Models of human habits in smart spaces can be expressed by using a multitude of formalisms, whose readability in uences the possibility of being validated by human experts. Given the growing availability of low-cost sensing devices promoted by the emerging Internet-of-Things, the analysis of huge amount of data produced by these systems will assume an utmost importance in the near future. But most of them are designed for single user cases. Moving forward in their development, often they hardly t a realistic environment with many users. In this paper, we rst review the most relevant approaches in the area during the last decade, and then we present an analysis pipeline that allows, starting from the sensor log of a smart space, to model human habits in a multi-user environment. The approach is based on exploit BLE beacons to discriminate the di erent users, then applying techniques borrowed from the area of business process automation and mining on a version of the sensor log preprocessed in order to translate raw sensor measurements into human actions. The paper also presents some hints of how the proposed method can be employed to automatically extract models to be reused for ambient intelligence in a multi-users environment.
preferences and habits. All of these solutions are based on models that relate the output of the sensors during a (potentially very short) temporal window, to a speci c contextual information that can be then employed to act or reason on the state of the environment. Models can be either manually de ned (speci cation-based methods) or obtained through machine learning techniques (learning- based methods). In the rst case, models are usually based on logic formalisms, relatively easy to read and validate (once the formalism is known to the reader), but their creation requires an heavy cost in terms of expert time. In the latter case, the model is automatically learned from a training set (whose labeling cost may vary according to the proposed solution), but employed formalism are often less immediate to understand1 . Another di erence between the two approaches is that whereas speci cation-based methods use human actions as main modeling elements, learning-based ones directly refer to sensor measurements, thus loosing the focus on human actions and making even more di cult to visually inspect and validate produced models. On the other hand, taking as input raw sensor measurements usually makes learning-based methods easier to apply in a practical context; whereas, in the vast majority of cases, speci cation-based methods do not face the problem of translating sensor measurements into actions. As argued in [LMM15], applying methods originally taken from the area of (business) process mining [vdA16] to human habits may represent a compromise between speci cation-based and learning-based methods, provided that the gap between raw sensor measurements and human actions can be lled in by performing a log preprocessing step. Such a log preprocessing step may consist of simple inferences on data or complex machine learning algorithms.
Moreover other challenges are related to many users management. The most of the algorithms and approaches in the state of the art are devised for single-user scenario. In other words they make the hypothesis that the environment is populated only by an user at the time. But this is a very strong condition, commonly not true. Here we propose a rst approach, based on BLE beacons, to organize the multi-users sensor log to be used with the state of the art activities also devised for single user conditions. 2
In this paper, we aim at proposing an approach that merges human habits mining and multi-user managing methodology. We present in this section some relevant research papers, that adopted di erent approaches for the modeling technique and in the application context. In de ning habits mining approaches there are two phases to approach that are the modeling phase and the runtime phase. The modeling phase is in charge of creating the models of human habits and environmental dynamics, whereas the runtime phase covers the aspect related to how these models are employed at runtime to recognize the context and to act onto the environment. These two phases can even overlap, in the cases where the system is able to re ne models at runtime (in collaboration or not with the user) or even to completely create them from scratch at runtime. Models in the literature can be roughly divided into speci cation-based and learning-based. Speci cation-based models are usually more humanreadable (even though a basic experience with formal logic languages is required), but creating them is very expensive in terms of human resources. Most learning-based models are instead represented using mathematical and statistical formalisms (e.g., HMMs), which make them di cult to be revised by experts and understood by nal users. Learning-based techniques can be divided into supervised and unsupervised techniques. The former expect the input to be previously labeled according to the required output function, hence they require a big e ort for organizing input data in terms of training examples, even though active learning can be employed to ease this task. Unsupervised techniques (or weakly supervised ones, i.e., those where only a part of the dataset is labeled) can be used to face this challenge but a limited number of works is available in the literature. Unsupervised techniques for AmI knowledge modeling can be useful since knowledge should not be considered as a static resource; instead it should be updated at runtime without a direct intervention of the users [RC09a], hence updating techniques should rely on labeling of sensor data as little as possible.
