Dermatology). DERM includes 466 real samples of six dermatological problems (six classes). We divide DERM data set to two sets: 244 samples for training and 122 samples for testing. Each data sample has 34 attributes whose values are numbers: 32 attributes take integer values in range [0, 3], one attribute takes integer value in range [0, 1] and one attribute takes value in range [0, 75]. We also express each data sample as a binary vector. In which, binary vector attributes are 1s if corresponding sample attribute values are greater than mean of its range, i.e., 2, 0 and 33 correspondingly. Otherwise, binary vector attributes are 0s.

Fig. 6

Examples of handwritten digits in MNIST dataset

The characteristics of these three data sets are summarized in Table 3.

Table 3 Characteristics of data sets MNIST, WDBD and DERM

Classification process follows Algorithm 1 in Sect. 2.1. We choose values for parameter K as 5, 10 and 15. Similarity between any two samples is Jaccard similarity, computed using formula (3). The detailed performance of k-NN on these three data sets is shown in Table 4.

Table 4 Performance of k-NN with $K\in \{5,10,15\}$ on three datasets using Jaccard similarity

Generally, we note the high performance of k-NN on all data sets with different parameter settings. The lowest and highest accuracies are 86.9% and 96.3%.