The learning based techniques rely on some well known algorithms. Widely used are approaches like Bayesian classi cation techniques, that are based on the well known Bayes theorem or P (HjX) = P (XjH)P (H) , where H P (X) denotes the hypothesis (e.g., a certain activity is happening) and X represents the set of evidences (i.e., the current value of context objects). As calculating P (XjH) can be very expensive, di erent assumptions can be made to simplify the computation. For example, nave Bayes (NB) is a simple classi cation model, which supposes 1Notably, the lack of understandability of machine learning solutions is increasingly becoming a concern in both the AI and CS scienti c communities [ACM17,RDT15], and has been recently taken up by DARPA, through the DARPA-BAA-16-53 \Explainable Arti cial Intelligence (XAI)" program, cf. https://www.darpa.mil/program/explainable-artificial-intelligence. For example, the ACM Statement on Algorithmic Transparency and Accountability [ACM17] says: \There is also growing evidence that some algorithms and analytics can be opaque, making it impossible to determine when their outputs may be biased or erroneous". the n single evidences composing X independent (that the occurrence of one does not a ect the probability of the others) given the situational hypothesis; this assumption can be formalized as P (XjH) = Qn k=1 P (xkjH).
The inference process within the nave Bayes assumption chooses the situation with the maximum a posteriori (MAP) probability. Hidden Markov Models (HMMs), that represents one of the most widely adopted formalism to model the transitions between di erent states of the environment or humans [Coo12, RC09b, SCSE10]. Here hidden states represent situations and/or activities to be recognized, whereas observable states represent sensor measurements. HMMs are a statistical model where a system being modeled is assumed to be a Markov chain, which is a sequence of events. A HMM is composed of a nite set of hidden states and observations that are generated from states. Some other learning-based techniques generally assume that all observations are independent, which could possibly miss long-term trends and complex relationships. Some of the most relevant algorithms in this eld are used in Ambient Intelligence eld. Follows an analysis of some examples. Conditional Random Fields - CRFs, for instance, eliminate the independence assumptions by modeling the conditional probability of a particular sequence of hypothesis given a sequence of observations. Modeling the conditional probability of the label sequence rather than the joint probability of both the labels and observations, as done by HMMs, allows CRFs to incorporate complex features of the observation sequence X without violating the independence assumptions of the model. The graphical model representations of a HMM (a directed graph) and a CRF (an undirected graph) makes this di erence explicit. For example in [VKNEK08] a comparison between HMM and CRF is shown, where CRF outperforms HMM in terms of timeslice accuracy, while HMM outperforms CRF in terms of class accuracy.
Other statistical tools often employed is represented by Markov Chains (MCs), which are based on the assumption that the probability of an event is only conditional to the previous event, or Support Vector Machines (SVMs), that allow to classify both linear and non-linear data. SVMs are good at handling large feature spaces since they employ over tting protection, which does not necessarily depend on the number of features. Binary Classi ers are built to distinguish activities. Arti cial Neural Networks (ANNs) are a sub-symbolic technique, originally inspired by biological neuron networks. They can automatically learn complex mappings and extract a non-linear combination of features. Some other techniques stem from data mining methods for market basket analysis (e.g., the Apriori algorithm [AS+94]), which apply a windowing mechanism in order to transform the event/sensor log into what is called a database of transactions.
Initial approaches to the development of context-aware systems able to recognize situations were based on predicate logic. Loke [Lok04] introduced a PROLOG extension called LogicCAP; here the \in-situation" operator captures a common form of reasoning in context-aware applications, which is to ask if an entity E is in a given situation S. Ontologies (denoted as ONTO) represent the last evolution of logic-based approaches and have increasingly gained attention as a generic, formal and explicit way to \capture and specify the domain knowledge with its intrinsic semantics through consensual terminology and formal axioms and constraints" [YCDN07]. They provide a formal way to represent sensor data, context, and situations into well-structured terminologies, which make them understandable, shareable, and reusable by both humans and machines. A considerable amount of knowledge engineering e ort is expected in constructing the knowledge base, while the inference is well supported by mature algorithms and rule engines. Example of using ontologies in identifying situations is given by [RB09] (later evolved in [HRS13, RSCS16]). Instead of using ontologies to infer activities, they use ontologies to validate the result inferred from statistical techniques. The way an AmI system makes decisions on the actions can be compared to decision making in AI agents. As an example, re ex agents with state, as introduced in [RN95], take as input the current state of the world and a set of Condition-Action rules to choose the action to be performed. Similarly, Augusto [AN04] introduces the concept of Active DataBase (ADB) composed by EventCondition-Action (ECA) rules. An ECA rule basically has the form \ON event IF condition THEN action", where conditions can take into account time.
First attempts to apply techniques taken from the business process management - BPM [DLRM+13] area were the employment of work ow speci cations to anticipate user actions. A work ow is composed by a set of tasks related by qualitative and/or quantitative time relationships. Authors in [GGH06] present a survey of techniques for temporal calculus (i.e., Allen's Temporal Logic and Point Algebra) and spatial calculus aiming at decision making. The SPUBS system [AIB+09, AIB+10] automatically retrieve these work ows from sensor data.The Table 1 recaps details about some techniques modeling approaches: in particular about their type (Speci cation, Supervised/Unsupervised learning) and multiple users support.
It appears clear how only few works support multiple users with ad hoc systems, so multi-users management is still an open challenging problem. As introduced in the previous sections, this paper presents an approach that allows a multiuser management adaptation for already existing systems, originally designed on single user hypothesis. An extended description of the approach can be read in [SA18].
Figure 1 shows an high level description of the pipeline proposed. In the rst phase a log separation is performed. In other words from a sensor log created by the activity of many users into the space, the system automatically extracts single user sub-logs. The context which we are going to consider is a classical generic smart home: each room of the home is enriched with a set of heterogeneous sensors(i.e. motion Passive Infra Red based, doors contact, energy monitoring and so on). This sensors set can be formalized as: S = fS1 : : : Smg with jSj = m total number of installed sensors. Each sensor is associated to a state. We indicate the state of a sensor Si; 1 i m with the notation Si[t] where t is a temporal indication. Moreover the set of the possible states is Si[t] 2 f0; 1g. This means that the state activation is considered as a boolean value (not activated/activated). 3.1
Users separation: from multiple users log to single user traces fA1Hi ; A2Hi ; : : : ; ALHTiHi g with jTHi j = LTHi 2 N; 1 The users, acting inside the environment, cause sensors activations records. They are collected by the smart home system, paired with activation time stamp ts and stored into a list, A = [htsw; Awi]; w 2 N. This is the smart space described above. When assigned to a user Hi, they are going to compose data traces THi = i P . Notice that LTHi is di erent for each user, since it depends on the user's activities. Hence, since multi-users assumptions, more than one trace will be produced. The set of data traces will be T = fTH1 ; TH2 ; : : : ; THP g with jT j = P; P 2 N. This last formula implies jT j = jHj, so, we are imposing a trace for each user. This is not automatically obtained just recording activation data, but it is the nal goal of this work. By now the dataset produced by this kind of environment would be a confused interleaving of di erent THi ; 1 i P , without the possibility of reconstructing the di erent traces.
To perform the log separation we use a special sensor kind, the Bluetooth-Low-Energy sensor. The beacon set is de ned B as B = fB1; : : : Bng with B nite set and jBj = n number of beacons in the system. When a user Hi enters into a proximity beacon domain Bid, the system creates an association between Hi and Bid. An association is expressed as a coupled value hts; Bidi where ts the time stamp indicating when the association happens and Bid is the beacon involved. For each user, the multi user management system generates an association list
Hi = [hts; Bidi; : : : ]; 1 id n and ts is a progressive number. The set of all the association lists is = Hi for each i : 1 i P .
Figure 2 shows how the beacons subsystem works. For hypothesis, each user has a registered smartphone that brings always with him. Moving near the beacon, the smartphone registers the change of the nearest beacon encountered. In this way the subsystem has a complete beacon log. The system has a Speci cation Based de nition of the sensors related to that beacon. So combining the beacon log with the multiple users data log, we can separate the portion of the log related to every user. However there is the possibility that two di erent users get the registration to the same beacon: in this case the log records are duplicated and inserted into both traces of both the users. The generated traces are not completely clean, but they are good enough to apply the techniques.
In this paper we focus the attention on the well known problem of multi-users in a smart space system management. We provide a feasible solution to this problem: the main idea is to be able to distinguish between di erent users, for building the data traces of the sensor activations correlated to their activities. Naturally, the optimal result would be to obtain a log related to a given user containing only the correct measurements. The approach exploits simple technology like BLE beacons. Moreover we showed the generality of this approach involving it in a development pipeline that relies on Process Mining techniques (Fuzzy Mining) to model the Smart Space inhabitant habits. E ectiveness and precision depend on several factors, that can have an impact more or less important. For instance technology factors related to the proximity BLE. This kind of technology is rapidly and continuously evolving. There exists some protocols and formats, for instance Eddystone that can provide more data and metadata useful for improving precision. Moreover more complex computation on BLE signals can help in improving the system precision. In this rst approach the nearest beacon information is mined just looking at the maximum RSSI value given by all the reached beacons. So each beacon is analyzed independently from the others. Other more complex algorithms that involves triangulation techniques between many beacons can bring more precision in localizing the users and, consequently, in separating the user traces.
Models of human habits have an utility that goes beyond the mere analysis. A way to recognize their occurrences at runtime must be devised. At this point the models can be used either for conformance checking or to make the smart space work as a proactive agent. In the second case, controllable services provided by the smart house (e.g., automatic shutters) should be part of the model also in a real multi-user environment. [AAB+12] [ACM17] [AIB+09] [AIB+10] [ALM+08]
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